A review of fuzzy AHP methods for decision-making with subjective

judgements

Yan Liua, *, Claudia M. Eckertb, Christopher Earlb

a
School of Computer Science and Technology, Changchun University of Science and
Technology, Changchun, 130022, Jilin, China

b
School of Engineering and Innovation, The Open University, Walton Hall, Milton Keynes,
UK, MK7 6AA

*Correspondence detail: Office 412, Building of Shixun, Changchun University of Science

and Technology, No. 7186 Weixing Road, Changchun, Jilin Province, 130022 China; Email:
yanl@cust.edu.cn; Phone No. +86-0431-85583560

Claudia M. Eckert, Email: claudia.eckert@open.ac.uk

Christopher Earl, Email: c.f.earl@open.ac.uk

THIS PAPER HAS BEEN ACCEPTED BY EXPERT SYSTEMS WITH APPLICATIONS.

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 A review of fuzzy AHP methods for decision-making with subjective
judgements
Abstract: Analytic Hierarchy Process (AHP) is a broadly applied multi-criteria decision-
making method to determine the weights of criteria and priorities of alternatives in a structured
manner based on pairwise comparison. As subjective judgments during comparison might be
imprecise, fuzzy sets have been combined with AHP. This is referred to as fuzzy AHP or
FAHP. An increasing amount of papers are published which describe different ways to
derive the weights/priorities from a fuzzy comparison matrix, but seldomly set out the relative
benefits of each approach so that the choice of the approach seems arbitrary. A review of
various fuzzy AHP techniques is required to guide both academic and industrial experts to
choose suitable techniques for a specific practical context. This paper reviews the literature
published since 2008 where fuzzy AHP is applied to decision-making problems in industry,
particularly the various selection problems. The techniques are categorised by the four aspects
of developing a fuzzy AHP model: (i) representation of the relative importance for pairwise
comparison, (ii) aggregation of fuzzy sets for group decisions and weights/priorities, (iii)
defuzzification of a fuzzy set to a crisp value for final comparison, and (iv) consistency
measurement of the judgements. These techniques are discussed in terms of their
underlying principles, origins, strengths and weakness. Summary tables and specification
charts are provided to guide the selection of suitable techniques. Tips for building a fuzzy
AHP model are also included and six open questions are posed for future work.
Keywords: fuzzy Analytic Hierarchy Process; fuzzy set; multi-criteria decision-making;
subjective judgement; selection problem

Glossary
AHP Analytic Hierarchy Process
ANP Analytic Network Process
CFCS Converting the Fuzzy data into Crisp Scores
COA Centre of Area
COG Centre of Gravity
CI Consistency Index
CR Consistency Ratio
DEA Data Envelopment Analysis
EAM Extent Analysis Method
ELECTRE ELimination Et Choix Traduisant la REalité
FAHP Fuzzy Analytic Hierarchy Process
2
FP Fuzzy Programming
GA Genetic Algorithm
GCI Geometric Consistency Index
GP Goal programming
IFWA Intuitionistic Fuzzy Weighted Averaging
LP Linear programming
MCDM Multi-Criteria Decision-Making
MOORA Multi-Objective Optimisation by Ratio Analysis
MP Mathematical Programming
PROMETHEE Preference Ranking Organization METHod for Enrichment of
Evaluations
RI Radom Index
TFN Triangular Fuzzy Number
TraFN Trapezoidal Fuzzy Number
TOPSIS Technique for Order of Preference by Similarity to Ideal Solution

1. Introduction

In many professional situations, experts are confronted with a given set of alternatives that they
need to choose from, for example when selecting a supplier or a technology. This type of
decision-making problem is intuitive when considering a single criterion, since experts can
choose the alternative of the highest preference. It becomes complicated when there are
multiple criteria. These criteria are often not of equal importance and the alternatives have very
varied performance. Formal methods are needed to ensure a structured means of making
decisions. Many methods are available such as Analytic Hierarchy Process (AHP), Technique
for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Data Envelopment
Analysis (DEA) (see Chai et al. (2013), Karsak and Dursun (2016) and Zimmer et al. (2016)
for an overview of available decision-making methods). Among them, AHP proposed by Saaty
(1980) has been applied extensively to evaluate complex multi-criteria alternatives in a number
of fields (Subramanian & Ramanathan, 2012; Emrouznejad & Marra, 2017). It outperforms by
ease of use, structuring problems systematically and calculating both criteria weights and
alternative priorities. As a popular methodology for handling imprecision, fuzzy sets proposed
by Zadeh (1965) are combined with AHP, namely fuzzy AHP or FAHP. This integrated method
maintains the advantage of AHP and has been widely applied (Mardani et al., 2015). The
procedure of building a fuzzy AHP model follows establishing the comparison matrix,
aggregating multiple judgements, measuring the consistency and defuzzifying the fuzzy
weights. Various techniques exist for each aspect. However, Little research has examined fuzzy
3
AHP in terms of these aspects and set out the relative benefits of the techniques. This paper
reviews the techniques regarding these four aspects, aiming to guide both academics and
industrial experts to choose suitable techniques according to their practical context.

AHP structures a problem in a hierarchical way, descending from a goal to criteria, sub-
criteria and alternatives in successive levels (Saaty, 1990). The hierarchy provides the experts
with an overall view of the complex relationships inherent in the context; and helps them
to assess whether the elements of the same level are comparable. Elements are then pairwise
compared according to 9 level-scales to derive their weights. However, pairwise comparison,
the essence of AHP, introduces imprecision because it requires the judgements of experts. In
practical cases, experts might not be able to assign exact numerical values to their preferences
due to limited information or capability (Chan & Kumar, 2007; Xu & Liao, 2014).

To handle the imprecision in AHP, exact numbers are replaced with fuzzy numbers
representing the linguistic expressions in fuzzy AHP. This tolerates the vague judgements by
assigning membership degrees to exact numbers to describe to what extent these numbers
belong to an expression. However, introducing fuzzy sets to AHP makes the calculation
process less straightforward because different fuzzy sets exist and the associated operations
are complex. The techniques for AHP such as eigenvector method and geometric mean
cannot directly be used to derive the weights/priorities from a fuzzy comparison matrix.
Many techniques for building a fuzzy AHP model have been proposed. They vary in terms of
essential features, strengths and weakness. To the best of our knowledge, limited research has
reviewed fuzzy AHP except Kubler et al. (2016) who discuss the application areas.

The earliest reference that we have found dates from 1983 (Van Laarhoven & Pedrycz, 1983).
Now, fuzzy AHP has become a popular fuzzy multi-criteria decision-making (MCDM)
method (Kubler et al., 2016). It is applied in various industries, for example airline retail
(Rezaei et al., 2014), agriculture (Hashemian et al., 2014; Liu et al., 2019), automobile
(Büyüközkan& Güleryüz, 2016; Zimmer et al., 2017), logistics (Yayla et al., 2015),
manufacturing (Kar, 2014; Ayhan & Kilic, 2015), maritime (Celik & Akyuz, 2018), pharmacy
(Alinezad et al., 2013) and service (Khorasani, 2018), and to solve various problems, for
example location selection (Erbas et al., 2018; Singh et al., 2018), machine selection (Nguyen
et al., 2015; Parameshwaran et al., 2015), supplier selection (Akkaya et al., 2015;
Shakourloo et al., 2016; Kumar et al., 2017; Awasthi et al., 2018), technique selection
(Budak & Ustundag, 2015; Naderzadeh et al., 2017; Balusa & Gorai, 2018), sustainability
management (Calabrese et al., 2016; 2019), business
4
impacts assessment (Lee et al., 2015), risk analysis (Mangla et al., 2015), intellectual capital
assets management (Calabrese et al., 2013) and teaching performance evaluation (Chen et al.,
2015). These decision problems all deal with the assessment and prioritisation of the
alternatives which could be physical entities (e.g. machines, suppliers and locations) or
abstract items (e.g. business impact indicators and risk factors). The results are used for
selection if a preferred solution is required. The fuzzy AHP models built for the assessment
problem in one field are applicable to other fields. This review paper is based on a
systematic search of literature published since 2008 where fuzzy AHP is applied to the
decision-making problems in industry. Our research originates from supplier selection and
then branches out to other topics such as machine selection, location selection, ERP system
selection, project selection and technology selection.

The rest of paper is organised as follows. Section 2 explains the principle of fuzzy AHP method.
Section 3 shows the research methodology of this study. There are four important aspects to
develop a fuzzy AHP model, which are explained in Sections 4 to 7.

⚫ Section 4 explains how different fuzzy numbers, as a special type of fuzzy set, can be
defined for judgement representations when establishing the comparison matrix.
⚫ Section 5 discusses how these fuzzy numbers are aggregated for group decisions and
for deriving the weights.
⚫ Section 6 identifies the defuzzification method to obtain a crisp value from a fuzzy
value for intuitive comparison.
⚫ Section 7 examines the consistency measurement which is an important way to ensure
valid pairwise judgements.

To help readers extract quick information, the reviewed techniques are summarised in
graphical and tabular forms. Discussions and insights are provided at the end of each section
for choosing appropriate techniques. We also point out mistakes in few papers and indicate
possible corrections, along with the review. Section 8 concludes this study with open
questions for future research and a general guidance for building a fuzzy AHP model.

2. Principle of fuzzy AHP

The development of a fuzzy AHP model overall follows the process to develop an AHP
model as illustrated in Figure 1. The white and the light grey boxes show the common steps
between AHP and fuzzy AHP but different techniques are applied in the steps of light grey
boxes. The
5
dark grey box is the step in fuzzy AHP but not in AHP. We illustrate the process with supplier
selection using a special type of fuzzy set, triangular fuzzy number.

Figure 1. The calculation process of fuzzy AHP using triangular fuzzy numbers

Structure the problem: The problem is decomposed in a hierarchy, which includes goal
(‘select best suppliers’ in Figure 1), criteria/sub-criteria (Criterion 1 to Criterion 3) and
alternatives (Supplier 1 to Supplier 3).

Establish the fuzzy pairwise comparison matrix: Let F = [cij ]n n be the matrix for n criteria

against the goal. cij is a fuzzy set representing the relative importance of criterion i over j. Its

reciprocal, 1/ cij , is equal to the relative importance of criterion j over i, c ji . For example, the

triangular fuzzy number (2,3,4) in the judgement table of expert 1 is the relative importance of
criterion 1 over criterion 2 and thus (1/4,1/3,1/2) is that of criterion 2 over criterion 1. Replacing
crisp values with fuzzy sets is the fundamental difference between fuzzy AHP and AHP. It
results in that the techniques to derive weights/priorities in AHP cannot directly be used.
Several fuzzy sets are applicable to establish the comparison matrix as explained in section 4.
6
Synthesise the judgements: if there are multiple experts, their opinions will be aggregated.
As illustrated in Figure 1, it takes place either before or after calculating the fuzzy weights,
i.e. synthesising the pairwise comparisons (as labelled by ① in Figure 1) or the fuzzy weights
(as labelled by ②). In the example, the relative importance of criterion 1 over criterion 2
from the two experts are different, i.e. (2, 3, 4) and (1, 2, 3). They are aggregated first. The
techniques are examined in section 5.

Calculate the fuzzy weights of the criteria: This step aggregates multiple fuzzy sets in the
matrix into a single fuzzy set. Some aggregation methods in the previous step are applicable.
Specialised methods are presented in section 5.

Defuzzify the fuzzy weights: This is an extra step compared with AHP which maps a fuzzy
set (i.e. fuzzy weight) to a crisp value (i.e. crisp weight) for further comparison. Fuzzy sets
are difficult to compare directly because they are partially ordered rather than the linear or
strictly ordered crisp values. Section 6 identifies the most prevalent defuzzification methods.

Check the consistency: Without this step, weights can still be obtained, and thus it is
overlooked by some research. However, it is necessary to measure the fuzzy
pairwise comparison matrix for the consistency. Suppose that criterion 1 is more important
than criterion 2 and much more important than criterion 3. Logically, criterion 2 is more
important than criterion 3. If the expert judges criterion 2 less important than criterion 3, then
the judgements between criteria 1, 2 and 3 are in conflict. This step takes place after the
comparison matrix is established (either the one from an individual expert or the
aggregated one from multiple experts). The matrix is considered consistent if the
contradictions among the pairwise comparisons are within a predefined threshold,
namely consistency ratio. Otherwise, the experts need to re-compare the criteria. The
discussion is in section 7.

The calculations of the sub-criteria weights and the alternative priorities follow the
same process as described above. The calculated weights of sub-criteria are ‘local weights’,
which are transformed to ‘global weights’ by multiplying with the weight of their parent
criterion. For ease of explanation, we use ‘weight’ for ‘global weight’. The overall priority of
alternative Si is the aggregation of its priorities under all the criteria/sub-criteria. wj is
the weight of criterion/sub-criterion j; pjSi is the priority of Si under criterion j; n is the
number of criteria/sub-criteria. n
Priority Si =  w j  p Sij (1)
j =1

7
The overall calculation process in Figure 1 reveals the four important aspects in developing a
fuzzy AHP model: (1) representation of judgements for pairwise comparison to establish the
matrix, (2) aggregation of fuzzy sets for group decisions and criteria weights, (3)
defuzzification of a fuzzy set for further comparison and (4) consistency measurement
for limited contradiction, which will be addressed in turn.

3. Research methodology

This research was carried out in two stages as shown in Figure 2. In the first stage, we chose
‘supplier selection’ as the primary investigation topic. Fuzzy AHP is a generic decision-
making method, applicable to most problems. Supplier selection is a typical and
representative decision-making problem, involving prioritisation, assessment and ranking. It
has a mixture of subjective and objective criteria and brings out many situations for
which fuzzy AHP is required. As listed in Table A.9, it has been applied in a number of
industries. Therefore, supplier selection is a potential target for many of the techniques. It is
also a topic where fuzzy AHP has been most commonly used, according to the numbers of
the reviewed articles. This corresponds to the survey result of Kubler et al. (2016). We
selected 57 articles to analyse the methodological development of fuzzy AHP in terms of the
four aspects. Under each aspect, the identified techniques were further categorised
according to their properties (cf. fishbone diagram in Figure 2). Each part of the fishbone
diagram is presented in details in the following sections (cf. Figure 4, Figure 12, Figure 15
and Figure 18).

In the second stage, the study branched out to other domains to cover more techniques under
the categorisations defined in the first stage, and included literature on machine
selection, location selection, ERP system selection, project selection and technology
selection. The topics were selected according to the number of articles using fuzzy AHP in
the review paper by Kubler et al. (2016) and complemented by other important topics
in industry including evaluation, management and diagnosis. Compared with supplier
selection, fewer articles apply fuzzy AHP to rank the alternatives. Almost all the techniques
in the selected 52 articles are covered by the review results of the first stage except the
defuzzificaiton method proposed by Opricovic and Tzeng (2003), which is problematic as
discussed in section 6.1.3. In addition, Mirhedayatian et al. (2013) propose a different
fuzzy programming model to calculate the weights and measure the consistency for
selecting the best tunnel ventilation system.

8
 Figure 2. Research framework

The study targeted journals in four main library databases, i.e. ScienceDirect, Springer,
Taylor & Francis and EBSCOhost. Some of the journals cited in this review are Applied
Mathematical Modelling, Applied soft computing, Computers & Industrial Engineering,
Energy, European Journal of Operational Research, Expert Systems with Applications,
International Journal of Production Economics, International Journal of Production Research
and Journal of Intelligent & Fuzzy Systems. Articles were searched with keywords ‘FAHP/
Fuzzy AHP/Fuzzy Analytic Hierarchy Process’. They were screened according to three
criteria:
⚫ it was published after 2008;
⚫ fuzzy AHP is used partially (for criteria weights) or completely (for both criteria
weights and alternative priorities) in the evaluation process;
⚫ it presents clearly how fuzzy AHP is developed or applied.

In total, 109 articles were selected. Figure 3 shows the distribution of these articles across the
journals (the number of the selected articles is presented after the journal name). During the
review, the original papers and highly cited papers were also looked back.

9
 Figure 3. Journal distribution

Table A.9 and Table A.10 in the appendix summarise the literature on supplier selection and
the other topics respectively. The column of ‘With methods’ shows the methods fuzzy AHP
is combined with, if there are any. The rest of the tables follows the structure of this paper.
‘-’ means ‘not applicable’.

4. Representation for pairwise comparison

It is the fundamental step of building a fuzzy AHP model to establish the pairwise
comparison matrix with the expert’s judgement. Linguistic terms describe the relative
importance of a criterion or an alternative over another (e.g. ‘equally preferred’, ‘fairly
strongly preferred’ and ‘absolutely preferred’). In fuzzy AHP, such a term is represented by a
fuzzy set which consists of two components, a set of elements x and an ( xassociated
)
membership function (Klir & Yuan, 1995). The membership function assigns to each
element a value between 0 and 1 as its membership degree to the set. The mappings between
the fuzzy set and the linguistic term must conform to a scale so that the same judgement
produces the same measurable value. Such a scale is called fuzzy scale. Figure 4 outlines
the structure of this section. Different types of fuzzy sets are explained by referring to the
application context.

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 Figure 4. Categorisation of the judgement representations

4.1 Type-1 fuzzy set

The fuzzy set described by a set of elements and crisp values as their membership degrees is
called type-1 fuzzy set. A crisp number can be fuzzified. For example, 2 is definitely close to
itself, so its membership degree to ‘approximate 2’ is 1. If 1.5 is considered neither close nor
far to 2, 0.5 can be assigned as its membership degree to ‘approximate 2’. A series of such
numbers with their membership degrees compose a fuzzy set ‘approximate 2’, denoted as 2 .
Let 2 describe ‘moderate importance’ of one criterion over another in AHP. In fuzzy AHP
2
replaces 2. Including a series of numbers addresses the problems that experts in some cases
are unable to assign an exact number to the judgement. Their memberships indicate to what
extent the experts are sure about the numbers to be used for the judgemnt. Mathematically, a
fuzzy number is a convex normalised fuzzy set of the real line such that its associate
membership function is piecewise continuous (Zimmermann, 2001). Because complicated
fuzzy numbers may cause important difficulties in data processing such as hard to define
arithmetic operations, several simple and representative fuzzy numbers have been
proposed (Yeh, 2008; Ban & Coroianu, 2012; Yeh, 2017). Triangular fuzzy number
(TFN) and trapezoidal fuzzy number (TraFN) are two kinds of such fuzzy numbers that have
been well studied.

TFN is the mostly popular means of judgement

A representation in the(reviewed
l , m, h) articles (99 out
of the 109 articles, i.e. 91%). A TFN can be expressed as a triple where l and h
are the smallest and the largest values with the smallest membership respectively and m is the
11
value
with the largest membership. The membership function of a TFN is defined as follows and
illustrated in Figure 5 (a).

 ( x − l ) (m − l ), l  x  m
 ( x) =  (2)
(h − x) (h − m), m  x  h

Figure 5. (a) A TFN, A ; (b) α-cut of a TFN, A

The α-cut set of a fuzzy set A , denoted as A , is a crisp value set containing all the elements
with membership degrees greater than or equal to the specified value of α:
A = {x |  ( x)   } (3)

The α-cut set of a TFN can be represented as an interval, i.e. A = [l + (m − l ) , h − (h − m) ]

shown in Figure 5 (b). It helps defuzzify a TFN.

TFN is useful when the expert is definitive about a single point representing the total
belongingness. For example, if 30℃ is considered as a definitely high temperature, slightly
below it is hot but not so hot and above it is also hot but too hot, then TFN describes this
judgement (i.e. m = 30℃). But if the expert is certain within an interval, such as any
temperature between 28 to 32 ℃ is considered as a definitely high temperature while below
28 ℃ is hot but not so hot and above 32 ℃ is also hot but too hot, then TraFN is needed. It is
characterised by a quadruple (l, ml, mh, h) as shown in Figure 6. In the example, ml = 28℃ and
mh = 32℃. When ml = mh, a TraFN reduces to a TFN. Sometimes, there is a mixed use of TFN
and TraFN, for example, Aydin and Kahraman (2010).

Figure 6. A trapezoidal fuzzy number

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4.2 Type-2 fuzzy set

The membership space of type-1 fuzzy set is assumed to be the space of real numbers. A natural
extension is the definition of type-2 fuzzy set whose membership values are type-1 fuzzy sets
rather than real numbers (Zimmermann, 2001). Type-2 fuzzy set captures more imprecision
because it expresses the imprecision on both the elements and their memberships. It helps when

the expert is not sure about the membership of an element to a set. A type-2 fuzzy set A in the
universe set X is defined as follows (Mendel & John, 2002):

A = ( ( x, u ),  ( x, u ) ) | x  X , u  J x  [0,1], 0   ( x, u )  1 (4)

where x is the element, u is a primary membership degree of x and Jx is the value set of u under
x.  ( x, u ) is called the secondary membership function, which is a type-1 fuzzy set. Figure 7
depicts  ( x, u ) for x and u where X = (1, 2, 3, 4, 5) and U = {0, 0.2, 0.4, 0.6, 0.8}. Each of the
rods represents  ( x, u ) at a specific pair (x, u). For example, the length of the rod for (2, 0) is
0.5 in Figure 7, which means μ(2, 0) = 0. J1 = J2 =J4 =J5 = {0, 0.2, 0.4, 0.6, 0.8} and J3 =
{0.6, 0.8}. An example of the secondary membership function at x = 2 is:
 (2, u ) = {(2,0),0.5;(2,0.2),0.35;(2,0.4),0.35;(2,0.6),0.2;(2,0.8),0.5}

The union of the five secondary membership functions at x = 1, 2, 3, 4, 5 is  ( x, u ) of the set.

Figure 7. Example of a type-2 membership function, adapted from (Mendel & John, 2002)

In the above example, the complexity of operations is acceptable because it is a small discrete
set where the elements are finite. For a continuous set, the computation becomes extremely
difficult and even its literal description is problematic. Take for example the continuous type-
2 fuzzy set defined on [1, 5] in Figure 8 (a). The shadow illustrates the membership function
μ(x,u) which is hardly described in formulas. But in the case of all μ(x,u) = 1, this 3-dimensional
set becomes a 2-dimensional set on axes x and u as shown in Figure 8 (b), the complexity of
13
which reduces greatly. This special type-2 fuzzy set is called interval type-2 fuzzy set. It is the
most widely used type-2 fuzzy set because this special kind is relative simple and it is also very
difficult to justify the use of any other kind (Mendel & John, 2002).

Figure 8. Example of continuous type-2 fuzzy set with: (a)  ( x, u )  1 and (b) all μ(x,u) = 1

The interval type-2 fuzzy set can be further distinguished by the shapes of the membership
functions, such as triangular and trapezoidal. The adoption of trapezoidal interval type-2 fuzzy
set has been found in the reviewed articles of Görener et al. (2017) and Celik and Akyuz (2018).
As shown in Figure 9, a trapezoidal interval type-2 fuzzy set can be characterised by the
reference points and the heights of its upper and the lower membership functions. The reference
points are the elements whose membership degrees can be used to define the shape of
membership functions. The trapezoidal ring in Figure 9 is the analogue of the U shape plane in
Figure 8 (b). A trapezoidal interval type-2 fuzzy set is defined as:

(
A = ( AU , AL ) = (a1U , aU2 , a3U , aU4 ; H1 ( AU ), H 2 ( AU )),(a1L , a2L , a3L , a4L ; H1 ( AL ), H 2 ( AL )) ) (5)

AU and AL are type-1 fuzzy sets; a1U, a2U, a3U, a4U, a1L, a2L, a3L and a4L are the reference
points; H i ( AU ) is the membership degree of element aiU+1 in the upper trapezoidal membership
U
function A ; H i ( AL ) is the membership degree of element aiL+1 in the lower trapezoidal

membership function A ; 1  i  2 , H i ( AU )  [0,1] , H i ( AL )  [0,1] .

L

Figure 9. A trapezoidal interval type-2 fuzzy set

14
4.3 Intuitionistic fuzzy set

The membership degree in a type-1 fuzzy set indicates to what extent an element belongs to
the set. There could correspondingly be a value for the extent that the element does not belong
to this set. The belongingness and non-belongingness do not necessarily complement each
other because of the imprecision of judgement or the possibility of this element belonging to
another set. Intuitionistic fuzzy set proposed by Atanassov (1986) is characterised by two such
functions expressing the degree of belongingness and the degree of non-belongingness
respectively. Intuitionistic fuzzy set deals with the situation that the membership or the non-
membership cannot be determined to the expert’s satisfaction and an indeterministic part
remains (De et al., 2000; Grzegorzewski & Mrówka, 2005). An intuitionistic fuzzy set A in the
universe of discourse X is a set of ordered triples (Atanassov, 2012):
A = {( x,  ( x), v( x)) | x  X } (6)

where μ(x) and v(x): X→ [0,1] are the membership function and non-membership function
respectively; 0   ( x) + v( x)  1 . For each A, there is another parameter π(x), called the degree
of non-determinacy of the membership of x to the set A; π(x) = 1 - μ(x) - v(x). In intuitionistic
fuzzy AHP, (μ(x), v(x), π(x)) is used to describe the preference degree of one
criterion/alternative over another. Büyüközkan and Güleryüz (2016) choose intuitionistic fuzzy
sets to express the linguistics terms.

Cuong (2014) introduces the concept of a picture fuzzy set that extends the intuitionistic fuzzy
set by adding a degree of neutral belongingness. A picture fuzzy set A in the universe of
discourse X is defined as:
A = {( x,  ( x), ( x), v( x)) | x  X } (7)

where μ(x),  ( x) and v(x): X→ [0,1] are degree of positive membership, degree of neutral
membership and degree of negative membership respectively. They satisfy the condition:
0   ( x) +  ( x) + v( x)  1.  ( x) = 1 −  ( x) −  ( x) − v( x) is the degree of refusal membership.

Models based on picture fuzzy sets can be applied in the situation when experts have opinions
involving more answers such as yes, abstain, no and refusal. An example is voting that the
voters may be divided into four groups of those who vote for, abstain, vote against and refusal
of the voting (invalid voting or not taking the vote) (Cuong, 2014; Son, 2015). However, due
to the lack of mathematical discussions with its aggregation and defuzzification, picture fuzzy
sets are hardly applied in constructing pairwise comparison decision matrix. For example, Ju

15
et al. (2018) apply picture fuzzy sets for site ranking but still use TFNs to construct
the comparison matrix in fuzzy AHP.

4.4 Fuzzy scales

A fuzzy set describes a particular linguistic term. A fuzzy scale defined by a series of
fuzzy sets depicts the levels of linguistic terms, which links the verbal and numerical
expressions. 9-level and 5-level fuzzy scales for relative importance are commonly
adopted (34 and 43 out of the 109 articles respectively) as illustrated in Figure 10 (a) and
Figure 10 (b). We take TFNs as example to discuss how literature defines these scales
because TFNs are largely applied.

The literature uses different linguistic terms when describing the same scale. For
example, Ayhan and Kilic (2015) use ‘equally important’, ‘equally to weakly
important’, ‘weakly important’, ‘weakly to fairly important’, ‘fairly important’, ‘fairly
to strongly important’, ‘strongly important’, ‘strongly to absolutely important’ and
‘absolutely important’ to describe

the 9 levels that correspond to TFNs 1, 2, 3, 4, 5 , 6 , 7 , 8 and 9 . Pitchipoo et al.

(2013) map those TFNS with ‘equally preferred’, ‘equally to moderately preferred’,
‘moderately preferred’, ‘moderately to strongly preferred’, ‘strongly preferred’, ‘strongly
to very strongly preferred’, ‘very strongly to extremely preferred’ and ‘extremely
preferred’.

Figure 10. fuzzy scale of: (a) 9-level and (b) 5-level

16
Most researchers define the scales in the way as shown in Figure 10. Slight differences exist in
defining TFNs. The TFN 9 could also be interpreted as (7,9,11) (e.g. Viswanadham and
Samvedi (2013) ), (8, 9, 10) (e.g. Beikkhakhian et al. (2015), (9, 9, 9) (e.g. Kannan et al. (2013))
and (9,9,10) (e.g. Taylan et al. (2014)). 1 could also be defined as (0,1,1) (e.g. Taylan et al.
(2014)). Some researchers take totally different TFNs. For example, Zimmer et al. (2017) use

1 , 1.5 , 2.5 , 3.5 and 4.5 for the 5 levels. Other scales are also applied, including 6-level and
7-level fuzzy scales. The number after ‘TFN’ in the column of ‘Pairwise’ in Table A.9 and
Table A.10 indicates the scale used by the article.

4.5 Short discussion

When type-1 fuzzy set uses one value to deal with the imprecision of an element belonging to
a set, type-2 fuzzy set expresses the imprecision of this imprecision (i.e. the imprecision of the
membership degree), and intuitionistic fuzzy set complements this imprecision by adding a
non-membership. Type-2 fuzzy set and intuitionistic fuzzy set are considered more capable to
capture imprecision. However, their arithmetic operations needed in calculations are more
complicated due to the introduction of more parameters in their definitions.

There are no specific choice rules as to which type of fuzzy set should be used. A general
guidance is suggested as a tree diagram in Figure 11.

Figure 11. Fuzzy set specification chart

17
The proper fuzzy set(s) emerge(s) by answering the subsequent questions. The choice should
also consider the properties of the fuzzy sets, as concluded in Table 1. The table shows ‘when’
the fuzzy set is applicable, ‘what’ it describes, ‘how’ it is defined and the complexity of its
arithmetic operations.

Table 1. Summary of the fuzzy sets applied in fuzzy AHP

Fuzzy set When What How Complexity

TFN The opinions Describe the Define the upper and Simple
involve answers: imprecision of a crisp lower boundaries and
partly yes and number with precise the middle point.
TraFN partly no. membership. Define the upper and Simple
lower boundaries and
the two middle
points.
Trapezoidal The opinions Describe the Define the upper and Very
interval type- involve quite imprecision of a crisp lower boundaries and complicated
2 fuzzy set unsure answers. number with the two middle
imprecision points of the upper
membership. and lower trapezoidal
fuzzy numbers
respectively.
Intuitionistic The opinions Describe the Define the degrees of Complicated
fuzzy set involve answers: imprecision of a crisp belongingness and
yes, no and not number with precise non-belongingness.
sure. membership and
precise non-
membership.

5. Aggregation method

The main purpose of aggregation is to produce appropriate results from the pairwise
comparison matrix. This involves methods for: (1) synthesising the decisions of multiple
experts and (2) deriving the fuzzy weights of criteria and priorities of alternatives. The
methods are further categorised according to the types of fuzzy set as discussed in the
previous section. Figure 12 shows the categorisation of the identified methods
annotated by their main characteristics. The strength and weakness of each method is
discussed at the end of this section.
18
 Figure 12. Categorisation of the aggregation methods

5.1 Aggregation for group decision

One challenge of using subjective values is that the judgements of different experts could vary.
Their opinions need to be aggregated to produce a final result. Let (DM1, DM2, …, DMq) be
the q experts and (C1, C2,…, Cn) be the n performance criteria. This subsection starts with three
techniques for type-1 fuzzy set (mainly for TFN) and then discusses the aggregation for type-
2 fuzzy set and intuitionistic fuzzy set.

5.1.1 Mean method

Mean methods for fuzzy numbers are based on the mean methods for crisp values. They
emphasis ‘average’ among all the judgements. Their underlying principle and operations are
simple. Geometric mean and arithmetic mean are two popular ones (25 and 16 respectively
out of 44 papers that have considered group decision and applied type-1 fuzzy sets).

Let Cij(t ) = (lij(t ) , mij(t ) , hij(t ) ) be a TFN representing the relative importance of Ci over Cj judged by

DMt, Cij = (lij , mij , hij ) be the aggregated relative importance of Ci over Cj and wi be the fuzzy

weight of Ci. Some research applies geometric mean, for example, Yang et al. (2008), Chen
and Yang (2011), Kannan et al. (2013) and Zimmer et al. (2017).
q 1 1 q 1 q 1 q 1

Cij = (lij , mij , hij ) = ( Cij(t ) ) q = (Cij(1)  Cij(2)   Cij( q ) ) q = (( lij( t ) ) q ,( mij( t ) ) q ,( hij( t ) ) q ) (8)
t =1 t =1 t =1 t =1

19
An extension to geometric mean is weighted geometric mean that accommodates the weights
of experts. Let (α1, α2, …, αq) be the exponential weighting vector of the q experts. Weighted
geometric mean for the collective relative importance of Ci over Cj or weight of Ci is as
equation 9, where Wi ( q ) is the weight of Ci judged by DMq.

Cij = (Cij(1) )1  (Cij(2) )2   (Cij( q ) ) q or
q
(9)
Wi = (Wi (1) )1  (Wi (2) )2   (Wi ( q ) )

With equation 9, Ertay et al. (2011) aggregate the pairwise comparison matrices while Kar
(2014; 2015) aggregate the weights calculated from the pairwise comparison matrix of each
expert.

Similarly, arithmetic mean (Viswanadham & Samvedi, 2013; Ayhan & Kilic, 2015) and its
weighted extension (Büyüközkan, 2012) are as equations 10 and 11 respectively. (α1, α2, …,
αq) is the normalised weighting vector.
1 1 q (t )
Cij = (Cij1  Cij2 
q
 Cijq ) =  Cij
q t =1
(10)

q
Cij =  t Cij( t ) (11)
t =1

The two mean methods can also be applied to aggregate TraFNs where the operations are on
the quadruples instead of the triples. For example, equation 8 is changed to the following form
for TraFNs.

q 1 1

Cij = (lij , m1ij , m2ij , hij ) = ( Cij(t ) ) q = (Cij(1)  Cij(2)   Cij( q ) ) q

t =1
q 1 q 1 q 1 q 1
(12)
= (( l ) ,( m ) ,( m ) ,( h ) )
(t ) q
ij
(t ) q
1ij
(t ) q
2 ij
(t ) q
ij
t =1 t =1 t =1 t =1

5.1.2 Max-min method

Compared to the mean methods using an average solution, max-min methods extend the
aggregated value range by including the ‘worst’ and the ‘best’ judgements. Max and min, as
two aggregation operators, choose the largest and smallest values respectively. They decide the
upper and lower bounds of the aggregated TFN (h and l in Figure 5). The middle value m is
calculated by geometric mean or arithmetic mean (Awasthi et al., 2018; Prakash & Barua,
2016a). The aggregated TFN Cij = (lij , mij , hij ) by max-min with geometric mean is:

20
 hij = max ( hij( t ) )
t =1,2,..., q
q
mij = ( mij( t ) ) q
1
(13)
1

lij = min (lij( t ) )

t =1,2,..., q

The aggregated TFN Cij = (lij , mij , hij ) by max-min with arithmetic mean is:

hij = max ( hij( t ) )

t =1,2,..., q

1 q (t )
mij =  mij
q t =1
(14)

lij = min (lij( t ) )

t =1,2,..., q

Chen et al. (2010) combine multiple crisp values of judgements to a TFN as the aggregated
relative importance of Ci over Cj. Let crisp value e(t) be the judgement of expert DMt. The

aggregated result Cij = (lij , mij , hij ) is computed as:

hij = max (e( t ) )

t =1,2,..., q

lij = min (e( t ) ) (15)

t =1,2,..., q
q
1
e
1
mij = ( (t )
) q −2
hij  lij t =1

The article on this method referred to by Chen et al. (2010) (i.e. Kuo et al. (2002)) computes
the middle value with geometric mean rather than with equation 15.

5.1.3 Method based on consensus degree

A method based on consensus degree is proposed by Chen (1998) to handle trapezoidal fuzzy
number (TraFN). Its aggregation principle is similar to weighted arithmetic mean. This method
introduces a variable of ‘consensus degree coefficient’ for each expert and multiplies it with
the individual judgement instead of weight of expert in weighted arithmetic mean. This variable
is a compromise between the weight of expert and the difference of its opinion from the
opinions of all the others. The process is as follows.

Step 1: Translate the judgement given by expert DMt into a standardised TraFN characterised
by a quadruple C (t ) = (l (t ) , m1( t ) , m2( t ) , h ( t ) ) , where 0  l (t )  m1( t )  m2( t )  1 .

Step 2: Calculate the degree of agreement S (C (t ) , C ( j ) ) of the opinions between each pair of

experts DMt and DMj, where S (C (t ) , C ( j ) )  [0,1] , 1  t  q, 1  j  q, and t  j . The degree is

21
calculated by equation 16. The larger value of S (C (t ) , C ( j ) ) , the greater the similarity between
the two standardised TraFNs.
| l (t ) − l ( j ) | + | m1( t ) − m1( j ) | + | m2( t ) − m2( j ) | + | h( t ) − h( j ) |
S (C (t ) , C ( j ) ) = 1 − (16)
4
Step 3: Calculate the average degree of agreement A(DMt) of expert DMt (t = 1, 2, …, n) with
all the others.
q
1
A( DM t ) = 
q − 1 j =1, j t
S (C (t ) , C ( j ) ) (17)

Step 4: Calculate the relative degree of agreement RA(DMt) of expert DMt (t = 1, 2, …, n).
A( DM t )
RA( DM t ) = (18)

q
t =1
A( DM t )

Step 5: Calculate the consensus degree coefficient C(DMt) of expert DMt (t = 1, 2, …, n).
y1 y2
C ( DM t ) =  wDM t +  RA( DM t ) (19)
y1 + y2 y1 + y2

wDMt is the weight of expert DMt; y1 and y2 are the weight of the importance of experts and the
weight of the relative degree of agreement of experts.

Step 6: Aggregate the fuzzy judgements. The result Cagg is:

Cagg = C ( DM 1 )  C (1)  C ( DM 2 )  C (2)   C ( DM q )  C ( q ) (20)

Büyüközkan et al. (2017) employ this method directly to TFNs without adaptation. They
calculate the similarity of two TFNs based on equation 16 in the following way.

| l ( t ) − l ( j ) | + | m( t ) − m( j ) | + | h ( t ) − h ( j ) |
S (C (t ) , C ( j ) ) = 1 − (21)
4

For TFNs, equation 16 should be revised as equation 22 (Chen & Chen, 2001) rather than
equation 21.

| l ( t ) − l ( j ) | + | m( t ) − m( j ) | + | h ( t ) − h ( j ) |
S (C t , C j ) = 1 − (22)
3

5.1.4 Fuzzy interval geometric mean

Geometric mean is also applied to type-2 fuzzy set but the calculation process is different from
type-1 fuzzy set due to the different arithmetic operations defined on these sets. It seems to be
the only aggregation operation defined for trapezoidal interval type-2 fuzzy set and does not

22
involve much calculation effort. Görener et al. (2017) use geometric mean to aggregate the

multiple interval type-2 fuzzy sets as the multiple judgements. Let C = ( AU (t ) , AL (t ) ) = ( ( a1U ( t ) ,
(t )

a2U (t ) , a3U (t ) , a4U (t ) ; H1 ( AU (t ) ), H 2 ( AU ( t ) )),(a1L ( t ) , a2L ( t ) , a3L ( t ) , a4L ( t ) ; H1 ( AL ( t ) ), H 2 ( AL ( t ) )) ) be the judgement

of expert DMt. The aggregation result C agg is:

1

=  C  C   C 
(1) (2) q (q)
C agg (23)
 
Where

(
= ( a1U ( t )  a1U ( j ) , a2U (t )  a2U ( j ) , a3U (t )  a3U ( j ) , a4U (t )  a4U ( j ) ;
(t ) ( j)
C C

( ) (
min H1 ( AU (t ) ), H1 ( AU ( j ) ) , min H 2 ( AU (t ) , H 2 ( AU ( j ) ) , )
(24)
(a L (t )
1  a1L ( j ) , a2L ( t )  a2L ( j ) , a3L ( t )  a3L ( j ) , a4L ( t )  a4L ( j ) ;

( ) (
min H1 ( AL ( t ) ), H1 ( AL ( j ) ) , min H 2 ( AL ( t ) , H 2 ( AL ( j ) ) ))
(
q (t )
C = ( q a1U ( t ) , q a2U ( t ) , q a3U ( t ) , q a4U ( t ) ; H1 ( AU ( t ) ), H 2 ( AU ( t ) )),
(25)
( a q L (t )
1
q
, a L (t )
2
q
, a L (t )
3
q
, a L (t )
4 ; H1 ( A L (t )
), H 2 ( A L (t )
)) )
5.1.5 Intuitionistic fuzzy weighted averaging

Intuitionistic fuzzy weighted averaging (IFWA) includes weighted arithmetic and geometric
averaging operators (Xu, 2007). If the weights of experts are equal, the two operators reduce
to intuitionistic fuzzy arithmetic and geometric averaging operators. Büyüközkan and Güleryüz
(2016) and Büyüközkana et al. (2019) apply intuitionistic fuzzy weighted arithmetic averaging
operator. Let Ct = (μt, vt, πt) be the judgement of expert DMt and v = (α1, α2, …, αq) be the
weight vector of the experts. The aggregation result is Cagg, where
Cagg = 1C (1)   2C (2)    qC (q)
 q q
 (26)
= 1 −  (1 −  (t) )t ,  (v (t) )t ,  (1 −  (t) )t −  (v (t) )t 
 t =1 t =1 

5.2 Aggregation for fuzzy weights/priorities

Aggregation of judgements on a single criterion are usually done as a mean or an average value.
By contrast, the methods for the weights of criteria are more varied in that they deal with the
judgements on different criteria from the fuzzy pairwise comparison matrix. This section starts
with four techniques for the matrix of type-1 fuzzy sets. Let F = [Cij ]nn be a fuzzy pairwise

23
comparison matrix and (C1, C2,…, Cn) be the n performance criteria. Cij is the relative

importance of Ci over Cj. We describe the methods with notations related to criteria. The
calculation of the alternative priorities is the same.

5.2.1 Mean method

Geometric mean is a valid means of synthesising different perspectives and also an

approximation to eigenvalues of a matrix. It has been widely used to calculate fuzzy weights,
e.g. Yang et al. (2008), Sun (2010), Yu et al. (2012), Kar (2014) and Görener et al. (2017). It
is immune to the problem of rank reversal and independent on order of operations (Barzilai,
1997). The ‘mean’ value by geometric operation is then normalised to generate the fuzzy
weight of a criterion, as shown in equation 27.
1
Ci = (Ci1  Ci 2   Cin ) n
Ci (27)
Wi =

n
j =1
Cj

Rezaei and Ortt (2013) and Chen et al. (2010) apply arithmetic mean as equation 28. It is also
utilised in Extent Analysis Method (EAM) to get the fuzzy weights. Some research obtains
the weights by applying row sums and then normalising the sums instead of averaging, which
is also a simple and convenient methods, for example, Calabrese et al. (2016; 2019).

1
Ci = (Ci1  Ci 2   Cin )
n
Ci
(28)
Wi =

n
j =1
Cj

Another method in this group is fuzzy logarithmic least-squares method proposed by Van
Laarhoven and Pedrycz (1983). It is grouped in mean methods because geometric mean is
considered by researchers for example, Büyüközkan (2012), as one optimal solution to this
programming problem. However, the weights estimated by logarithmic least-squares might not
be valid fuzzy numbers (Csutora & Buckley, 2001). In other words, it can produce fuzzy weight
W = (l , m, h) with h < l. cij is the entry of the pairwise comparison matrix and wi is the weight

of criteria i. The method is:

n n
min  (ln cij − (ln wi − ln w j )) 2 (29)
w
i =1 j =1

Subject to
n

w
i =1
i = 1, wi  0, 1 i  n

24
With regards to the capability of processing size of the matrix, fuzzification level and
inconsistency, fuzzy logarithmic least-squares has the best overall performance, followed by
geometric mean and then arithmetic mean (Ahmed & Kilic, 2018).

5.2.2 Lambda-max method

The lambda-max method proposed by Csutora and Buckley (2001) transforms the fuzzy
comparison matrix into three crisp comparison matrices through the α-cut of a TFN, and then
calculates the fuzzy weights. This method directly fuzzifies Saaty’s λmax method (eigenvector
method) and reduces the fuzziness in the final fuzzy weights. It can also handle any type-1
fuzzy number used for pairwise comparison. Compared with mean method, it is complicated
due to the multiple steps involving calculating eigenvalues, minimising the fuzziness, adjusting
the boundaries of the weights. Wang et al. (2009) apply this method in their fuzzy AHP model.
It has the following steps. As introduced in section 4.1, the α-cut of a TFN Cij = (lij , mij , hij ) can

be represented as Cij = [lij + (mij − lij ) , hij − (hij − mij ) ] .

Step 1: Set α =1. The middle value of each entry of the fuzzy pairwise comparison matrix is
F = [Cij ]nn , i.e. Cij =1 = mij. The corresponding crisp comparison matrix is Fm = [mij]n×n. The

middle value of the fuzzy weight of criterion Ci, wim, is calculated by solving equation 30. λmax
is the largest eigenvalue of Fm. wm is the weight vector, wm = (w1m, w2m, …, wnm)T.
Fm wm = max wm (30)

Step 2: Set α =0. This calculates the lower and upper bounds of the fuzzy weight of criterion
Ci, wil and wih. The two crisp comparison matrices are Fl = [lij]n×n and Fh = [hij]n×n. wl and wh
are the weight vectors generated from Fl and Fu respectively. The calculation procedure is the
same with that of wm by equation 30.

Step 3: Find constants Kl and Kh. They are used to minimise the fuzziness of the weights, which
refers to the lengths of the α-cuts.
wim
K l = min{ |1  i  n}
wil
(31)
w
K h = max{ im |1  i  n}
wih

Step 4: Use the two constants to adjust the lower and upper bounds of the fuzzy weight of
criterion Ci obtained in step 2. The adjusted bounds are wil* and wih*.

25
 wil* = Kl wil
(32)
wih* = K h wih

The fuzzy weight of criterion Ci is as Wi = ( wil* , wim , wih* ) .

5.2.3 Eigenvector based on index of optimism

Calculating the eigenvector is the original method to derive weights from the matrix in AHP.
This method can be adapted to fuzzy AHP but requires transforming fuzzy values to crisp
values. In other words, the fuzzy comparison matrix needs to be transformed to crisp
comparison matrix. One common method for this transformation uses α-cut and an index of
optimism. Different from Lambda-max method that solely uses α-cut for several crisp matrices,
the weights obtained in this manner are crisp values rather than fuzzy numbers. Let cijαU and
cijαL denote the upper and lower bounds of α-cut set Cij , i.e. Cij = [cijαL, cijαU]. cijαU indicates

an optimistic expert’s point of view towards the priority of criterion Ci over Cj while cijαL is a
pessimistic view (Kim & Park, 1990). An expert’s attitude may not be purely optimistic or
pessimistic, but somewhere in between. Therefore, they are combined with an index of
optimism μ as:
cij =  cijU + (1 −  )cij  L ,   [0,1] (33)

The larger the value of μ is, the higher the degree of optimism is. cij is also named as degree of
satisfaction. The fuzzy comparison matrix is transformed into a crisp matrix F = [cij]n×n by
equation 33. By setting the values of α and μ (usually set as 0.5 and 0.5), weight calculation
turns to finding the eigenvector by Saaty’s λmax method. The application can be found in Soroor
et al. (2012), Büyüközkan et al. (2017) and Beikkhakhian et al. (2015).

Awasthi et al. (2018) calculate the weights in a similar way that the fuzzy matrix is defuzzified
first by equation 34 and then the eigenvector is computed. cij is the defuzzified value from TFN.
1
cij = (lij + 4  mij + hij ) (34)
6
Pitchipoo et al. (2013) also calculate weights by converting fuzzy numbers into crisp values.
They apply centroid method for defuzzification, given in equation 35.
k

D i
p  oi n
Weights (Crisp value)Wi = i −1
k
, where Dip =  mli (35)
 Dip
i =1
i =1

26
k is the number of rules. Oi is the class generated by rule i (from 0, 1, …, L-1). L is the number
of classes, n is the number of inputs, and mli is the membership grade of feature l in the fuzzy
regions that occupy the ith rule. However, it is not clear how the method in Pitchipoo et al.
(2013) actually works without a further explanation on ‘rules’, ‘class’ and ‘inputs’ as well as
their mapping with criteria, alternatives and TFNs.

The main principle of the methods based on eigenvector is to transform the fuzzy matrix to a
crisp matrix first, so all the defuzzification methods introduced later can be applied here. With
the crisp matrix, researchers can also choose geometric mean or arithmetic mean instead of
eigenvector to calculate the crisp weights, for example, Balusa and Gorai (2018). However,
Csutora and Buckley (2001) argue that this kind of method is not about fuzzy AHP since there
are no fuzzy weights.

5.2.4 Fuzzy programming method

Fuzzy programming methods are iterative algorithms that search every possible value and
gradually achieve a solution to a prescribed accuracy (Luenberger & Ye, 2008). The advantage
of programming methods is producing a consistency index while computing the weights. But
they require more computational effort than other aggregation methods. Mathematical models
have to be established first, and assistant tools like Excel solver are needed to solve the models.
Rezaei et al. (2013; 2014) use a fuzzy non-linear programming method to derive crisp weights
from a fuzzy comparison matrix, which saves the efforts to defuzzify. This method first
distinguishes TFNs from their reciprocals and then defines the non-linear model as equation
36 where wi is the weight and λ is a variable that measures the degree of membership of the
fuzzy feasible area (i.e. the height of the intersection region of the fuzzy judgements).
max 
s.t.
( mij − lij ) w j − wi + lij w j  0, 
 for TFNs
(uij − mij ) w j + wi − uij w j  0 
( m ji − l ji ) wi − w j + l ji wi  0,  (36)
 for reciprocals
(u ji − m ji ) wi + w j − u ji wi  0 
n

w
k =1
k = 1, wk  0,

i = 1,..., n − 1, j = 2,...n, j  i, k = 1,..., n

Solving the problem described in equation 36 results in the optimal crisp weight vector W* and
λ*. λ* > 0 indicates that all solution ratios approximately satisfy the fuzzy judgement, i.e.
27
lij  ( wi* / w*j )  uij . It means that the pairwise comparisons are approximately consistent. λ* as a

fuzzy consistency index will be discussed in section 7.2.1. Equation 36 is an extension to the
programming method proposed by Mikhailov and Tsvetinov (2004) in equation 62.

Mirhedayatian et al. (2013) develop a programming model based on Data Envelopment

Analysis to calculate the fuzzy weight Wi = ( wil , wim , wih ) as follows:
max t
n
s.t. wil :  lij u j  t ,
j =1
n
wim :  mij u j  t ,
j =1
n
(37)
wih :  hij u j  t ,
j =1
n

m u
j =1
ij j  1, r = 1,...n,

n
u j   mij u j nmij , j = 1,..., n
j =1

5.2.5 Fuzzy interval geometric mean and IFWA

Fuzzy interval geometric mean as equations 20 and 21 also calculates the weights from the
pairwise comparison matrix of interval type-2 fuzzy sets, for example Celik and Akyuz (2018)
and Görener et al. (2017).

Similarly, IFWA operators, introduced in aggregation for group decisions, are also applied to
calculate the weights from the matrix of intuitionistic fuzzy sets. The calculation procedure
shown in equation 22 is used by Büyüközkana et al. (2019).

5.3 Short discussion

Various methods are available to aggregate TFNs while few methods exist for interval type-2
and intuitionistic fuzzy sets, which indicates a potential research topic of exploring more
applicable aggregation means for the latter two types of fuzzy sets. There are no specific choice
rules as to which method should be used for group decisions. Different methods are introduced
for different situations. A general guidance is suggested as shown in Figure 13. The appropriate
method(s) emerge(s) by answering the subsequent questions. These methods are also
summarised in Table 2 in terms of their characteristics, complexity of the computation and
extension (how they can be extended) to help the choice.
28
 Figure 13. Specification chart of aggregation methods for group decisions

Table 2. Summary of the aggregation methods for group decisions

Method Characteristic Complexity Extension

Arithmetic Emphasis ‘average’. There Very simple, only (1) Weighted arithmetic mean
mean should be no extreme value involving arithmetic by incorporating the weights of
due to its sensitivity. addition and experts; (2) intuitionistic fuzzy
division. weighted arithmetic averaging
for intuitionistic fuzz sets by
adding the weights of experts.
Geometric Emphasis ‘average’. It is less Very simple, only (1) Weighted geometric mean
mean affected by extreme value involving arithmetic by incorporating the weights of
and more suitable to average multiplication and experts; (2) fuzzy interval
normalised values. There rooting. geometric mean for interval
should be no negative value. type-2 fuzzy sets; (3)
intuitionistic fuzzy weighted
geometric averaging for

29
 intuitionistic fuzz sets by
adding the weights of experts.
Max-min Include the ‘worst’ and the Simple, involving -
method ‘best’ judgements but arithmetic addition
with introduce more fuzziness and division, max
arithmetic due to the enlarged value and min operations.
mean range. There should be no
extreme value.
Max-min Include the ‘worst’ and the Simple, involving Produce a TFN as the
method ‘best’ judgements but arithmetic aggregated judgement by
with introduce more fuzziness multiplication and combining crisp values of the
geometric due to the enlarged value rooting, max and min experts’ judgements.
mean range. operations.
Method Consider the distances Complicated due to -
based on between the opinions of the the calculation of
Consensus experts but assume the degree of agreement.
degree weight of the importance of
expert and the weight of the
relative degree of agreement
are known.

It can be seen from Table 2 that the mean methods have wider application because they are
easier to implement and produce valid results. The arithmetic mean has been adapted to
intuitionistic fuzzy sets and the geometric mean has been adapted to interval type-2 fuzzy sets
and intuitionistic fuzzy sets. Arithmetic mean should also be applicable to aggregate interval
type-2 fuzzy sets since geometric mean can be expressed as the exponential of the arithmetic
mean of logarithms. Max-min method with geometric mean has been used to aggregate crisp
values into a TFN while max-min with arithmetic mean should also work. It is worth studying
whether and how the mean methods can be extended to other types of fuzzy sets.

The choice as to which method is used for weights/priorities also first depends on the chosen
type of fuzzy set. A general guidance is presented in Figure 14. These methods are summarised
in Table 3 in terms of the underlying principle, the complexity of the computation and the pros
and cons.

30
 Figure 14. Specification chart of the aggregation methods for weights

Table 3. Summary of the aggregation methods for weights/priorities

Method Principle Complexity Pros and Cons

Arithmetic Row sum divided by n (the Very simple, only Perform least in the
mean number of criteria), which involving arithmetic mean group.
is then normalised. addition and division.
Geometric Nth-root of row Very simple, only Produce the same
mean multiplication, which is involving arithmetic weights as Saaty’s
then normalised. multiplication and rooting. eigenvector method, if
the matrix is consistent.
Perform better than
arithmetic mean.
Logarithmic A mathematical Complicated because it is May produce fuzzy
least-squares programming method indeed a programming weights that are not
method but the objective fuzzy numbers, which
and constraint functions could lead to
are simple. inconsistency. It could
generate multiple
results as the weight.
31
 Perform best in the
mean group.
Lambda-max Transform the fuzzy A little complicated due to Reduce certain
method matrix into multiple crisp the multiple steps fuzziness in the final
matrices by α-cut, and then involving calculating results; can be applied
calculates the fuzzy eigenvalues, minimising to all other fuzzy
weights by generating and the fuzziness, adjusting the numbers.
adjusting the eigenvectors boundaries of the weights.
of the crisp matrices.
Eigenvector Transform the fuzzy A little complicated, It is worth considering
method matrix into a crisp matrix involving defuzzifying the how much this kind of
and then calculate the crisp fuzzy matrix and method is about fuzzy
weights from the crisp calculating eigenvalue. AHP since there are no
matrix. fuzzy weights.
Fuzzy Iterative algorithms that Very complicated due to Produce a consistency
programming search every possible the iterative search and the index while computing
methods value and gradually need of assistant tools to the weights.
achieve a solution to a solve the model. The
prescribed accuracy. constraint functions are
complicated.

6. Defuzzification method

Defuzzification converts the fuzzy results produced by aggregation methods into crisp values.
Compared with a fuzzy value, a crisp value is more intuitive and easier for the final comparison
because fuzzy sets have partial ordering. As shown in Figure 15, this section discusses the
defuzzification methods for type-1 fuzzy set and then for type-2 and intuitionistic fuzzy sets.

Figure 15. Categorisation of the defuzzification methods

32
6.1 Defuzzification method for type-1 fuzzy set

There are two dominant defuzzification methods applied by researchers, i.e. centroid method
and extent analysis method. 33 papers apply the centroid method and 50 paper use the extent
analysis method.

6.1.1 Centroid method for type-1 fuzzy set

The centroid method, also called as centre of area (COA) or centre of gravity (COG), is the
most prevalent defuzzification method (Ross, 2004). The underlying principle is as equation
38 where x* is the defuzzified value, x indicates the element, and μ(x) is its associated
membership function.

x* =
  ( x) xdx (38)
  ( x)dx
The centroid method can be translated into different forms when defuzzifying a TFN
= (lexample,
.CFor , m, h) equation 39 is applied by Sun (2010), Yu et al. (2012), Pitchipoo et al. (2013),
Rezaei and Ortt (2013), Ayhan and Kilic (2015), Yayla et al. (2015) and Calabrese et al.
(2016; 2019).
l+m+h
x* = (39)
3
Kar (2014; 2015) uses equation 40. Awasthi et al. (2018) utilise equation 41.

l + 2m + h
x* = (40)
4
l + 4m + h
x* = (41)
6
Büyüközkan (2012) defuzzify a TFN by taking α-cut set, C , as shown by equation 42.
1 1
2 0
x* = (inf C + sup C )d (42)

With the α-cut set C = [l + (m − l ) , h − (h − m) ] , equation 42 can be further transformed as:
1 1
2 0
x* = (l + (m + l ) + h − (h − m) )d

l+h 1 1
= +  (2m − l − h) d  (43)
2 2 0
l + 2m + h
=
4

33
Equation 43 corresponds to Yager’s approach (Yager, 1981) that analyses the mean of the
elements within an interval. It has been proved by Facchinetti et al. (1998) that this way takes
into consideration both the worst and best results arising from a fuzzy number.

6.1.2 The extent analysis method

The extent analysis method (EAM), proposed by Chang (1996), aims to calculate the weights

and translate TFNs into crisp values in the fuzzy pairwise comparison matrix. Let F = [Cij ]nn

be a fuzzy pairwise comparison matrix. The fuzzy weight of element i is:

m n m
Wi =  Cij  [ Cij ]−1 (48)
j =1 i =1 j =1

Equation 48 is actually the fuzzy arithmetic mean as in equation 28. The crisp weight of i is
determined as the minimal degree of possibility of its fuzzy weight wi being greater than the

fuzzy weights of the others. Given two TFNs A1 = (l1 , m1 , h1 ) and A2 = (l2 , m2 , h2 ) as shown in

Figure 16, The degree of possibility of A1  A2 is defined as:

V ( A1  A2 ) = 1 iff m1  m2
(49)
V ( A2  A1 ) = hgt ( A1  A2 ) = (l1 − h2 ) ((m2 − h2 ) − (m1 − l1 ))

Figure 16. Fuzzy Triangular Number of A1 and A2

The crisp weight of i is then defined by equation 50.

wi = V ( Ai  A1 , A2 ,..., An )
= V [( Ai  A1 ) and ( Ai  A2 ) and ... and ( Ai  An )] (50)
= min V ( Ai  Ak ), k = 1, 2,.., n, k  i

EAM is simple to implement but does not produce proper weights. There is a zero assigned
when there is no intersection of the two TFNs. Also, the way of calculating is incorrect because
it neglects the role of l2 and h1 in determining the relative importance. This leads to a big
inconsistency between the results and the original judgments. Considering EAM is widely
applied, we explain how EAM is problematic in details in the short discussion section.
34
6.1.3 Other methods

Opricovic and Tzeng (2003) propose a defuzzification method, namely Converting the Fuzzy
data into Crisp Scores (CFCS), which is applied by Sarfaraz et al. (2012) to rank ERP
implementation solutions. Let F = [Cij ]nn be a fuzzy pairwise comparison matrix and (C1,

C2,…, Cn) be the n performance criteria. Cij = (lij , mij , hij ), j = 1, 2,..., n is the pairwise comparison

of Ci over Cj. The crisp value for each TFN is computed by the following four steps.

Step 1: Normalisation.
h max
j = max hij , l min
j = min l ij ,  max
min = h j
max
− l min
j (51)
i i

Normalise the matrix. Let F = [ X ij ]nn be the normalised result; X ij = ( xlij , xmij , xhij ) .

xlij = (lij − l min

j ) /  max
min

xmij = (mij − l min

j ) /  max
min
(52)
xhij = (hij − l min
j )/ max
min

Step 2: Compute left (ls) and right (hs) normalised values for i = 1, 2, … n. j = 1, 2, …, n.
xijls = xmij / (1 + xmij − xlij )
(53)
xijhs = xhij / (1 + xhij − xmij )

Step 3: Compute total normalised crisp value.

xijcrisp = [ xijls (1 − xijls ) + xijhs xijhs ] / (1 − xijls + xijhs ) (54)

Step 4: Compute crisp values. Let aij be the crisp value correspondent to Cij .

aij = l min
j + xijcrisp  max
min (55)

A major problem of CFCS we have noticed is that it produces varied crisp values for a
particular TFN. This is due to the normalisation in step 1. Consider one scenario with 2 criteria
and another with 3 criteria. Table 4 shows their comparisons against C1. The crisp values for
TFN (5, 7, 9) are different in the two scenarios.

Table 4. Defuzzification results by CFCS

Scenario 1: 2 criteria
Criterion TFNs Normalised fuzzy value Crisp value
C1 (1, 1, 1) (0, 0, 0) 1
C2 (5, 7, 9) (1/2, 3/4, 1) 6.867
Scenario 2: 3 criteria
35
 C1 (1, 1, 1) (0, 0, 0) 1
C2 (5, 7, 9) (4/9, 6/9, 8/9) 6.916
C3 (6, 8, 10) (5/9, 7/9, 1) 7.86

Mathematically, defuzzifying a fuzzy set is the process of rounding it off from its location to
the nearest vertex, which reduces the set into the most typical or representative value (Ross,
2004). However, CFCS contradicts this principle because the defuzzification result changes as
the number of criteria/alternatives changes and also depends on the values of the other TFNs
in the comparison matrix. It seems not a suitable defuzzification method.

Mean of limits of a TFN is another method. Alaqeel and Suryanarayanan (2018) apply the
geometric mean to the upper and lower limits (i.e. l and h) for a crisp value. This way of
defuzzification ignores the middle value of a TFN, which might lead to improper weight.

Index of optimism is also used to defuzzify the fuzzy numbers through their α-cut sets, which
has been introduced in section 5.2.3, for example, Jung (2011), Soroor et al. (2012),
Beikkhakhian et al. (2015) and Büyüközkan et al. (2017).

Other applicable defuzzification methods are max membership principle, weighted average and
mean of maxima (Ross, 2004) but they are rarely applied in the selection literature.

6.2 Centroid method for type-2 fuzzy set

The centroid of an interval type-2 fuzzy set is the union of the centroids of all its embedded
type-1 fuzzy sets. Based on this principle, Kahraman et al. (2014) propose equations 56 and
(57) to defuzzify triangular and trapezoidal interval type-2 fuzzy set.
( a3U − a1U ) + ( aU2 − a1U )
+ a1U +  ( ( a3 −a1 ) +3 ( a2 −a1 ) + a1L )
L L L L

x *
TFN = 3
(56)
2
( aU4 − a1U ) + ( H1 ( AU ) aU2 − a1U ) + ( H 2 ( AU ) a3U − a1U )
+ a1U + ( a4 −a1 ) +( H1 ( A ) a2L − a1L ) + ( H 2 ( AL ) a3L − a1L )
L L L
+ a1L
x*
TraFN = 4 4
(57)
2
In equation 56, α is the maximum membership degree of the lower membership function; a3U
and a1U are the largest and least possible value of the upper membership function respectively;
a2U is the most possible (middle) value of the upper membership function; a3L and a1L are the
largest and least possible value of the lower membership function; a2L is the middle value of
the lower membership function.

In equation 57, H1 and H2 are the two maximum membership degrees; a4U, a3U a2U and a1U are
the largest, the two middle and least possible values of the upper membership function
36
respectively; a4L, a3L a2L and a1L are the largest, the two middle and least possible values of the
lower membership function respectively. Celik and Akyuz (2018) and Ayodele et al. (2018)
use this equation in their fuzzy AHP model.

6.3 Intuitionistic fuzzy entropy for defuzzification

The defuzzification methods for type-1 and type-2 fuzzy sets transform fuzzy values to
representative crisp values. Fuzzy entropy also generates crisp values but measures the
fuzziness of the set. Whether it can be considered as a weight is worth considering.
Büyüközkana et al. (2019) treats the intuitionistic fuzzy entropy wi as the crisp weight value.

Let wi = {i , vi ,  i } be intuitionistic fuzzy weight. Equation 58 is used to calculate wi .

1
wi = − [ i ln i + vi ln vi − (1 −  i )ln(1 −  i ) −  i ln 2] (58)
n ln 2

Büyüközkana et al. (2019) have not provided the reference or proof for this equation. Based on

the format of the equation, it might be an extension of Shannon’s function as equation 59,

which is used to measure the fuzziness of type-1 fuzzy set (Zimmermann, 2001).

S (  ) = −  ln  − (1 −  ) ln(1 −  ) (59)

6.4 Short discussion

EAM is applied by a large proportion of articles (50 out of the total 109 papers, 46%), which
corresponds to the survey results (i.e. 109 out of the 190 papers) by Kubler et al. (2016).
However it has been criticised by many researchers for its significant shortcomings in deriving
the weights/priorities. Zhu et al. (1999) notice that EAM cannot deal with the comparison if
there is no intersection between two fuzzy numbers. This problem is solved by assigning a
value of 0 in the case of no intersection and equation 49 is extended as:
V ( A1  A2 ) = 1 iff m1  m2
(l − h ) ((m2 − h2 ) − (m1 − l1 )), if l1  h2 (60)
V ( A2  A1 ) =  1 2
0, otherwise.

Introducing this zero weight leads to some criteria or alternatives being ignored in the analysis
and results in a wrong decision (Wang et al., 2008).

EAM is still inappropriate to attain the relative importance even if every two fuzzy numbers
have intersection. Let A1 = (l1 , m1 , h1 ) and A2 = (l2 , m2 , h2 ) be two TFNs. Consider the scenario in
37
Figure 17 (a) that m1 = m2 but l2 < l1 and h2 < h1. A1 should have a priority above A2 , but

according to equation 49, when m1 = m2, V ( A1  A2 ) = V ( A2  A1 ) = 1 that the two TNFs are of
the same priortity. Consider another case as Figure 17 (b). m2 = m1 + ε where ε is a very small
positive number close to 0. h2 = m2 + ε, l1 = m1 – ε, l2 = m2 + α, h1 = m1 + α, where α is a large
positive number. According to equation 49, V ( A2  A1 ) = 1  V ( A1  A2 ) which indicates A2 has

a higher priority. However, it is apparent that A1 should be preferred over A2 . The ordinate of

the highest intersection in EAM cannot represent the degree of possibility of A2  A1 or their
relative weights, because it only depends on the two lines defined by m2, h2 and l1, m1
respectively. Values l2 and h1 should also play a role to determine the relative importance and
neglecting them leads to improper weights. EAM has the advantage of ease of use and simple
logic, which might be the reason why it is still widely applied.

Figure 17. Two example cases:(a) m1 = m2; (b) m2 >m1 but m1 , m2, l1 , h2 are very close to each other

It seems that centroid method is the most suitable choice for type-1 and type-2 fuzzy sets as
concluded in Table 5.

Table 5. Summary of defuzzification methods

Method Principle Complexity Pros and cons

Centroid Calculate the centre of Very simple (single Have various forms but
method the area defined by the equation), involving equation 40 has been well
fuzzy number. arithmetic addition and proved. Its application has
division been extended to type-2
fuzzy set.
EAM Calculate the smallest Simple, involving Cannot derive proper crisp
possibility of one TFN arithmetic and min weights.
bigger than another as operations but having few
the defuzzified result. steps to follow.

38
 CFCS Calculate the crisp A little complicated, Produce varied crisp values
value based on the involving arithmetic, for a particular TFN. It
normalised fuzzy min/max, and seems not a proper
numbers. normalisation operations defuzzification method.
and having several steps to
follow.
Mean of Calculate the geometric Very simple (single Might result in improper
limits mean of the upper and equation), involving results due to ignoring the
lower limits of a TFN. arithmetic multiplication middle value of a TFN.
and rooting.
Index of Calculate the crisp Very simple (single The experts need to set
optimism value based on the α- equation), involving values for the two
cut of a TFN and the arithmetic operations. parameters α and μ. But it
index of optimism μ. seems little literature
discusses how to set proper
values.
Fuzzy Calculate the fuzziness Simple (single equation), Be used to defuzzify
entropy of the fuzzy set. involving arithmetic and intuitionistic fuzzy set. But
logarithm operations. fuzzy entropy is used to
measure the fuzziness.

7. Consistency measurement

Consistency measurement ensures that there are limited contradictions among the pairwise
comparisons in the matrix. It is a necessary step because a big inconsistency may indicate
a lack of understanding of the problem. There are two ways of measuring the consistency of
the fuzzy pairwise comparison matrix. ‘Crisp consistency’ is computed by translating the
fuzzy matrix to a representative crisp one. ‘Fuzzy consistency’ calculates a consistency index
directly from a fuzzy matrix. Figure 18 outlines the methods.

Figure 18. Categorisation of the consistency measurement methods

39
7.1 Crisp consistency

The principle of crisp consistency is to defuzzify the fuzzy matrix first and then use Saaty’s
consistency ratio (CR) (see Jung (2011), Kilincci and Onal (2011), Büyüközkan
(2012), Pitchipoo et al. (2013), Calabrese et al. (2016; 2019), Büyüközkan
et al. (2017) and
Ayodele et al. (2018)). The implementation would be different in defuzzification as there
are various defuzzification methods as introduced in section 6. The defuzzified matrix with a
CR less than 0.1 is considered as adequately consistent.
CR = CI RI
(61)
CI = (max − n) (n − 1)

CI is consistency index; λmax is the max eigenvalue of the comparison matrix; RI is the random
index. The value of RI depends on the size of the matrix that can be looked up in Saaty (2008).

Büyüközkana et al. (2019) check the intuitionistic fuzzy matrix by Saaty’s method, but
calculate the consistency ratio in the following way:

CR =  RI −
 ij 
 (n − 1) (62)
 n 

where n is the number of the elements and πij is the degree of non-determinacy of the
membership. The value of RI is taken from Saaty’s method. CR is considered acceptable if less
than or equal to 0.1. However, they did not explain why the ratio from equation 62 works to
measure the consistency. It seems that mathematical proof is needed.

7.2 Fuzzy consistency

This way of measuring consistency usually requires establishing and solving fuzzy
programming models. The consistency index is derived along with the weights of criteria from
the models. This section first introduces various programming models starting from the
explanation of their origin and then presents a different fuzzy consistency method.

7.2.1 Fuzzy programming method

According to Buckley (1985), the fuzzy comparison matrix F = [ Aij ]nn is consistent if and only

if:
Aik  Akj  Aij (63)

40
The approximate equal ‘  ’ between two fuzzy numbers A1 and A2 whose membership
functions are µA1(x) and µA2(x) is defined as:
min(v( A1  A2 ), v( A2  A1 ))   (64)
Where v( A1  A2 ) = sup(min(  A1 ( x),  A2 ( y ))) and  is a fixed positive fraction less than or equal
x y

to 1. Literally speaking, A1 and A2 are approximately equal if A1 is not greater than A2 and A2

is not greater than A1 .

Based on equation 63, Arbel (1989) further proves that a fuzzy comparison matrix can be
considered as consistent when the ratio of the weight wi of criterion Ci to the weight wj of
criterion Cj is within the upper and lower bounds of the corresponding TFN Aij = (lij , mij , hij ) ,

i.e.
lij  ( wi / w j )  hij (65)

This equation is the base of the following non-linear programming model (Mikhailov &
Tsvetinov, 2004). The outcomes of fuzzy programming method provide the optimal crisp
weight vector and a consistency index λ.
max 
s.t.
(mij − lij ) w j − wi + lij w j  0
(hij − mij ) w j + wi − hij w j  0 (66)
n

w
k =1
k = 1, wk  0,

i = 1,..., n − 1, j = 2,...n, j  i, k = 1,..., n

That the optimal value λ* > 0 means that all solution ratios completely satisfy the fuzzy
judgements. A negative value indicates that the judgements are inconsistent.

As discussed by Mikhailov (2004), in inconsistent cases, there does not exist a weight vector
that satisfies all inequalities in equation 65 simultaneously. But it is reasonable to try to find a
vector satisfying all inequalities as well as possible, which introduces ‘approximately less than
or equal to’, i.e. ‘  ’ , to equation 65.
lij  ( wi / w j )  hij (67)

The following non-linear programming model is then proposed, which adds a tolerance
parameter pij. This parameter extends the feasible region by extending the lower and upper
bounds.

41
 max 
s.t.
pij  w j + (lij − pij ) w j − wi  0
pij  w j − (hij + pij ) w j + wi  0 (68)
n

w
k =1
k = 1, wk  0,

i = 1,..., n − 1, j = 2,...n, j  i, k = 1,..., n

That the optimal value λ*  1 indicates consistent fuzzy judgements. For a weak consistency
but the solution ratio is within the extended bounds, λ* is a value between 1 and 0, depending
on the degree of inconsistency and the values of the tolerance parameters. Chen and Yang
(2011) use Mikhailov (2004)’s method to examine the consistency. In the first example of Chen
and Yang’s paper (i.e. Example 1), a consistency index value 0.7602 is obtained so they
consider the comparison matrix consistent. But according to Mikhailov (2004), a value within
[0, 1] should be weakly inconsistent.

7.2.2 Geometric consistency index

Kar (2014; 2015) apply Geometric consistency index (GCI) to the fuzzy matrix F = [ Aij ]nn as

equation 69:
n
2
GCI ( F ) =  (log Aij − (log wi − log w j )2 )
(n − 1)(n − 2) j i
(69)

If GCI ( F )  GCI , the matrix is consistent. GCI are fixed values that GCI = 0.31 for n = 3,

GCI = 0.35 for n=4 and GCI = 0.37 for n > 4.

This consistency measure is proposed by Crawford and Williams (1985) for crisp matrix. The
thresholds of CGI are determined by Aguarón and Moreno-Jiménez (2003) who provide an
interpretation of GCI analogous to the consistency index in AHP proposed by Saaty. It checks
the consistency only after the weights of alternatives are obtained. Considering that row
geometric mean instead of right eigenvector is used for the prioritisation, the computation
efforts do not increase compared with Saaty’s method. The problem when applying this
measure to the fuzzy matrix is how to calculate the logarithm of a fuzzy number. Kar (2014;
2015) do not explain this and it seems that crisp values are used though the equation presents
fuzzy numbers. There is also a mistake in their used equation (i.e. equation 69) that the square
should be placed in the outer bracket as shown in equation 70.
n
2
GCI ( F ) = 
(n − 1)(n − 2) j i
(log Aij − (log wi − log w j )) 2 (70)

42
7.3 Short discussion

Crisp consistency based on Saaty’s method is mostly used and suitable for all types of fuzzy
sets. Mahmoudzadeh and Bafandeh (2013) explain why a crisp consistency can represent the
consistency of the fuzzy matrix. In the case of calculating a fuzzy inconsistency ratio, they
have proved that if the comparison matrix obtained from an α = 1 cut set of A is consistent,
then the original fuzzy comparison matrix is consistent. For a TFN A = (l, m, n), its α = 1 cut
set reduces to a crisp number, i.e. Aα = m. The consistency check of the fuzzy matrix F = [ Aij ]nn

becomes the check of the crisp matrix Fα=1 = [mij]n×n. Saaty’s consistency ratio then can be
used.

Table 6 summarises the methods to measure the consistency in terms of the underlying
principle, the complexity of the computation and the pros and cons.

Table 6. Summary of the methods for consistency measurement

Method Principle Complexity Pros and cons

Saaty’s Check the consistency of the Simple (simple The choice of
method defuzzified fuzzy matrix by equations), involving defuzzification methods
Saaty’s consistency ratio. arithmetic operations may influence the results
and calculation of max since different
eigenvalue of the defuzzification methods
matrix. could produce different
crisp matrices. It is
extended to type-2 and
intuitionistic fuzzy sets.
Fuzzy Establish the objective and Very complicated due It generates the
programming constraint functions based to the iterative search consistency ratio while
method on that the weight ratio of a and the need of producing the weights.
criterion to another is assistant tools to solve
bounded by the lower and the model.
upper limits of the TFN
representing their pairwise
comparison.
Geometric Calculate the consistency Simple (simple It is hard to apply the
consistency ratio based on the distance equations), involving equation to fuzzy set
index between pairwise because little research has

43
 comparison and the weight arithmetic and been done for logarithm
ratio which are taken the logarithm operations. calculation on fuzzy sets.
logarithm first. It checks the consistency
after the weights are
obtained.

8. Conclusion and future research

How the expert’s judgements are represented by fuzzy sets is fundamental to the development
of fuzzy AHP. The choice of the fuzzy sets determines the overall calculation complexity of
the model. Among the three types of fuzzy sets, type-1 fuzzy set requires the least effort,
followed by intuitionistic fuzzy set and interval type-2 fuzzy set. This is because the operations
on fuzzy sets are defined via the elements and their memberships, as compared in Table 7.

Table 7. Operation comparisons between fuzzy sets

Fuzzy set Operation on Membership value
Type-1 fuzzy set Element, membership Crisp values
Intuitionistic fuzzy Element, membership,
Crisp values
set non-membership
Type-2 fuzzy set Element, membership Type-1 fuzzy sets

Aggregation is the key operation to produce the weights/priorities. Different techniques may
produce different results and have distinct performance. According to the experimental analysis
of Ahmed and Kilic (2018), the logarithmic least-squares method outperforms the fuzzy
geometric mean and the fuzzy geometric mean outperforms the fuzzy arithmetic mean. To the
best of our knowledge, no comparison has been done between these mean methods and other
methods such as lambda-max, which could be a future research topic.

Defuzzification assists the comparison of the results because crisp values are more intuitive
than fuzzy values. It also simplifies the calculation if the matrix is defuzzified before
computing the weights, which translates a fuzzy matrix into a crisp matrix. The consistency
check ensures that the results are produced based on effective judgments since inconsistency
may indicate a lack of understanding of the problem.

As indicated in Figure 1, there is no fixed execution sequence of synthesising multiple

judgments, checking consistency, calculating weights/priorities and defuzzifying the fuzzy

44
values. However, the sequence along with the chosen techniques influences the effect of the
fuzzy AHP model.

8.1 Suggestion on the choice of sequence and technique

This review concludes the techniques used to develop a fuzzy AHP model in the literature.
Except the problematic ones (i.e. EAM and CFCS), it is hard to identify which one is the best
because each has its advantages and varies in their underlying principles as discussed in the
previous sections. Experts could determine according to their practical context. As discussed
in section 4.5, if they are relatively confident in their judgement, then type-1 fuzzy set can be
chosen. If preferring a simple but practical tool, they can use geometric mean for aggregation,
centroid method for defuzzification and Saaty’s method for consistency measurement. If the
experts have good mathematical background and look for more optimal solutions, fuzzy
programming method is a nice option. But the following should be avoided when building the
fuzzy AHP model.

8.1.1 Using fuzzy arithmetic mean for aggregation and centroid method for defuzzifying when
symmetrical TFNs are used for judgement representation.

For a symmetrical TFN Ci = (li , mi , hi ) , there is mi − li = hi − mi =  i . Symmetrical TFNs are

commonly used to define the fuzzy scales as seen in section 4.4. Applying fuzzy arithmetic
mean as equation 10 to such TFNs for aggregation also produces a symmetrical TFN C :
1 n 1 n 1 n
C = (l , m, h) = (  i i n
n i =1
( m −  ),
i =1
mi ,  (mi + 1 )
n i =1

1 n
where m − l = h − m =  i , n is the number of the TFNs.
n i =1

Defuzzifying a symmetrical TFN C = (l , m, h) by the centroid method as equations 39, 40 or 41,

a crisp value equal to m is obtained.

In this case, if the model is built in the sequence where the TFNs of the pairwise judgements
is defuzzified before calculating the weights, the problem of solving a fuzzy AHP model
F = [Cij ]nn = [(lij , mij , hij )]nn reduces to solving an AHP model F = [mij ]nn . The use of a fuzzy

scale does not make any sense because it is equal to the use of crisp scale with the same level.

45
If the sequence of steps is used where the weights are calculated and then defuzzified, the
method will produce the same unnormalised weight vector W with AHP model that calculates
the weights by arithmetic mean.
n n n
W = { m1 j ,  m2 j ,... mnj }
j =1 j =1 j =1

8.1.2 Checking the consistency after multiple judgements synthesis.

The inconsistent judgement from an individual expert might be overlooked if checking the
consistency after synthesising the multiple judgements. Consider the following two fuzzy
comparison matrices F1 and F2 from two experts and their synthesised matrix Fagg .

 (1,1,1) (2,3, 4) (4,5,6)   (1,1,1) (7,8,9) (1, 2,3) 

 1 1 1   
F1 =  ( 4 , 3 , 2 ) (1,1,1) (1, 2,3)  F2 =  ( 19 , 18 , 17 ) (1,1,1) (1,1,1) 
 ( 1 , 1 , 1 ) ( 1 , 1 ,1) (1,1,1)   ( 1 , 1 ,1) (1,1,1) (1,1,1) 
 6 5 4 3 2   3 2 
 (1,1,1) (3.74, 4.90,6) (2,3.16, 4.24) 
 
Fagg =  (0.17,0.20,0.27) (1,1,1) (1,1.41,1.73) 
 (0.24,0.32,0.5) (0.58,0.71,1) 
 (1,1,1) 

After defuzzifying the matrices by the centroid method (equation 39), the consistency is
checked using Saaty’s method. The consistency ratios of the three matrices are 0.0036, 0.209
and 0.066 respectively. If the consistency is measured after synthesis, the judgements are
considered consistent ( CRFagg = 0.066 < 0.1) and the weights are calculated based on actually

inconsistent judgement from expert 2 ( CRF 2 = 0.209 > 0.1). The almost perfect consistency

from expert 1 ( CRF 1 = 0.0036) compensates the big inconsistency from expert 2 via aggregation.

8.2 Future work

This section presents some open questions that arise from the review and the discussion of the
techniques. We hope these questions could inspire researchers for future work.

8.2.1 Open questions on fuzzy scale

There are 5, 6, 7 and 9-level scales that have been applied to describe the relative importance
between every two criteria/alternatives. There seems no explanation on the choice of the scale
in the research that have applied the fuzzy scale.

46
Saaty (2008) discusses that psychologically people are able to distinguish between high,
medium and low at one level and for each in a second level below to also distinguish between
high, medium and low. This produces nine different categories, where the smallest is (low, low)
and the highest is (high, high). This is the principle that AHP has a 9-level scale for the top of
pairwise comparisons as compared with the lowest value on the scale. A scale provides a
reference for comparison. It is reasonable that other scales exist as long as they cover the
spectrum of possibilities and discriminate the alternatives in their application context. Small
changes in judgement lead to small changes in the derived weights/priorities (Wilkinson, 1965).
When two or more scales are applicable to one problem, for example, supplier selection where
the four types of fuzzy scales can be used. Several questions arise:

Q1: Do different scales have different impacts on the final result in terms of accuracy and
reliability?

To define a particular expression in the scale, various types of fuzzy sets are used such as type-
1 and type-2 fuzzy sets. If using the same type, the choices of the fuzzy numbers by the
researchers can also be different. For example, Zimmer et al. (2017) specify ‘moderately
important’ with 1.5 while most research adopts 2 in the 5 level scale. The same fuzzy number
may also be defined differently. As discussed in section 4.4, 9 is interpreted as (9, 9, 9) or (8,
9, 10). This leads to the concern:

Q2: What are the impacts on the results if using different fuzzy sets regarding the types, the
chosen fuzzy numbers and the definitions on the same scale?

8.2.2 Open questions on aggregation

Some aggregation methods accommodate the weights of the experts, which are assumed as
known. Experts may have different capabilities since they come from different functional
departments, such as purchasing, financing, engineering and quality assurance. People from
purchasing have better knowledge to compare the cost related criteria while those from quality
assurance are more reliable to analyse the quality related criteria. It is hard to judge which
expert overall is more important than another. Two questions arise.

Q3: When experts judge the relative importance between criteria, who judges their importance?

Q4: When people have distinctive expertise, how is their importance judged?

47
One possible solution is that the experts evaluate the criteria within their capabilities, and those
of the same capability are weighted by their experience such as the working years, reputation
and position in the department. This brings a new research topic in decision-making.

8.2.3 Open questions on consistency

When research focuses on the consistency measurement problem, it seems little attention has
been paid to dealing with inconsistency. If the matrix is consistent, then the process continues.
Otherwise, the experts need re-compare the criteria/alternatives until the consistency ratio is
within the acceptable range. This is the usual solution to adjust the matrix. However, this is
still insufficient because it is not clear that:

Q5: Which part of matrix needs adjustment?

Q6: How can the inconsistent part be adjusted to meet the condition?

To re-compare the whole matrix consumes effort, especially when the number of
criteria/alternatives is large. In addition, re-comparison cannot guarantee the consistency of the
judgements if the experts have no idea about the adjustment. The answers to the above two
questions might help make decision making more efficient.

8.3 Concluding remarks

Fuzzy set theory has been proposed as a valid means of dealing with imprecision and vagueness.
However, as discussed in Kubler et al. (2016), the extent of benefits brought by introducing
this fuzzy paradigm to AHP is not clear, especially given that Saaty (2006) argued that the
pairwise judgements are fuzzy enough. Using fuzzy numbers is not only for fuzziness (certain
inconsistency among the judgements) but also for ‘uncertainty’ or ‘hesitation’ of the experts
towards their judgements. Different types of fuzzy numbers provide choices to express ‘not
sure’ to different extents. Although the extent to which fuzzy AHP solves the problem of
uncertainty is disputed, it is a simple and useful decision-making method that has been widely
applied. It retains the advantages of AHP, i.e. structuring the problems, calculating both
weights and priorities and well-proved mathematical properties. This paper provided guidance
on how to choose appropriate techniques for building fuzzy AHP models in term of
representation, aggregation, defuzzification and consistency. In offering the guidance, this
research traced the origin of the methods and matched the context to the techniques. The
methods are also analysed regarding their characteristics, complexity and extension.
48
TFN stands out from other types of fuzzy set, because of its simplicity in representing
the judgements. It seems able to deal with uncertainty in most cases (applied by 91% of
reviewed articles in various fields), but is limited because the degree of membership is
expressed as real numbers. In the cases where the decision makers find it difficult to
determine the memberships, trapezoidal interval type-2 or intuitionistic fuzzy sets can help.
Mean methods are mostly used in aggregating group decisions and deriving weights, for the
three reviewed types of fuzzy sets. In particular geometric mean has proved a valid approach
of approximating the eigenvalues of a matrix. The fuzzy programming methods are also
efficient ways of computing the weights because they also generate a consistency index.
But they require more computational effort. Centroid methods are valid means of
defuzzifying fuzzy sets, which come in several forms. The one of equation 40 is a nice
choice, because it considers both the worst and best results arising from a fuzzy number.
This equation can also be inferred from Yager’s approach and has been proved by
Facchinetti et al. (1998). It is worth mentioning that the EAM is problematic as
shown in the discussion but still widely applied because of its ease of use in obtaining the
weights and crisp values. This indicates that ‘a simple but practical’ method is what the
decision makers need.

Therefore, the reviewed techniques are summarised according to their complexity as listed in
Table 8. More properties can be found in Tables 2-3 and Tables 5-6. It is also noticed that
more than half of articles (61 out of 109 articles) do not check the consistency of the
pairwise comparison matrix. Consistency measurement is necessary to reduce the
contradictions among different decision makers.

Table 8. Summary of the techniques

Simple Complicated Very complicated

Representation for TFN, TraFN Intuitionistic Trapezoidal

pairwise comparison fuzzy set interval type-2
fuzzy set
Aggregation group Arithmetic mean, Method based on
decision Geometric mean, Max- Consensus degree
for
min method with
arithmetic mean, Max-min
method with geometric
mean

49
 weights/ Arithmetic Logarithmic Fuzzy
priorities mean, Geometric least-squares, programming
mean, Lambda-max method
method,
Eigenvector
method
Defuzzification Centroid method, EAM,
Mean of limits, Index of CFCS
optimism, Fuzzy entropy

Consistency Saaty’s method, Fuzzy

Geometric consistency programming
index method

Figure 19 presents the paths with simple and commonly used techniques in the four important

aspects of a fuzzy AHP model, starting with the types of fuzzy sets. Figures 11, 13 and 14

explains which fuzzy set and aggregation methods should be chosen. The appropriate

techniques(s) emerge(s) by answering the subsequent questions.

Figure 19. Paths of building fuzzy AHP models

This research has adopted a two-stage approach to examine the fuzzy AHP models used
in different decision-making topics in industry. Although many techniques have been
50
reviewed,
there may still be ones that have been overlooked. The guidance of this paper could help to
categorise and analyse the techniques by reflecting what they describe, when they are
applicable, how they are defined and the complexity of the computation.

Funding: This research was supported by the Natural Science Foundation of Jilin Province of
China (Grant No. 20180101035JC) and the Education Department of Jilin Province of China
(Grant No. JJKH20200796KJ).

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Appendix

It is noted that the number after the types of fuzzy sets in the column ‘Pairwise’ indicates the levels of the fuzzy scales. For example, ‘TFN 9’

means this paper takes a 9-level scale based on TFNs.

Table A.9 Supplier selection articles with the techniques in their fuzzy AHP models
With Representation Aggregation Defuzzifi Consis
Authors Industry
method(s) Pairwise Performance Weight/Priority Multi-experts cation tency
Manufactur TFN 9
1 Chan et al. (2008) - - EAM - EAM -
ing
Büyüközkan et al. TFN 5 TFN
2 e-logistics TOPSIS EAM - EAM -
(2008)
Non-
additive
3 Yang et al. (2008) - TFN 9 TFN Geometric mean Geometric mean COA -
fuzzy
measure
4 Celik et al. (2009) Maritime - TFN 5 - EAM - EAM -
Manufactur
5 Lee (2009) - TFN 9 - EAM Geometric mean EAM -
ing
Wang et al.
6 - TOPSIS TFN 5 TFN Lambda-max Geometric mean - Saaty
(2009)
Aydin and Manufactur Arithmetic mean Weighted
7 - TraFN - COA -
Kahraman (2010) ing (defuzzify first) arithmetic mean
Max-min for TFN
Manufactur
8 Chen et al. (2010) - TFN 7 - Arithmetic mean construction COA -
ing
& Arithmetic mean
Chen and Hung Pharmaceut Arithmetic
9 TOPSIS TFN 6 TFN Geometric mean - Saaty
(2010) ical (alternative)&

59
 With Representation Aggregation Defuzzifi Consis
Authors Industry
method(s) Pairwise Performance Weight/Priority Multi-experts cation tency
Geometric mean
(criteria)
Manufactur Average but not
10 Kuo et al. (2010) DEA TFN 5 Lambda-max - Saaty
ing specified
Crisp (criteria
11 Şen et al. (2010) Electronic Max-min TFN 9 EAM - EAM -
weights)
COA (but
fuzzy
12 Sun (2010) - TOPSIS TFN 9 TFN Geometric mean - -
values are
used)
Chen and Yang
13 - TOPSIS TFN 6 TFN Modified EAM Geometric mean EAM FP
(2011)
Chiouy et al. -(not
14 Electronic - TFN 9 - Lambda-max Geometric mean Saaty
(2011) specified)
Pharmaceut ELECTRE Weighted
15 Ertay et al. (2011) TFN 9 Crisp EAM EAM -
ical III Geometric mean
Manufactur GP for Index of
16 Jung (2011) TFN 5 - Geometric mean - Saaty
ing allocation optimism
Kilincci and Onal Manufactur
17 - TFN 5 - EAM - EAM Saaty
(2011) ing
Arithmetic mean Y no
Zeydan et al.
18 Automobile TOPSIS TFN 9 TFN 7 EAM (for performance, - metho
(2011)
no for criteria) d
Yücenur et al. TFN –(not
19 Logistics - - EAM - EAM -
(2011) mention)
Büyüközkan Weighted
20 Automotive TOPSIS TFN 11 TFN Geometric mean COA Saaty
(2012) arithmetic mean

60
 With Representation Aggregation Defuzzifi Consis
Authors Industry
method(s) Pairwise Performance Weight/Priority Multi-experts cation tency
Kubat and Yuce
21 - GA TFN 9 - EAM - EAM -
(2012)
Manufactur LP for
22 Shaw et al. (2012) TFN 9 - EAM Geometric mean EAM -
ing allocation
Eigenvector based
Soroor et al. Index of
23 - - TFN 9 - on index of Saaty
(2012) optimism
optimism
Manufactur
24 Yu et al. (2012) MP TFN - - Geometric mean - COA -
ing
Zouggari and
25 - TOPSIS TFN 5 TFN EAM Max-min EAM Saaty
Benyoucef (2012)
Alinezad et al. Pharmaceut
26 - TFN 4 - EAM - EAM -
(2013) ical
Ghorbani et al. agricultural TOPSIS
27 TFN 5 TFN EAM - EAM -
(2013) machinery
TOPSIS
Kannan et al.
28 Automobile MP for TFN 9 TFN 9 EAM Geometric mean EAM Saaty
(2013)
allocation
Pitchipoo et al. electroplati Crisp weights by
29 GRA TFN 9 - - COA Saaty
(2013) ng defuzzifying first
(Rezaei & Ortt,
30 food - TFN 7 TFN 7 Arithmetic mean - COA -
2013)
Roshandel et al.
31 material TOPSIS TFN 5 TFN Arithmetic mean Arithmetic mean - -
(2013)
Viswanadham
Arithmetic mean
32 and Samvedi - TOPSIS TFN 5 TFN EAM EAM -
(in performance)
(2013)

61
 With Representation Aggregation Defuzzifi Consis
Authors Industry
method(s) Pairwise Performance Weight/Priority Multi-experts cation tency
Hashemian et al. PROMETHE
33 Diary TFN 5 TFN EAM Geometric mean EAM -
(2014) E
Manufactur Weighted
34 Kar (2014) MP TFN 5 - Geometric mean COA GCI
ing geometric mean
Rezaei et al. Airline
35 - TFN 9 - FP (non-linear) - FP FP
(2014) retail
36 Shad et al. (2014) LP TFN 5 TFN Geometric mean - - -
Ayhan and Kilic MILP for Arithmetic
37 Manuf TFN 9 Crisp values Geometric mean COA -
(2015) allocation mean
Eigenvector based
Beikkhakhian et Index of
38 - TOPSIS TFN 9 TFN 5 on index of Geometric mean Saaty
al. (2015) optimism
optimism
NN for
Manufactur Weighted
39 Kar (2015) classificatio TFN 5 crisp Geometric mean COA GCI
ing geometric mean
n
Sultana et al. Manufactur Delphi,
40 TFN 5 TFN EAM Geometric mean COA Saaty
(2015) ing TOPSIS
Uyguna et al. Communic ANP,
41 TFN 5 TFN EAM Arithmetic mean EAM -
(2015) ation DEMATEL
Yayla et al. COA for
42 Logistics TOPSIS TFN 5 TFN Geometric mean - -
(2015) BNP
Weight of a
criterion from an
Büyüközkan and Intuitionistic Intuitionistic
43 Automotive TOPSIS individual DM is IFWA - Saaty,
Güleryüz (2016) fuzzy sets fuzzy sets
supposed as being
given
Prakash and
44 Electronic VIKOR TFN 7 crisp EAM - EAM -
Barua (2016b)
62
 With Representation Aggregation Defuzzifi Consis
Authors Industry
method(s) Pairwise Performance Weight/Priority Multi-experts cation tency
Prakash and
45 Logistics TOPSIS TFN 7 TFN EAM Max-min EAM -
Barua (2016a)
PrasannaVenkates
PROMETH
46 an and Goh - TFN 5 TFN EAM - EAM Saaty
EE
(2016)
Shakourloo et al. Manufactur LP for
47 TFN 6 - Updated EAM - EAM -
(2016) ing allocation
Wang Chen et al. Manufactur
48 TOPSIS TFN 6 TFN EAM Arithmetic mean EAM -
(2016) ing
RFID Fuzzy AD Eigenvector based Aggregation based
Büyüközkan et al. Index of
49 service (Axiomatic TFN 11 TFN on index of on consensus Saaty
(2017) optimism
provider design) optimism degree
Kumar et al.
50 Automobile LP TFN 9 TFN EAM Geometric mean EAM -
(2017)
-Fuzzy
Görener et al. Interval type 2 Interval type 2
51 Airline TOPSIS Geometric mean Geometric mean weights Saaty
(2017) fuzzy set fuzzy set
are used
Zimmer et al.
52 Automobile IO TFN 5 Crsip EAM Geometric mean EAM Saaty
(2017)
Awasthi et al. Eigenvector by Max-min with
53 electronic VIKOR TFN 5 TFN COA Saaty
(2018) defuzzifying first arithmetic mean
Celik and Akyuz Maritime Interval type-2 Interval type-2
54 TOPSIS Geometric mean - COA -
(2018) trans fuzzy sets fuzzy sets
55 Khorasani (2018) Service Copras TFN 9 TFN Geometric mean Geometric mean - -
56 Liu et al. (2019) Agriculture TOPSIS TFN 9 TFN Geometric mean Geometric mean COA Saaty
Büyüközkana et Intuitionistic Intuitionistic Fuzzy
57 Chemistry VIKOR IFWA IFWA Saaty
al. (2019) fuzzy sets fuzzy sets entropy

63
Table A.10 Other selection articles with the techniques in their fuzzy AHP models
Representation Aggregation Defuzzifica Consis
Authors With method(s)
Pairwise Performance Weights/Priorities Multi-experts tion tency

Machine/tool selection
Index of
1 Taha and Rostam (2011) ANN TFN 9 - Eigenvector - Saaty
optimism
Yazdani-Chamzini and Arithmetic
2 TOPSIS TFN 9 TFN EAM EAM -
Yakhchali (2012) mean
3 Ic et al. (2013) - TraFN - Geometric mean - COA -
4 Nguyen et al. (2015) COPRAS TFN 7 TFN Arithmetic mean - COA -
Delphi and
5 Parameshwaran et al. (2015) TFN 9 TFN EAM - EAM -
TOPSIS/VIKOR

Location/site selection
EAM/COA
6 Vahidnia et al. (2009) - TFN 9 - EAM - / index of Saaty
optimism
Choudhary and Shankar
7 TOPSIS TFN 9 TFN EAM - EAM -
(2012)
TFN scale is
8 Mosadeghi et al. (2015) - - EAM - EAM -
not specified
Samanlioglu and Ayag Index of
9 PROMETHEE TFN 5 TFN Eigenvector - Saaty
(2017) optimism
Interval type 2 Geometric
10 Ayodele et al. (2018) - - Geometric mean COA Saaty
fuzzy set mean
11 Erbas et al. (2018) TOPSIS TFN 5 TFN Geometric mean - COA Saaty
Grey relational Picture fuzzy
12 Ju et al. (2018) TFN 6 EAM - EAM -
projection set
13 Singh et al. (2018) - TFN 6 - EAM - EAM -

64
 Representation Aggregation Defuzzifica Consis
Authors With method(s)
Pairwise Performance Weights/Priorities Multi-experts tion tency

ERP selection
14 Cebeci (2009) - TFN 5 - Geometric mean - COA -
TraFN (fuzzify Weighted
Crisp weights but
15 Kahraman et al. (2010) - the judgements - arithmetic COA -
defuzzify first
first) mean
16 Onut and Efendigil (2010) - TFN 9 - EAM - EAM -
Geometric
mean but
Crisp weights but
17 Sarfaraz et al. (2012) - TFN 9 - defuzzify the CFCS Saaty
defuzzify first
decision
matrix first
Arithmetic
18 Kilic et al. (2014) TOPSIS TFN 9 Crisp value Geometric mean COA -
mean
Fuzzy cognitive
19 Ahmadi et al. (2015) TFN 6 - EAM - EAM -
maps
20 Efe (2016) TOPSIS TFN 5 TFN EAM - EAM/COA Saaty

Project selection
-Mentioned
21 Taylan et al. (2014) TOPSIS TFN 5 TFN EAM averaging but EAM -
not specified
Index of
22 BAYSAL et al. (2015) TOPSIS TFN 5 - Arithmetic mean - -
optimism

Technology selection
Index of
23 Ayag (2010) - TFN 5 - Eigenvector - Saaty
optimism
24 Garcí
a-Cascales (2012) TOPSIS TFN 5 TFN Arithmetic mean - - -
65
 Representation Aggregation Defuzzifica Consis
Authors With method(s)
Pairwise Performance Weights/Priorities Multi-experts tion tency
25 Mirhedayatian et al. (2013) DEA TFN 5 - FP (based on DEA) - - FP
Index of
26 Avikal et al. (2014) PROMETHEE TFN 5 crisp Eigenvector - Saaty
optimism
27 Demirtas et al. (2014) TFN 9 - EAM - EAM -
28 Tan et al. (2014) - TFN 5 - FP - FP FP
29 Vinodh et al. (2014) TOPSIS TFN 9 TFN Geometric mean - COA -
30 Wang and Wang (2014) Kano TFN 5 - Eigenvector Max-min COA Saaty
Arithmetic
31 Budak and Ustundag (2015) - TFN 5 - Geometric mean COA -
mean
Arithmetic
32 Mahjouri et al. (2017) TOPSIS TFN 5 TFN Geometric mean - -
mean
33 Naderzadeh et al. (2017) - TFN 5 - EAM - EAM -
Alaqeel and Suryanarayanan Geometric
34 - TFN 9 - Eigenvector - Saaty
(2018) mean
Index of
35 Balusa and Gorai (2018) - TFN 9 - Geometric mean - Saaty
optimism
Geometric
36 Canan et al. (2018) - TraFN - Geometric mean COA Saaty
mean
TFN self-
37 Goyal et al. (2018) - - FP/EAM - FP/EAM FP
defined scale
TFN (not Mentioned but
38 Wang et al. (2019) VIKOR - EAM EAM -
specified) not specified
39 Bostancioglu (2020) - TFN 9 - EAM - EAM -
Evaluation of engineering sector, teaching performance and health service
40 Akkaya et al. (2015) MOORA TFN 5 TFN EAM - EAM -
41 Chen et al. (2015) - TFN 6 - EAM Max-min EAM Saaty
42 Singh and Prasher (2017) - TFN 5 - Geometric mean - COA -
Management of risk, sustainability, resource and process

66
 Representation Aggregation Defuzzifica Consis
Authors With method(s)
Pairwise Performance Weights/Priorities Multi-experts tion tency
43 Mangla et al. (2015) - TFN 9 - EAM - EAM -
Row sum (similar to
44 Calabrese et al. (2016) - TFN 5 - - COA Saaty
arithmetic mean)
Row sum (similar to
45 Calabrese et al. (2019) - TFN 5 - - COA Saaty
arithmetic mean)
Max-min
Arithmetic and
46 Zyoud et al. (2016) TOPSIS TFN 5 TFN EAM EAM -
geometric
mean
Sirisawat and Kiatcharoenpol
47 TOPSIS TFN 9 TFN EAM EAM -
(2018)
Interval type
48 Celik and Akyuz (2018) TOPSIS - Geometric mean - COA Saaty
2 fuzzy set
49 Khan et al. (2019) - TFN 6 - EAM - EAM Saaty
TFN self-
50 Singh and Sarkar (2019) TOPSIS TFN EAM - EAM -
defined scale
Geometric
51 Tavana et al. (2020) MOORA TFN 5 TFN EAM EAM Saaty
mean
Diagnosis of diseases
Geometric
52 Nazari et al. (2018) FIS TFN 5 TFN EAM EAM -
mean

67
E3 Journal of Business Management and Economics Vol. 3(3). pp. 106-117, March, 2012
Available online http://www.e3journals.org
ISSN 2141-7482 © E3 Journals 2012

Full length research paper

ERP consultant selection problem using AHP, fuzzy

AHP and ANP: A case study in Turkey
Ozalp Vayvay1, Yigit Ozcan1 and Maria Manuela Cruz-Cunha2*
1
Marmara University, Turkey
2
Polytechnic Institute of Cávado and Ave; CITEPE–Research Center in Production Technologies and Energy, Portugal

Accepted 11 February, 2012

In the information technology industry, projects are often carried out simultaneously and with limited human
resources, being of major relevance to adequately allocate consultants (using either the company's own
consultants or outsourcing) to each project. At the company analyzed, consultants’ allocation to concurrent
projects, especially when outsourcing is done, is complex. To solve the decision problem, the Project Resource
Planning method (PRP), Analytic Hierarchy Process (AHP), fuzzy AHP and Analytic Network Process (ANP)-
based methodologies were used. The experiments suggested that both AHP and fuzzy AHP led to the same
results, but neither of these considered the interactions within decision elements during the selection process,
while ANP, which takes into account these interactions, most correctly weighs the sub-criteria and gives the
best composite weights.

Keywords: Analytic Hierarchy Process (AHP); Analytic Network Process (ANP); Consultant selection; fuzzy AHP; Multi-
criteria decision making; Project management

INTRODUCTION

This paper discusses the application of Project Resource projects simultaneously, and each project is undertaken
Planning (PRP) in Anadolu Bilişim Hizmetleri A.Ş. (ABH), by a project team consisting of a number of resources. In
one of the most prominent companies in the information brief, a consultant deals with more than one project with
technologies (IT) industry in Turkey, and one of the 50 different team-mates in each, and hence the adequate
fastest growing technology companies, according to the assignment of resources to projects is critical and
results of Deloitte Fast50 Turkey 2009 (Deloitte, 2009). determinant to the success or failure of the project. It is,
ABH offers project management, consultancy and however, a complex problem, because of all the
application development (both structural and parameters involved, as this paper highlights. This study
nonstructural) in different platforms. The company also aims at supporting the selection and flow of consultants
provides support and training services in various fields within various projects efficiently, via PRP applications,
from organizational IT planning, infrastructure design and contributing to ABH’s success with its projects in terms of
operation, and optional custom application development the parameters time, cost and quality, suggested by
to improving and optimization of business processes via Zarnekow et al., (2006).
Enterprise Resources Planning (ERP) solutions. Its The word “project” with its broad meaning can be
activity is mostly based on consultants, here referred to defined as a set of activities which occur only once, in a
as its resources. Each resource deals with several specified time frame, with specific goals and conditions;
in other words, two projects cannot be completely equal
(Project Management Institute, 2004). Different
intervenients may be needed in different phases of the
project, and are assigned according to the tasks
*Corresponding Author email: mcunha@ipca.pt;
Phone: +351 - 253 802 500; Mobile: +351 – 96 56 56 566;
requirements and consultants’ skills (Madic et al., 2011;
Fax: +351 - 253 812 281 Sridhar et al., 2009). Besides the assignment issue, it is
 Ozalp et al. 107

necessary to coordinate the participants’ tasks in projects of different techniques to the ERP consultants selection,
(Madic et al., 2011). Due to the characteristics of this paper contributes to a better understanding of the
humans, they probably will not accomplish all their tasks methodologies to be used by organizations face with this
with the same harmony (psychological effects on human complex problem.
beings, which do not affect machines, cultural The second section of the paper presents a literature
differences, etc., should be considered). As a result, survey on project scheduling and MCDM methods.
human resources management is a major factor Section three introduces the problem and section four is
influencing a project success (Belout and Gauvreau, dedicated to the application of the methods. Section five
2004; Karen and Vasudevan, 1985; Zmud, 1980). presents and discusses some results and section six
In companies, the size and duration of the projects and concludes the paper with some discussion about the
the number of people involved can be very high and face outcomes.
such complexities, that efficient and effective project
management becomes vitally important. Consultants
should be assigned or allocated in such a way that the LITERATURE REVIEW
efficiency of the projects in terms of time, cost and quality
should be accomplished. To achieve this, a technique The concept of PRP is newly established, so there are
called PRP (Project Resource Planning) is used (Al- not many research studies directly related to it. Instead,
jibouri, 2002; Deckro and Hebert, 2003; Gollenbeck- various research articles are found about project
Sunke and Schultmann, 2010; Hiermann and Höfferer, scheduling and MCDM methods, which are important
2003). parts of PRP.
Studies made in ABH using PRP were divided into two PRP for modeling project scheduling in situations
main parts. In the first part, the Critical Path Method involving diminishing returns was studied by several
(CPM) and Project Evaluation and Review Technique authors, e.g. (Deckro, 2003; Al-jibouri, 2002; Hebert,
(PERT) were used, which enabled the company to 2011). In project scheduling issues, PERT (Project
manage the activities of projects effectively; to determine Evaluation and Review Technique) is applied in multi-
the critical activities required to finish the projects without objective resource allocation problems (Azaron et al.,
any delay; at the same time, it was defined the 2006). After understanding the activities of the projects,
possibilities to finish the projects within given time limits efficient schedules are necessary to accomplish these
(Hebert and Deckro, 2011; Laslo, 2010). Supported by activities within time limits. For this purpose, two
the studies of the first part, some criteria were determined commonly used project scheduling techniques, CPM and
in order to enable the project leader to assign consultants PERT, are used.
to the projects. By means of these and other criteria, The AHP process, introduced by Saaty in the
Multi Criteria Decision Making (MCDM) techniques seventies, (Saaty, 1980) has been one of the most
(Massam, 2002; Xu et al., 2007) were used in the second extensively used methods for MCDM and has been
part to select the best consultant, where more than one extensively studied and refined since then. It provides a
alternative exists. comprehensive and rational framework for structuring a
Decision making involves many criteria and sub-criteria decision problem, for representing and quantifying its
used to rank the alternatives of a decision, analyzing elements, relating these elements to overall goals, and
dependencies between alternatives and implications of for evaluating alternative solutions. AHP has been used
these in terms of higher goals (Power and Sharda, 2007; to solve MCDM problems in several different areas such
Saaty, 2008; Xu et al., 2007). Within the MCDM, the as economic planning, energy policy, project selection,
authors have defined a model to support the selection of budget allocation (Soh, 2010), software selection
the most suitable consultant using the Analytic Hierarchy (Štemberger et al., 2009) among other.
Process (AHP) (Saaty, 1980, 2008), Fuzzy Analytic ANP is a more general form of the AHP, used in
Hierarchy Process (Fuzzy AHP) (Chang, 1996) and MCDM. While AHP structures a decision problem into a
Analytic Network Process (ANP) (Saaty, 1996, 2005) hierarchy with a goal, decision criteria and alternatives,
techniques. A method from the literature, called Fuzzy the ANP structures the problem as a network. Both then
Analytic Network Process (Fuzzy ANP) (Kahraman et al., use a system of pair-wise comparisons to measure the
2006), was not handled in detail due to its computational weights of the components of the structure, and finally to
complexity. rank the alternatives in the decision (Saaty, 2005).
Organizations need to have a tool to support decision- Many valuable contributions in the MCDM field are
making concerning the “optimal” or the best possible mentioned in different literature (Daşdemir and Güngör,
allocation of resources to projects (Carazo et al., 2010; 2002; Ho et al., 2010), and the most relevant
Gutjahr et al., 2010; Saremi et al., 2009; Yang and Chou, contributions are synthesized in Table 1.
2011), and literature offer many examples and case Given that the main PRP solution approach is a broad
studies. By presenting this case study with the application concept, it is needed to focus on some closer approaches
108 E3. J. Bus. Manage. Econ.

Table 1: Relevant contributions to the MCDM from the literature

Authors Contribution
Zadeh (1965) Introduced the fuzzy set theory in situations with incomplete and uncertain information,
in order to model the imprecision of human decision-making.
Saaty (1980) First application and implementation of AHP.
Al-Harbi (2001) Application and implementation of AHP in project management.
Felek et al. (2002) Application of AHP and ANP in the determination of market share in mobile
communication industry and comparison of results.
Başlıgil (2005) Application of fuzzy AHP in the software selection.
Akman and Alkan (2006) Application of fuzzy AHP to the evaluation of performance measurement of suppliers in
the automotive industry.
Chang et al. (2007) Utilization of AHP and ANP decision models in Evaluating digital video recorder systems
Liang et al. (2008) Utilization of ANP in Enterprise information system project selection
Gümüş (2000) Utilization of fuzzy AHP in the evaluation of hazardous waste transportation firms.
Wang et al. (2008) Discussed the shortcomings of fuzzy AHP extent analysis method.
Gencer and Gürpınar Discussed ANP application in a supplier selection problem.
(2007)
Sevkli et al. (2008) Proposed the analytical hierarchy process weighted fuzzy linear programming model
(AHP-FLP)” for supplier selection problems.
Demirtas et al. (2008) Utilization of ANP in supplier selection and definition of optimum quantities among
selected suppliers to maximize the total value of purchasing and minimize the budget
and defect rate.
Dağdeviren et al. (2008) Implementation of fuzzy ANP to identify faulty behavior risk in work systems.
Saaty (2005) Decision making with the ANP
Liu and Wang (2009) An integrated fuzzy approach (fuzzy delphi, fuzzy inference, and fuzzy linear
assignment) for providers evaluation and selection.

under the PRP concept and to examine these important to assign the most suitable resources to each
approaches in detail. For this purpose, the study includes project, considering simultaneously various constraints.
two phases: (1) project scheduling issues and (2) MCDM These assignments can be performed in three ways: (1)
methods. For the first phase - project scheduling issues -, Completely from inside the company, (2) Partially
CPM and PERT enables the company to manage the outsourcing, and (3) Totally outsourcing.
activities of projects effectively. Here the word “outsourcing” means that the
With the help of the analysis undertaken in the first assignment of the consultants to the projects is
phase, the project leader needs to know the details of the performed by means of other IT companies, i.e., it
projects that she/he handles and in this way she/he may consists of hiring consultants of other IT companies to
define the selection criteria for consultants for specific take part in the projects of ABH Company. The business
activities of the projects. After the definition of all the processes department of ABH Company has some
selection criteria, MCDM methods are used in a second problems with the identification of the adequate
phase to conduct to the optimal consultant selection. assignments and this fact becomes a relevant problem
Within the MCDM methods, the authors established a especially when outsourcing is performed.
model to select the best consultant using AHP, fuzzy
AHP and ANP. Fuzzy ANP was not handled in detail due
to its computational complexity. ANP was selected due to The Problem Model
its compatible structure with the structure of the selection
problem and the existence of a useful software program The problem has a hierarchy with four levels which are
to perform its mathematical calculations. Furthermore, discussed in this section. The overall objective is placed at
the shortcomings of the other methods are explained in level 1, criteria at level 2, attributes at level 3, and the
detail with examples. decision alternatives at level 4. The main objective here is
the selection of the most suitable consultant for the sample
company. The criteria to be considered in the selection are
PROBLEM Definition cost, work experience, education level, and communication
ability. According to these decision elements, the hierarchy
As many projects are concurrent in time, it is very for the problem is presented in Figure 1.
 Ozalp et al. 109

Selection of the most suitable consultant

Cost Work experience Education level Communication ability

Transportation Consultancy Companies Projects References Department Occupational Awareness of Ability to

cost cost employed completed graduated seminars responsibility persuade

Consultant Consultant Consultant

A B C

Figure 1. The hierarchy for the consultant selection problem

The Definition of Criteria -Occupational Seminars (OS): Points out the

occupational seminars in which the consultants
The most suitable consultant selection problem is participated so far.
modeled with decision making criteria, sub-criteria and
alternatives. Alternatives are at the end of the hierarchy. • Communication ability (CA)

• Cost (CO) -Awareness of Responsibility (AR): Refers to the

responsibility of the consultants in terms of their
-Transportation Cost (TC): The cost that arises job.
from the consultants transportation travel to the -Ability to Persuade (AP): Refers to the
working place. consultants´ ability to persuade customers in
-Consultancy Cost (CC): The payment made to order to purchase IT products and implement IT
the consultants due to their consultancy. projects.

• Work experience (WE)

Decision alternatives
-Companies Employed (CE): Defines in which
companies consultants are employed. The decision alternatives correspond to the set of
-Projects Completed (PC): Defines in which consultants where the selection for a given project is to
projects consultants have taken part. take place: Consultant A, Consultant B and Consultant C.
-References (R): Defines the references of the
consultants.
APPLICATION
• Education level (EL)
The problem of selecting the most adequate consultant is
-Department Graduated (DG): Points out the systematically considered by the decision makers of the
department from which the consultants company under analysis. In this paper AHP, fuzzy AHP
graduated. and ANP approaches were used to help in solving this
problem. This section introduces the application of AHP,
110 E3. J. Bus. Manage. Econ.

Table 2. Comparison matrix for criteria using AHP

Cost Work experience Education level Communication ability

Cost 1 1/3 3 1/5
Work experience 3 1 5 1/3
Education level 1/3 1/5 1 1/3
Communication ability 5 3 3 1

Table 3. Fuzzy comparison matrix for criteria

Cost Work experience Education level Communication Ability

Cost (1, 1, 1) (2/3, 1, 3/2) (2/3, 1, 3/2) (2/5, 1/2, 2/3)
Work experience (2/3, 1, 3/2) (1, 1, 1) (3/2, 2, 5/2) (2/3, 1, 3/2)
Education level (2/3, 1, 3/2) (2/5, 1/2, 2/3) (1, 1, 1) (2/3, 1, 3/2)
Communication ability (3/2, 2, 5/2) (2/3, 1, 3/2) (2/3, 1, 3/2) (1, 1, 1)

fuzzy AHP and ANP and compares the results obtained. sub-criteria. After evaluating all the decision alternatives
with respect to the decision sub-criteria the calculation of
weights for each decision element in AHP is complete. All
Application of AHP the weights are given in Figure 2. According to these
weights, the composite weight for each consultant is
As its name implies Analytic Hierarchy Process, calculated and consultants are ranked based on their
considers the problem in a hierarchical way. At the top of composite weights.
the hierarchy there is a goal that is affected only by Composite weight for Consultant A equals: 0.135 *
decision criteria, which are on the second level in (0.125*0.430 + 0.875*0.133) + 0.284 * (0.260*0.284 +
hierarchy. If there exist sub-criteria (the third level in 0.633*0.474+ 0.107*0.648) + 0.085 * (0.250*0.600 +
hierarchy), these are only affected by criteria, and finally, 0.750*0.643) +0.496 * (0.500*0.230 + 0.500*0.455) =
at the bottom of the hierarchy there will be alternatives, 0.372
which are only affected by sub-criteria (if there are no In the same way, the composite weights for consultants
sub-criteria, alternatives are affected by main-criteria). B and C are 0.299 and 0.329 respectively. According to
After defining the relative importance of all the decision AHP, the best alternative is Consultant A.
criteria via pair-wise comparisons, the results of the pair-
wise comparisons are represented in a comparison
matrix. Table 2 shows the comparison matrix for the Application of Fuzzy AHP
criterion defined as the goal. It results from the analysis
of the relative weight among all the possible Fuzzy means imprecise or not being exact and fuzzy
combinations of decision criteria. AHP is the fuzzy version of AHP. To understand fuzzy
Then the normalization of this matrix is necessary in AHP better, it is needed to talk about fuzzy set theories.
order to find the relative weights of all the decision An everyday conversation contains many vague
criteria. The normalization process requires dividing the expressions such as “the girl next door is pretty” or “the
elements of each column by the sum of the elements of man I saw in the street is fat” (Tanaka, 1996). As seen,
the same column. Up to this point, decision criteria were these expressions are completely subjective and not true
compared and their relative weights calculated. The for everyone. The man on the street may not be fat or the
normalization leads to the following weights: Cost 0.135; girl next door may not be pretty depending on the
Work experience 0.284; Education level 0,085 and perceptions of different people. Fuzzy sets were
communication ability 0.496. Now, comparison and proposed to deal with such vague expressions. On the
weighting of the sub-criteria in terms their main-criteria other hand, when exactly defined expressions are point
will be handled in the same way. of issue, it is used the conventional set theory called crisp
So far, comparison and weighting of decision criteria sets. Table 3 shows comparison matrix for criteria with
and sub-criteria were handled. Now it is time to compare respect to the goal with fuzzy numbers. Using Table 3,
all the decision alternatives with respect to each decision fuzzy synthetic extent values are found as:
 Ozalp et al. 111

Selection of the most suitable consultant

Cost Work experience Education level Communication ability

(0.135) (0.284) (0.085) (0.496)

Transportation Consultancy Companies Projects Department Occupational Awareness of Ability to

Cost Cost Employed Completed References Graduated Seminars responsibility Persuade
(0.125) (0.875) (0.260) (0.663) (0.107) (0.250) (0.750) (0.500) (0.500)

Cons. A Cons. A Cons. A Cons. A Cons. A Cons. A Cons. A Cons. A Cons. A

(0.430) (0.133) (0.284) (0.474) (0.648) (0.600) (0.643) (0.230) (0.455)
Cons. B Cons. B Cons. B Cons. B Cons. B Cons. B Cons. B Cons. B Cons. B
(0.430) (0.212) (0.097) (0.474) (0.295) (0.200) (0.283) (0.122) (0.455)
Cons. C Cons. C Cons. C Cons. C Cons. C Cons. C Cons. C Cons. C Cons. C
(0.140) (0.655) (0.619) (0.052) (0.057) (0.200) (0.074) (0.648) (0.090)

Figure 2. Relative weights of all decision elements in AHP

SCO = (2.74, 3.50, 4.67)*(1/22.34, 1/17.00, 1/13.16) = According to these weights, is calculated the composite
(0.12, 0.21, 0.35); weight for each consultant and consultants are ranked
SWE = (3.84, 5.00, 6.50)*(1/22.34, 1/17.00, 1/13.16) = based on their composite weights.
(0.17, 0.29, 0.49); The composite weight for Consultant A equals:
SEL = (2.74, 3.50, 4.67)*(1/22.34, 1/17.00, 1/13.16) = 0.204* (0*0.33 + 1*0.15) + 0.296* (0.33*0.47 + 0.45*0.50
(0.12, 0.21, 0.35); + 0.22*0.58) + 0.204*(0.50*0.33 +
SCA = (3.84, 5.00, 6.50)*(1/22.34, 1/17.00, 1/13.16) = + 0.50*0.58) + 0.296* (0.50*0.33 + 0.50*0.50) = 0.396
(0.17, 0.29, 0.49). In the same way, the composite weights for consultants B
Then the possibility of one criterion being greater than or and C are 0.314 and 0.290 respectively. According to
equal to another criterion is found as: fuzzy AHP the best alternative is Consultant A. The result
V (Sco ≥ SWE) = 0.69, V (Sco ≥ SEL) = 1.00, V (Sco ≥ SCA) = is the same as in AHP. In both cases, Consultant A is the
0.69; best alternative, but the second best alternative is not the
V (SEL ≥ SCo) = 1.00, V (SEL ≥ SWE) = 0.69, V (SEL ≥ SCA) = same using the two methods. There is some conflict
0.69; within two methods when the second best alternative is
V (SWE ≥ SCo) = 1.00, V (SWE ≥ SEL) = 1.00, V (SWE ≥ SCA) considered.
= 1.00;
V (ScA ≥ SCO) = 1.00, V (ScA ≥ SWE) = 1.00, V (ScA ≥ SEL) =
1.00. Application of ANP
According to the above possibilities (these are not
probabilities, in fuzzy logic), non-normalized weighted Many decision problems cannot be built as in a
matrix is found as W* = (0.69, 1, 0.69, 1), and after hierarchical structure as modeled in both AHP and fuzzy
normalization, is obtained the normalized final matrix W AHP. Interactions and/or dependencies within the
= (0.204, 0.296, 0.204, 0.296). elements of the same hierarchy usually happen. Also the
According to extent analysis method, weights of Cost, interactions may be in various levels of hierarchy, for
Work Experience, Education Level and Communication instance the top level may affect the bottom level due to
Ability are 0.204, 0.296, 0.204 and 0.296 respectively. the structure of the model. In such situations, the ANP
In the same way, comparison of sub-criteria with respect (Analytic Network Process) should be used, instead of
to criteria and comparison of alternatives with respect to AHP and fuzzy AHP. ANP is a quantitative judgment
sub-criteria are performed in a hierarchical way and all process like AHP, but it is based on the interactions
the weights assigned to all decision elements are found among various levels in decision hierarchy (Wu and Lee,
out. The weight of sub-criteria Transportation Cost is zero 2007).
because the three consultants present the same In the modeling of this problem, interactions within sub-
Transportation Cost (0.333). All the weights in fuzzy AHP criteria are not considered. For instance, due to the high
are given in Figure 3. number of “Occupational Seminars” (OS), “References”
112 E3. J. Bus. Manage. Econ.

Selection of the most suitable consultant

Cost Work experience Education level Communication ability

(0.204) (0.296) (0.204) (0.296)

Transportation Consultancy Companies Projects Department Occupational Awareness of Ability to

Cost Cost Employed Completed References Graduated Seminars responsibility Persuade
(0.000) (1.000) (0.330) (0.450) (0.220) (0.500) (0.500) (0.500) (0.500)

Cons. A Cons. A Cons. A Cons. A Cons. A Cons. A Cons. A Cons. A Cons. A

(0.333) (0.150) (0.470) (0.500) (0.580) (0.333) (0580) (0.330) (0.500)
Cons. B Cons. B Cons. B Cons. B Cons. B Cons. B Cons. B Cons. B Cons. B
(0.333) (0.150) (0.060) (0.500) (0.420) (0.333) (0.420) (0.220) (0.500)
Cons. C Cons. C Cons. C Cons. C Cons. C Cons. C Cons. C Cons. C Cons. C
(0.334) (0.700) (0.470) (0.000) (0.000) (0.334) (0.000) (0.450) (0.000)

Figure 3. Relative weights of all decision elements in fuzzy AHP

(R) of a consultant may increase. In other words, applied to all of other sub-criteria by using the affecting
References sub-criterion is affected by the Occupational sub-criteria.
Seminars sub-criterion. Moreover, due to fine After weighting the sub-criteria by considering
“References” the consultant may be given “Occupational interactions among them, all of the decision alternatives
Seminars”. In this case will be pair-wise compared with respect to each of the
Occupational seminars sub-criterion is affected by the sub-criterion. After these calculations, the weighted super
References sub-criterion. This way, there is a mutual matrix will be constructed and converted to the limit
dependence within these two sub-criteria, which should matrix in order to find out the constant effect of each sub-
be considered in the evaluations. In the same way, there criterion on the other sub-criteria. Then the weights of
are other influences within the sub-criteria and these are sub-criteria will be combined with the weights assigned to
determined by the decision maker as stated in Table 4. each decision alternative with respect to each sub-
In this model, it is appropriate and enough to establish criterion and will be found the composite weights for all
interactions only within the sub-criteria cluster, but in the three alternatives.
different models, there may be interactions among other Then, all these weights will be displayed in the
clusters such as the alternatives and the main-criteria. In weighted super-matrix given in Table 5.
such a case, the decision maker should consider the From the weighted super matrix, it is seen that TC is
interactions within alternative cluster in addition to criteria affected only by CC; as a result, CC has a weight of 1 on
and/or sub-criteria clusters. However, for the selection of TC. In the same way, CC is affected from TC, CE, PC,
the best consultant model, it is not appropriate to assume OS and AP with weights of 0.044, 0.246, 0.476, 0.096
such an interaction within alternatives, because these and 0.138 respectively. Here be aware that, the total of
alternatives are independent from each other, the abilities each column must be equal to 1 and in order this
of one of them do not affect the other two. condition to be satisfied, all of the criteria must be
After introducing the influences among the sub-criteria affected by at least one of the other or the same sub-
in the model, sub-criteria will be pair-wise compared with criteria. When this is not true, that is, when a criterion is
respect to their effect to a specific sub-criterion. For not affected from any of the criteria; the next step which
instance, consider the “Consultancy Cost” (CC) sub- is the establishment of limit matrix fails for this calculation
criterion. It is affected from TC, CE, PC, OS and AP. All type. In such cases, in order the limit matrix not to fail,
of the TC, CE, PC, OS and AP will be pair-wise Consultant A, Consultant B and Consultant C rows and
compared with respect to CC and their weights in terms columns must be added to the weighted matrix, which
of CC will be found. If “Transportation Cost” (TC) sub- actually makes manual calculations more difficult.
criterion is examined, it is seen that it is only affected by After defining the weighted super-matrix, the limit
CC; as a result no pair-wise comparisons can be made matrix can be established as given in Table 6. By means
with respect to TC. CC will be given a weight of 1 with of the limit matrix, the constant effect of each sub-
respect to TC. This procedure applied to “Consultancy criterion on all of the other sub-criteria is determined. To
Cost” and “Transportation Cost” sub-criteria, will be achieve this, a higher power of the weighted super-matrix
 Ozalp et al. 113

Table 4. Interactions within Sub-criteria in ANP

Affected Sub-Criteria Affecting Sub-Criteria

Transportation cost (TC) CC
Consultancy cost (CC) TC, CE, PC, OS, AP
Companies employed (CE) CC, PC, R, DG, OS, AR
Projects completed (PC) CE, R, OS, AP
References (R) CE, PC, OS, AR, AP
Department graduated (DG) AR
Occupational seminars (OS) CE, PC, R, DG
Awareness of responsibility (AR) PC
Ability to persuade (AP) PC, OS

Table 5. Weighted super-matrix in ANP

Affected Sub-Criteria
TC CC CE PC R DG OS AR AP
TC 0 0.044 0 0 0 0 0 0 0
Affecting Sub-Criteria

CC 1 0 0.180 0 0 0 0 0 0
CE 0 0.246 0 0.269 0.060 0 0.164 0 0
PC 0 0.476 0.365 0 0.475 0 0.617 1 0.250
R 0 0 0.244 0.124 0 0 0.055 0 0
DG 0 0 0.045 0 0 0 0.159 0 0
OS 0 0.096 0.106 0.546 0.230 0 0 0 0.750
AR 0 0 0.060 0 0.090 1 0 0 0
AP 0 0.138 0 0.061 0.145 0 0 0 0

Table 6. Limit matrix in ANP

65th power of weighted super-matrix Final weights

TC CC CE PC R DG OS AR AP of sub-criteria
TC 0.001108 0.001106 0.001106 0.001105 0.001105 0.001108 0.001101 0.001106 0.001104 0.001
CC 0.025143 0.025111 0.025116 0.025078 0.025078 0.025001 0.025001 0.025110 0.025052 0.025
CE 0.133351 0.133184 0.133211 0.133010 0.133010 0.133345 0.132603 0.133178 0.132872 0.133
PC 0.311680 0.311288 0.311351 0.310883 0.10883 0.311666 0.309930 0.311274 0.310558 0.311
R 0.084073 0.083968 0.083985 0.083858 0.083858 0.084070 0.083501 0.083964 0.083771 0.084
DG 0.043005 0.042951 0.042960 0.042895 0.042895 0.043003 0.042764 0.042949 0.042851 0.043
OS 0.232393 0.232100 0.232147 0.231798 0.231798 0.232382 0.231088 0.232090 0.231556 0.232
AR 0.058647 0.058573 0.058585 0.058532 0.058532 0.058644 0.058317 0.058570 0.058436 0.059
AP 0.034716 0.034673 0.034680 0.034628 0.034628 0.034715 0.034521 0.034671 0.034592 0.034

must be calculated. If this is done, all the values in a row Table 6 shows the limit matrix for the ANP method.
th
will converge to the same decimal. It is taken the 65 Nearly the same numbers in each row gives the final
6
(2 +1) power of the weighted super-matrix and seen that weight of that sub-criterion. For instance, the final weight
since the numbers in each row converge to the same of TC is approximately 0.001. This is an extremely small
decimal, the values in each row are nearly the same. weight, because when interactions are modeled, it is
114 E3. J. Bus. Manage. Econ.

decided that TC only affects CC with a weight of 0.044 assignment of consultants comes from the inability to
and does not affect any other criteria. As a result, it has select the best consultant when there are various
such an extremely low weight. alternatives. To solve the problem, the MCDM methods
Now, it may be thought that eliminating the small effect were studied. To support the MCDM methods and to
of TC and what fuzzy AHP says is the same thing. Yes, enable the project manager to know about activities of
after defining the interactions it is seen that TC has an the projects, project scheduling issues were explained
extremely small weight and could be eliminated, but since and advised the company to use CPM and PERT
fuzzy AHP does not consider the interactions within sub- methodologies.
criteria and decides the elimination of the effect of TC by Within the MCDM methods, three different methods
only comparing it with CC, this method is not true. In namely AHP, fuzzy AHP and ANP were examined in
brief, it is not a good idea to eliminate the small effect of detail. During the studies of AHP and ANP, decision
TC in fuzzy AHP when it has the small effect in ANP. If making in crisp environment was handled. Then it was
TC was affected by more than one sub-criterion, its decided to reflect the indecisive nature of human-beings
weight would be increased in ANP. in decision making, by introducing fuzzy AHP. With the
As stated in the limit matrix, the weights of each sub- three methods, the selection problem was modeled and
criterion were determined. The total of the weights of sub- consultants were ranked based on subjective evaluations
criteria is not equal to 1, it is 0.922. This variation is due of the project leader with respect to the selected method.
to the calculations performed in the establishment of the Rankings in all of the three methods are given in Table 9.
limit matrix. It is assumed that the convergence in the 65th After studying the three methods, they were evaluated
power of the weighted super matrix is enough to establish and some serious shortcomings were discussed. After
nd
the limit matrix. If it was taken 32 power of weighted evaluating the three methods, ANP is selected as the
super matrix, the total weight of the sub-criteria would be best one due to its totally compatible structure with the
nearly 0.960 and again the three decimals would be the structure of the selection problem.
same for nearly all the rows, but since more precise
values are desired in the rows (nearly 4 decimals are the
same for each row) 65th power of the weighted super CONCLUSIONS
matrix is taken. On the other hand, it is not a big problem
the total of weights not equal to 1. In such case the AHP is a basic method for the structure of selection of the
normalization of the weights are suggested and as a best consultant problem. As it is applied to this problem, it
result, their total will be equal to one. As explained above, can be applied to various kinds of decision problems, as
the normalized new weights of the sub-criteria are listed we can see from Table 1. However, AHP has two
in Table 7. shortcomings: one of them is not serious, but the other
Now, if the weights given to each decision alternative one must be handled to get more accurate results within
with respect to each decision sub-criterion are found, the selection of best consultant problem.
then it is easy to find the composite weight of each The first shortcoming of AHP is that it does not allow
alternative (consultant). As stated in AHP, each decision the decision maker to make decisions in a broad
alternative was evaluated with respect to each decision environment; for instance, sometimes the decision maker
sub-criterion. The same weights assigned in AHP will be thinks that one decision element is weakly more
used. Table 8 lists the weights of consultants with respect important than another one (represented by number “3” in
to the decision sub-criteria and normalized weight of each AHP scale); but at the same time the decision maker may
sub-criterion. think that the mentioned decision element is somehow
From Table 8, the composite weight of consultant A is: equally important and somehow weakly more important in
(0.001*0.430) + (0.027*0.133) + (0.144*0.284) + terms of the other one (represented by number “2” in the
(0.337*0.474) + (0.091*0.648) + AHP scale). In brief, the decision maker may be
+ (0.047*0.600) + (0.252*0.643) + (0.064*0.230) + indecisive whether to represent the result of pair-wise
(0.037*0.455) = 0.485 comparison with the number 2 or 3. There is
Similarly the composite weights for Consultants B and impreciseness in the situation. Unfortunately, according
C are 0.312 and 0.203 respectively. According to ANP, to the AHP, the decision maker must select only one
the best alternative is Consultant A. number from the pair-wise comparison scale; s/he cannot
model his/her decision with 2 numbers. In such cases,
AHP does not allow the decision maker to make
RESULTS decisions in a broad environment. This may not be
considered as an important shortcoming, as the decision
This paper aimed to solve the consultant’s assignment maker should be enforced to select one of the numbers in
problem in the ABH Company. After interviews with the scale, 2 or 3 and the result will not be very different.
employees, it is understood that the main problem in the But in order to eliminate the decision makers’ indecisive
 Ozalp et al. 115

Table 7. Normalized weights of sub-criteria in ANP

Sub-criteria Weights Normalized-Weights

Transportation Cost (TC) 0.001 0,001
Consultancy Cost (CC) 0.025 0.027
Companies Employed (CE) 0.133 0.144
Projects Completed (PC) 0.311 0.337
References (R) 0.084 0.091
Department Graduated (DG) 0.043 0.047
Occupational Seminars (OS) 0.232 0.252
Awareness of Responsibility (AR) 0.059 0.064
Ability to Persuade (AP) 0.034 0.037
Total of Weights 0,922 1

Table 8. Weights of consultants with respect to sub-criteria and normalized weights of sub-criteria in ANP

Weight with respect to Sub-criteria

Normalized Weight
Sub-Criteria Consultant Consultant Consultant
of Sub-Criteria
A B C
Transportation Cost (TC) 0.001 0.430 0.430 0.140
Consultancy Cost (CC) 0.027 0.133 0.212 0.655
Companies Employed (CE) 0.144 0.284 0.097 0.619
Projects Completed (PC) 0.337 0.474 0.474 0.052
References (R) 0.091 0.648 0.295 0.057
Department Graduated (DG) 0.047 0.600 0.200 0.200
Occupational Seminars (OS) 0.252 0.643 0.283 0.074
Awareness of Responsibility (AR) 0.064 0.230 0.122 0.648
Ability to Persuade (AP) 0.037 0.455 0.455 0.090

Table 9. Rankings of consultants

Results of Consultant Selection

Rank AHP Fuzzy AHP ANP
st
1 Consultant A (0,372) Consultant A (0,396) Consultant A (0,485)
2nd Consultant C (0, 299) Consultant B (0,314) Consultant B (0,312)
rd
3 Consultant B (0,329) Consultant C (0,290) Consultant C (0,203)

manner in such situations, fuzzy AHP, overcomes the stated here is that in AHP interactions within the same
limitation. level of hierarchy and among random levels of hierarchy
The second shortcoming of AHP is related to its are not allowed. For instance, when the hierarchy for
structure. AHP considers the problem within a hierarchy selection of the best consultant problem in Figure 1 is
and a decision element in any level of the hierarchy is examined carefully, the sub-criteria may affect some
affected only by the elements one level below of that other sub-criteria and these interactions are not
element (the alternatives at the bottom of the hierarchy mentioned in AHP. To evaluate such additional interactions
are only affected from one level upper elements). What is within decision elements, ANP should be used.
116 E3. J. Bus. Manage. Econ.

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Neutrosophic Sets and Systems

Volume 41 Article 6

3-4-2021

Comparative analysis of AHP, FAHP and NeutrosophicAHP based

on multi-criteria for adopting ERPS
Amany A.Slamaa

Haitham A. El-Ghareeb

Ahmed Aboelfetouh

Follow this and additional works at: https://digitalrepository.unm.edu/nss_journal

Recommended Citation
A.Slamaa, Amany; Haitham A. El-Ghareeb; and Ahmed Aboelfetouh. "Comparative analysis of AHP, FAHP
and NeutrosophicAHP based on multi-criteria for adopting ERPS." Neutrosophic Sets and Systems 41, 1
(2021). https://digitalrepository.unm.edu/nss_journal/vol41/iss1/6

This Article is brought to you for free and open access by UNM Digital Repository. It has been accepted for
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 Neutrosophic Sets and Systems, Vol. 41, 2021
University of New Mexico

Comparative analysis of AHP, FAHP and Neutrosophic-

AHP based on multi-criteria for adopting ERPS
Amany A.Slamaa1*, Haitham A. El-Ghareeb2 and Ahmed Aboelfetouh3
1 faculty of computers and information sciences, Luxor University, Egypt

Amani.slamaa@fci.svu.edu.eg

2, 3 faculty of computers and information sciences, Mansoura University, Egypt

helghareeb@mans.edu.eg2, elfetouh@mans.edu.eg3

* Correspondence: Amani.slamaa@fci.svu.edu.eg; Tel: +201112282018

Abstract: Management business has successfully forced enterprises to rebuild its process and
adopt technology that help in integrating all process across different departments, analysis
information in real-time, improve decision-making. ERP is a key information system for these
purposes. There are many criteria in choice ERPS based on enterprise and application. Hence,
there are many consulting firms with huge number of experts and technicians in carrying out
analysis, evaluation ERPs and supporting IT-department in enterprises in selecting suitable
ERPS. As many systems are semi-similar in features or semi-suitable for specific organization
which leads to confusing decision making. Hence, using Multi-criteria decision method
(MCDM) is essential. Using decision-making tools doesn’t mean missing data or information
about what decision is made for. But sometimes more information creates a confusing
decision as in this case-study. The case-study covers two main folds; it provides proposed
criteria of ERPS adoption and studies their weights, then decision making process that is
established by AHP, FAHP and Neutrosophic-AHP. It compares between the results of these
approaches and measures the priority/weight effect of adding sub-criteria. This study
provides a comparative analysis of AHP, FAHP and Neutrosophic-AHP. This paper
contributes in emphasize the accuracy of Neutrosophic set in decision making. It also
emphasizes on importance of using multi-criteria (criteria and factors) in designing decision
model special in information system that have many factors for one aspect. The paper also
contribute in ERPS field by providing criteria that help decision maker board in adopting
ERPS cares on enterprise's culture, vision and business processes.

Keywords: ERPS, AHP, Fuzzy-AHP, Neutrosophic-AHP and MCMD.

1. Introduction

The basic idea of an Enterprise Recourse Planning (ERP) platform is based on one of
software engineering’s trends. It is "produce applications that help developers reduce the number of
lines of code which are written by the developer until they reach the zero line of code point” [1]. This
evolution in software engineering leads the Enterprise Recourse Planning system (ERPS) to
appear and grow. ERP architecture varies with the evolution of technology. As ERP is one of
information system type, and information management is a critical element in any system

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 65

whatever its activities [2]. Further, ERP is "business process management software that allows an
organization to use a system of integrated applications to manage the business and automate many
back office functions” [1]. In the last two decades, technical development has pushed
enterprises, whatever its size to rethink their process management with respect to the new
dynamics and changing in business environment, customer demands rising and market
competition. The implementing an ERPs become a critical and essential step must be adopted
by many businesses to help in organizing and optimizing the way they do business [3–6][7].

Enterprise architecture must have business elements, their relationship to each other and
environments and principles that governing its design and evolution. Where the
requirements of enterprises almost change based on customers, competitors and strategic
targets. So its architecture reflects that. Because ERPS is a software solution for enterprise
architecture and needs, so ERPS’s architecture also developed to serve that. Many enterprises
migrate their ERPS's architecture form monolith to service-oriented architecture (SOA) or to
Microservices (MSA), or changed from SOA to MSA. Each architecture has characteristics that
do not only reflect on ERPS‘s performance, but also in the enterprise repetition between
competitors, business and enterprise targets. Thereby, the selection of architecture is not only
based on its excellent.

The choice of ERP’s vendor is not an easy mission. Thereby, decision support system
(DSS) and decision making system (DMS) highlight their importance. DSS uses the analytical
model and database to support semi-structured business decision that is made by the
decision maker, while DMS analyzes alternatives based on factors to make a
recommendation/decision instead of human. Multi-criteria decision making (MCDM) studies
quantitative and qualitative characteristics of alternatives, and then assigning values to
intangible and tangible aspects of decisions, and estimating decision based on better or worst
calculated options. Models of decision making that are supported by the decision-making
community are TOPSIS, MAUT, MAVT, ELECTRE, BWM, VIKOR, PROMETHEE, AHP and
ANP [8], [9]. Analytic hierarchy process (AHP) is a broadly utilized tool for MCDM. It has
been generally used in complex decision because of its high flexibility [10–14].

Criteria for adopting an ERP system and studying the consistency of these criteria are
related to study a qualification of adopting a decision. This paper focuses on study factors
that effect of adopting ERPS and related to make decision about architecture of system
software. The paper proves the accuracy of using Neutrosophic-set in decision rather than
Saaty and Fuzzy sets although Fuzzy and Neutrosophic are semi-close. Further, the paper
proves that consistency of decision when supported with decision model uses factors and
criteria rather than model uses only criteria. Thereby, the paper addressed these proves by a
case study. The case study is handled in three main parts; analysis available alternatives by
SWOT analysis then make a decision by using applying two models are illustrated in figures
1 and 2, finally testing consistency of decision and criteria by three different scale sets for
AHP. This study is addressed in an empirical case study. Analysis part provides a
comparison between the most professional platform solutions in ERP market; Odoo and
Oracle e-Business Suite (EBS). They have same system architecture; SOA. The reason of
choice these ERP systems are regarded to ERP industry, where Odoo is justified as the best
open source ERP, and EBS is the main licensing ERP. These studies are visualized in SWOT

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 66

analysis. Eventually, Odoo is excelling Oracle e-Business Suite in some features and Oracle
does. The final choice of adopting one of them refers now to enterprise criteria and culture.
So, case study proposes critical criteria for purchasing an ERP system based on non-profit,
governmental enterprise with multi purposes, stakeholders and beneficiaries. This paper
chooses AHP because it is one of methods that used in the selection decision. The paper
applies AHP and its improved versions like FAHP and Neutrosophic approaches to grantee
accuracy and consistency decision after declaring the technical features and measuring their
relative values. As Neutrosophic is a development of Intuitionistic Fuzzy Sets (IFS) that
outline precise and improving understanding of uncertainty [15]. The study recommends
using it for the decision’s consistency and accuracy.

This paper helps decision maker in enterprises and researches in decision making
because of comparative analysis that is provided and proposed criteria of adopting ERPS.

The proposed criteria of adopting ERPS are produced in section 3, while the comparative
analysis is addressed by a case study in section 4. Further, studding the consistency of criteria
that used in this decision by three scale sets; Saaty, Fuzzy and Neutrosophic sets with AHP,
also weights of alternatives (decision) are provided in decision section 5.

2. Literature review

Critical success factors (CSF) are defined as ‘An area where an organization must perform
well if it is to succeed’. That means these factors enable enterprises to achieve its goals. CSF
targets things that affect quality, customer satisfaction, increase revenues, decrease cost and
market share. Effective performance measures helps in monitoring performance to detect
whether it is meeting enterprise’s goals, how well system is doing, degree of customer’s
satisfaction, and finally orient enterprise to take action that improve performance and
efficiency [16]. The measurement is observation and quantification, while evaluation is a
paired measurement with an observation of what would be desired, and comparison is
putting two evaluations against each other [17]. Although performance measurement and
evaluation are ensuring the successful implementation of information systems, also ERP
model consists of data models, Critical Success Factor (CSF) models and phase models [18].
Evaluation ERP solutions in post-implementation phase is under-research [19].

In [8], [20] previewed some researches that discussed the relation between criteria of ERP
selection and enterprise’s size, and concluded that the size does not significantly affect
criteria selection, but only on the judgment importance assigned in comparisons. For
example, flexibility and supplier support are two first selection criteria in large-sized
enterprise, however cost and adoptability are the most important criteria for small-medium
sized enterprises. [18] Mapped the critical success factors of ERP successful implementation
articles since 2002 until 2016 and classified all these factors into four main classes:
Organization-related, Customization of ERP, Project-related, and Individual-related. [21]
Studied different roles and participations of ERP’s users with factors that effect on their
missions via a comparison between four companies with different industrial fields used ERP
to solve problems but unfortunately, they gained new problems. [22] Mentioned what CSF
means, and all different CSF's factors from 2003 to 2010. In [23] handles the classification of
ERP implementation strategies (organization, technology and people), the context and
conceptual model of ERP system implementation and separate between them.

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All these models are not handled criteria and factors for selecting ERPS that fit
enterprise's culture and strategic targets. Section 3 addressed this gap by proposing these
criteria and studying their consistencies in section 4 by real case study in industry field.

the selection an ERP system is a nightmare for software consultant, system architect and
enterprise managers (chief executive officer (CEO), chief financial officer (CFO), chief human
resources officer (CHRO), general manager (GM), and marketing manager) due to its
importance. Decision making is selecting the most suitable among multiple and convergent
alternatives keeping in sight the heterogeneous decision criterion, objectives and priorities of
decision maker [24]. Decision making is very important at strategic-level management.
Therefore, Difficulty of decision making is a motivation for developing many approaches and
tools not only to support a decision but also making it. Multi-criteria decision making
(MCDM) aims to provide a model for decision problems by capturing and addressing both
qualitative and quantitative characteristics of alternatives, then assigning numerical values to
intangible aspects inherent to decisions, and estimating better or worst options that have
difficult cost and benefits relationships.

In [8] use AHP to measure nine criteria for small-size enterprise are concluded from
seven selection criteria models. In [25] used AHP with four criteria and 12subcriteria for
assessing the suitability of the existing waste landfill in Zanjan, Iran. It combines AHP and
Geographic information system to build suitability assessment model. This model is
recommended to use in reevaluating the suitability of any old operating reservoir such as
heavy industrial tanks, oil reservoirs, landfills. [26], [9] Used the criteria of updated DeLone
& McLean of success IS model, apply hybrid MCDM process (AHP and TOPSIS) on it to
detect that service quality is a best criterion (with its sub-criteria: on time delivery, knowledge
and competency, error network, availability, access, rate delay and reliability) for two
different IS in banking and construction industry sector. [19] after listed evaluation models
from 1999 to 2011 it modified to updated D&M model in 2004, it proposed 23 criteria of ERP
in post-implementation and 111 experts ranked them with important, essential, important but
not essential. [27] Studies the correlation between the results of fuzzy-ANP and classical-
ANP for software security assessment and proves that they are highly correlated. That was a
motivation to apply hybrid fuzzy-ANP-TOPSIS method to get better results in decision
problems in case of the uncertain and imprecise information. In spite of fuzzy-ANP-TOPSIS
results, but this study recommended that “for software security assessment issue, as it
complex and dynamic task faced by both developers and users, there may be better MCDM
symmetrical techniques rather than Hybrid fuzzy-ANP-TOSIS”.

Fuzzy sets were used with MCDM methods like in AHP to reduce uncertainty.
However, it does not solve this kind of problems in decision making. Saaty and et al. dose not
support fuzzy-AHP because AHP is fuzzy by itself. Neutrosophy is the origin of
Neutrosophic which is care neutral (indeterminate/unknown) part as in philosophy. Its
components are T, I, F. they are representing the membership (truth), indeterminacy
(intermediate) and non-membership (false) values respectively. Each element in
Neutrosophic set has three components which are considers a subset, contrary all other types
of sets as in fuzzy set, its three component are numbers [28]. Neutrosophic set is more general
than other set as fuzzy and thereby Saaty set. Neutrosophic set is more reliable in judgment
and pairwise comparison for criteria and alternative especial in Multi-Criteria Group

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Neutrosophic Sets and Systems, Vol. 41, 2021 68

Decision Making (MCGDM). Neutrosophic is more suitable for dealing with high degree
of imprecision and incomplete information [14]. Neutrosophic set provides accurate values in
decision rather than Saaty and fuzzy sets [8], [9], [29], [30].

3. A Proposed decision model of adopting ERPS

‘Which ERP system is enterprise purchase?’ This question is synonym to adopting an

ERP system decision. Where there are many ERP’s vendors with semi-different features. The
proposed criteria of ERPS selection form is illustrated in figure 1. the proposed criteria form
for purchasing ERP system that combines all desired features and nature of purchasing
system process are: 1- trust vendor, 2- Support different Technical platform (on-premises, on-
cloud, mobility, OS (Windows & Linux)), 3- Vendor package (deployment, recovery, training
staff, maintenance and customization), 4- Low Total costs (ownership licenses,
service/support, implementation, training staff cost, deployment, maintenance, consultancy
and customization), 5- Upper management support, 6- Accuracy, 7- Availability, 8- Risk
management and security, 9- Support different language ( Arabic and English is essential),
10- Database independency.

These criteria are ranked by experts. Experts are IT-staff, academic researchers, project
management manager, external technicians and key-users in different enterprises. It designed
based on the results of previous questionnaire, where the average of criterion’s importance is
calculated, and then criteria with average value less than 80% is eliminated. Essential vector is
numbered with 8/10, more important but not essential is numbered with 5/10 and important
is numbered with 3/10. The high ratio 80% is detected because selecting ERPS that supports
its culture, vision and strategic goal is not easy mission. Aforementioned, Neutrosophic
excels on fuzzy and saaty, thereby the Neutrosophic-AHP is suggested to use in making
decision of adopting ERPS to grantee an accurate decision. Steps of Neutrosophic-AHP are
illustrated in figure 1.

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Neutrosophic Sets and Systems, Vol. 41, 2021 69

Figure 1 flowchart of recommended set (Neutrosophic Set) for proposed model

To prove the accuracy of proposed decision model of adopting ERPS with Neutrosophic-
AHP and consistency of these criteria, the next section provides case study for applying a
proposed decision model with ten criteria and 15 factors by AHP, FAHP and Neutrosophic-
AHP. Briefly, the case study provides a comparative analysis and discusses an accuracy level
of decision for using Neutrosophic-AHP and factors for criterion.

Steps of applying AHP [12–14] are briefly previewed in figure 2. They are

1- Set problem in a hierarchical form

2- Estimate the pairwise comparison matrix
3- Estimate normalize pairwise comparison criteria matrix: By Get summation of each
column∑𝑛𝑗=1 𝑎𝑖𝑗 . Then, divide each value in a pairwise comparison matrix to previous
summation, final equation is: 𝐶𝑖𝑗= 𝑎𝑖𝑗 (1)
∑𝑛
𝑗=1 𝑎𝑖𝑗

4- Estimate weight criteria matrix: By: calculate average value for each row
∑𝑛𝑗=1 𝐶𝑖𝑗
𝑊𝑖 = (2)
𝑛
5- Confirm values of weight criteria is standard by estimate consistency index (CI),
consistency ratio (CR) By: Estimate consistency from following equation

∑𝑛𝑗=1(𝑊𝑖1 × 𝑎𝑖𝑗 )
𝐶𝑜𝑛𝑠𝑖𝑠𝑡𝑒𝑛𝑐𝑦𝑖𝑗 =
𝑊𝑖1
, Then, (3)

∑ 𝐶𝑜𝑛𝑠𝑖𝑠𝑡𝑒𝑛𝑐𝑦𝑖𝑗
calculate 𝜆𝑚𝑎𝑥 =
𝑛
, (4)

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𝜆𝑚𝑎𝑥 −𝑛
CI =
(𝑛−1)
, (5)

CR = CI / RI where RI is random consistency index value that detected based on a random

index’s table [29], [32]

6- Repeat same steps 2, 3, 4 5 for each alternative based on each criteria to get priority
weight for alternative and confirm from its consistency by estimating CR. By:
Estimate pairwise comparison matrix with same Saaty scale table, and normalized
pairwise matrix, then criteria/priority weight, Estimate 𝜆𝑚𝑎𝑥 , CI and CR.
7- Make a decision By: Calculate decision weight by the summation of Product criteria
weight matrix with alternative priority weight matrix according to the following
equation:
𝑗
𝐷𝑖𝑣 = ∑𝑖=1 𝐶𝑟𝑖𝑡𝑒𝑟𝑖𝑎𝑊𝑒𝑖𝑔ℎ𝑡𝑖 × 𝑃𝑒𝑟𝑖𝑜𝑟𝑖𝑡𝑦𝑊𝑒𝑖𝑔ℎ𝑡𝑖𝑗 (6)

The biggest value of decision weight is the most suitable alternative for these criteria.

Figure 2 flowchart of AHP steps

Further, Steps of using FAHP [10], [11], [33] are

1- The first step is the same step in AHP except using a Fuzzy triangular scale table as in
table 1.

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2- Estimate the pairwise comparison matrix , By: (Note: based on our criteria i and j = 10,
matrix size= 10×10), use the same rule in step 2 in AHP except replace crisp values with
fuzzy set values [10]

𝑎`𝑖𝑗 = (1,1,1) when i=j (7)

𝑎𝑖𝑗 = 𝑓𝑢𝑧𝑧𝑦 𝑠𝑒𝑡 𝑟𝑒𝑙𝑒𝑣𝑎𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑖𝑛 𝑓𝑢𝑧𝑧𝑦 𝑡𝑟𝑖𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑡𝑎𝑏𝑙𝑒 (𝐿, 𝑚, 𝑢) when i≠j
1
𝑎`𝑗𝑖 =
𝑎𝑖𝑗
(8)

After calculating the average of evaluation values for three judgments and apply rules of 𝑎`𝑖𝑗 ,
Hence, the pairwise comparison matrix in fuzzy form is created.

3- Estimate criteria weight matrix, By: Calculate geometric means for value as following
equation:

ŕ = ∏𝑛𝑗=1 á𝑖𝑗 (9)

then, calculate the fuzzy weight by equation:

W`i = r`i ⊗ (𝑟`1 ⊕ r`2 ⊕….⊕ r`n) (10)
And, calculate a crisp weight by equation
∑ 𝐿𝑤𝑖 , 𝑚𝑤𝑖 , 𝑢 𝑤𝑖⁄
𝑊𝑖 = 𝑛 (11)
Also, check the weight is normalized or not by summation all weights, if equal one it is true,
else it false.

4- Estimate weight alternative matrix for each criteria, By: the repeat same steps in 2& 3
for alternatives after converting crisp values of table in step 6 in AHP.
5- Estimate decision, By: Calculate decision weight by the summation of Product criteria
weight matrix with alternative priority weight matrix according to the following
equation:
𝑗
𝐷𝑖𝑣 = ∑𝑖=1 𝐶𝑟𝑖𝑡𝑒𝑟𝑖𝑎𝑊𝑒𝑖𝑔ℎ𝑡𝑖 × 𝑃𝑒𝑟𝑖𝑜𝑟𝑖𝑡𝑦𝑊𝑒𝑖𝑔ℎ𝑡𝑖𝑗 (12)

The biggest value of decision weight is the most suitable alternative for these criteria. These
steps are summarized in figure 3.

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Neutrosophic Sets and Systems, Vol. 41, 2021 72

Figure 3 flowchart of FAHP steps

While steps of Neutrosophic-AHP [14], [15], [34] are illustrated briefly in figure 1. They are

1- The first step in AHP and FAHP is also shared with this approach, except using a
triangular Neutrosophic scale in table 1.
2- Estimate the pairwise comparison matrix in crisp value, By: [34] (Note: based on
our criteria i and j = 10, matrix size= 10×10), use the same rule in step 2 in AHP except
replace values with Neutrosophic set values in table 1.

=< (1,1,1), 0.5, 0.5, 0.5 > when i=j (13)

𝑡ℎ𝑒𝑠𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑎𝑟𝑒 𝑓𝑢𝑧𝑧𝑦 𝑠𝑒𝑡 𝑟𝑒𝑙𝑒𝑣𝑎𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑖𝑛 𝑓𝑢𝑧𝑧𝑦 𝑡𝑟𝑖𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑡𝑎𝑏𝑙𝑒 (𝐿, 𝑚, 𝑢) , and T is the
truth-membership, I is indeterminacy, and F is falsity membership functions of Neutrosophic
set. So, pairwise-comparison matrix with Neutrosophic values is created.

To convert values of Neutrosophic form to crisp value , use the following equation:
𝑇𝑖𝑗 + 𝐼𝑖𝑗 + 𝐹𝑖𝑗

𝑠(𝑟𝑗𝑖) = |(𝑙𝑖𝑗 × 𝑚𝑖𝑗 × 𝑢𝑖𝑗 ) 9

| when i ≠ j (14)

After calculating the average of evaluation values for three judgments and applying rules
of𝑎`𝑖𝑗 , hence, pairwise comparison matrix in crisp values is created.

3- Estimate criteria weight matrix, By: Calculate weight matrix as the following
equations:

(Calculate each column, then divide the previous crisp value by each summation column)
𝑊𝑖
𝑊𝑖𝑚 = ∑𝑚
𝑤ℎ𝑒𝑟𝑒 𝑖 = 1,2, … 𝑚
𝑖=1 𝑊𝑖
Then, (calculate row average to get final criteria weight)

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∑𝑚
𝑗=1(𝑋𝑖𝑗 )
𝑊𝑖 = i= 1, 2, … m; j= 1,2 3 …n (15)
𝑛

Then calculate the total summation of weight, when it equals to 1 that means they are
normalization of weights. After that, check consistency of weights by calculating
consistence index (CI) and consistence Ratio (CR).

4- Estimate weight alternative matrix for each criteria, By: repeat same steps in 2& 3
for alternatives after converting crisp values of table in step 6 in AHP, the pairwise-
comparison matrix with Neutrosophic values is created.
5- Estimate decision, By: Calculate decision weight by the summation of Product
criteria weight matrix with alternative priority weight matrix according to the
following equation:
𝑗
𝐷𝑖𝑣 = ∑𝑖=1 𝐶𝑟𝑖𝑡𝑒𝑟𝑖𝑎𝑊𝑒𝑖𝑔ℎ𝑡𝑖 × 𝑃𝑒𝑟𝑖𝑜𝑟𝑖𝑡𝑦𝑊𝑒𝑖𝑔ℎ𝑡𝑖𝑗 (16)

The biggest value of decision weight is the most suitable alternative for these criteria.

All equations, that are used in previous steps of AHP, FAHP and Neutrosophic-AHP, are
listed in mentioned references.

4. An empirical application for a proposed model - Case study

‘ISLAH Charitable Foundation’ is a non-profit distributed enterprise in EGYPT, it starts

building its management information systems. The ERP market is studied to select one fit its
culture (non-profit and social organization), its vision and multiply-purposes.

Based on these criteria, Odoo13 and oracle e-business suite (EBS) are candidates. Because
Odoo is an open source suite of integrated business applications with most popular open
source ERP rank in 2016. While Oracle E-Business Suite is an integrated business applications
enable organizations to improve decision making, and increase corporate performance. To
detect which one of them is suitable. The trade-off is considered as a decision analysis and a
pre-step of making a decision. The decision analysis is represented in SWOT analysis for both
as declared in appendix A [36-43]. Unfortunately, this analysis caused confusion. More
information and more data do not mean making a decision, but support decision-making and
sometimes decision maker’s confusion as in this case. That was a motivation for using
decision-making tools and put structured steps for making a consistent and accuracy
decision.

Analytic Hierarchy Process (AHP) is proposed to select ERP system, where it is used
in many applications in project management, risk estimation, evaluation of knowledge
management tools and ERPs selection [31]. To get accurate and consistent decision, the
trusted decision is measured by AHP, Fuzzy AHP (FAHP) and Neutrosophic-AHP with three
different scale sets that are declared in table 1 and table 2 provides random consistency index
that used in consistency calculation. These approaches structure the decision problem into
objective, alternatives and criteria. Regarding to the case study, the objective is purchasing a
suitable ERPS, alternatives are Odoo 13 system and Oracle E-business Suite and ten criteria
that are declared in previous form in section 4.1. Section 4.2 provides a comparative analysis
for AHP, FAHP and Neutrosophic-AHP with using multi-criteria; ten criteria and 15 factors
(sub-criteria). These sections study accuracy decisions with three different sets, and with

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
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using multi-criteria instead of only criteria. Also these sections proves consistence of adopting
criteria in proposed decision model. Further, these sections discuss the proposed
recommendation of using Neutrosophic-AHP in proposed decision model.

Table 1: three Scale Set for AHP, FAHP and Neutrosophic – combined from [10], [15], [32]

Fuzzy
Saaty Neutrosophic triangular
Explanation triangular
Scale scale
scale
1 Equally significant (1, 1, 1) <<1,1,1>; 0.50, 0.50, 0.50>
3 slightly significant (2, 3, 4) <<2, 3, 4>; 0.30, 0.75, 0.70>
5 String significant (4, 5,6) <<4, 5, 6>; 0.80, 0.15, 0.20>
7 Very strong significant (6, 7, 8) <<6, 7, 8>; 0.90, 0.10, 0.10>
9 absolutely significant (9, 9, 0) <<9, 9, 0>; 1.00, 0.00, 0.00>
2 (1, 2, 3) <<1, 2, 3,>; 0.40, 0.60, 0.65>
4 (3, 4, 5) <<3, 4, 5>; 0.35, 0.60, 0.40>
6 Sporadic values between two (5, 6, 7) <<5, 6, 7>; 0.70, 0.25, 0.30>
8 Close scale (7, 8, 9) <<7, 8, 9>; 0.85, 0.10, 0.15>
Table 2: part of Random consistency index that listed in [29]

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
RI (random 0.0 0.0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.52 1.54 1.56 1.58 1.59
index)
4.1 Making decision by AHP, fuzzy-AHP (FAHP) and Neutrosophic-AHP:

The decision problem is visualized in hieratical form, as in figure 4 that represents

goals, alternatives and criteria at levels. The decision with Saaty set and AHP approach
recommended Odoo 13 rather than EBS.

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Figure 4 Hierarchical model of purchasing decision for AHP with 10 criteria only

Because of the complexity and uncertainty of real decision-making problems, decision makers
often find that it’s more realistic to assign linguistic variables to judgments rather than fixed
values. Hence, presenting data using fuzzy numbers is more appropriate instead of crisp
numbers [31]. Hence fuzzy-AHP is an improved version of AHP.

There are many methods to conclude priority vector such as the extent analysis
method (EAM), tolerance deviation, entropy concepts, Lambda-Max method, eigenvector
method, fuzzy preference programming and Fuzzy LinPreRa. The most widely applied and
popular is EAM but unfortunately weights from a fuzzy comparison matrix cannot be
estimated correctly. This paper uses geometric means to estimate priority vector (fuzzy
weight) because it is more accurate and consistency ratio in EAM are produced after the
evaluation process, this led decision makers to find it difficult to ensure continuous
comparison of decisions. In addition to it requires n(n-1)/2 of pairwise comparisons [11], [31].

After applying steps of decision making by using Neutrosophic-set, the decision of

using Neutrosophic-AHP is semi-agrees with FAHP, but there is high gap between AHP and
both FAHP and Neutrosophic-AHP. Weights of using Odoo by AHP, FAHP and
Neutrosophic-AHP are 27%, 40%, 46% respectively. While for EBS with same order of
different set of AHP are 63%, 60% and 54%. Thereby, the decision stills confuses.

4.2 Decision by using multi-criteria and AHP, fuzzy-AHP (FAHP) and Neutrosophic-AHP

In the previous section, decision is estimated by AHP, FAHP and Neutrosophic-AHP

for ten criteria, this section estimates decisions by same three scale set and AHP approach,
but with sub-criteria for some of the criteria as a method to measure the effect of using sub-

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criteria in the decision. Here, the hierarchy of decision is at four levels; where both levels
three and four for criteria and its sub respectively. Infrastructure platform and operating
system are sub-criteria for ‘support different technical platform’ criteria. Continuous
deployment, recovery, training staff, maintenance and continuous integration are sub-criteria
for ‘vendor package’ criteria. Ownership licenses, services, implementation, consultancy,
deployment and customization are sub-criteria for ‘low total cost’ criteria. Support different
language has Arabic and English sub-criteria. Hence, the hierarchy of purchasing decision
with criteria and sub-criteria are visualized in below figure 5.

Same steps of Steps of AHP, FAHP and Neutrosophic-AHP approaches in section 4.1 are
applied in respectively to calculate decision. The final equations 6, 12 and 16 are applied to
get values of recommendation for both alternatives. The steps are same for three approaches
as declared in figures 1, 2 and 3 but the equations are different because of used scale set.
Thereby, equations 13, 14 and 15 for in Neutrosophic-AHP are different on equations 7, 8 and
9 for FAHP and equations 1, 2 and 3 for AHP.

Decision's Weights of using Odoo system by AHP, FAHP and Neutrosophic-AHP are
46%, 44% and 45% in respective. While for EBS are 54%, 56% and 55% in respective. Values
of these decisions are more realistic than are listed in section 4.1. This proves that, using
multi-criteria (criteria and its factors) make decision more accurate and realistic.

The weights of decision with Neutrosophic-AHP with criteria model and multi-
criteria model is very approximate rather than in AHP and FAHP for two cases. A decision
with Neutrosophic-AHP in 10 criteria case and 10 criteria and 15 sub-criteria are 46% and 45%
for Odoo, while for EBS are 54% and 55%. However, a decision with FAHP in 10 criteria case
and 10 criteria and 15 sub-criteria are 60% and 44% for Odoo, while for EBS are 40% and 56%.
Furthermore, a decision with AHP in 10 criteria case and 10 criteria and 15 sub-criteria are
27% and 46%, while for EBS are 63% and 54%. That proves that using Neutrosophic-AHP
provide accuracy and consistency decision rather that AHP and FAHP.

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Neutrosophic Sets and Systems, Vol. 41, 2021 77

Figure 5 a hierarchy model of purchasing ERP system decision with 10 criteria and 15 factors (sub-
criteria)

5. Results and discussion:

5.1 Choosing optimal method of MCDM

Firstly, from these three approaches’ estimations, AHP ranked Odoo decision with
0.63 while EBS ranked with 0.27. Also, FAHP recommend Odoo system with 0.54 value while
EBS ranked with 0.46 value. Neutrosophic-AHP get a decision on purchasing Odoo system
0.56 while the decision of purchasing EBS system gets 0.44 It is noted that the values of
ranking Odoo system by three approaches is higher than EBS rank. Hence, the decision is
purchasing Odoo system.

The weights of decision with Neutrosophic-AHP with criteria model and multi-
criteria model is very approximate rather than in AHP and FAHP for two cases. A decision
with Neutrosophic-AHP in 10 criteria case and 10 criteria and 15 sub-criteria are 46% and 45%
for Odoo, while for EBS are 54% and 55%. However, a decision with FAHP in 10 criteria case
and 10 criteria and 15 sub-criteria are 60% and 44% for Odoo, while for EBS are 40% and 56%.
Furthermore, a decision with AHP in 10 criteria case and 10 criteria and 15 sub-criteria are

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Neutrosophic Sets and Systems, Vol. 41, 2021 78

27% and 46%, while for EBS are 63% and 54%. That proves that using Neutrosophic-AHP
provide accuracy and consistency decision rather that AHP and FAHP.

Secondly, three approaches that are used in selection decision provide same decision
with different recommendation values. These results have different preference distributions
despite having the same initial input from same decision makers and all used approaches
agreed on the same goal. The different Scale set value of AHP method is the reason to
different values for each alternative. To answer question “Which one of AHP, FAHP or
Neutrosophic-AHP is accurate approach?” there are three opinions. (1) One of them is ‘CI
and CR measures are used to prove the consistency of decision maker preferences [12]’, but
CI and CR already estimated in each approach for sure that criteria’s weights and
alternatives’ weights are consistent, so the decision for all approach is consistent. (2) Another
answer is “different judgment scales are influencing the results and decisions [12]”. This case
study, using different scale set values, i.e. Saaty scale, triangular scale and Neutrosophic scale
and they effects on stability of decision's weights in case of comparing between three values
of AHP, FAHP and Neutrosophic-AHP for two alternatives. Decisions with
recommendations round 63%, 54% and 56% for Odoo and 27%, 46%, and 44% for EBS with
small disparity. (3) Another answer is ‘using the Spearman’s correlation coefficient index [13],
[35]‘. A Spearman’s coefficient for the case study is estimated by using weights for criteria
and alternatives, then ascending them order, set ranks and apply coefficient equation: 𝜌 =
6 ∑ 𝑑𝑖2
(where n in case study =10). For AHP, Spearman’s coefficient for Odoo and EBS is
𝑛( 𝑛2 −1)

same value, it equals to 0.984. For Fuzzy-AHP, Spearman’s coefficient for Odoo equals to
0.975 while for EBS equals to 0.972. They are very close, where 0.003 is the disparity between
two decisions in the same method. For Neutrosophic-AHP, Spearman’s coefficient for Odoo
equals to 0.95 while for EBS equals to 0.18. Based on values of Spearman’s coefficient that are
estimated for three methods; Neutrosophic set is more accurate than AHP and FAHP, but
same coefficient not prove that AHP has same accuracy that FAHP has, and that conflict with
many literatures that documented other that. All these correlation coefficient values are
limited in the closed period [0.7, 1], that means that a strong direct correlation for all. Also, it
provides values are very close for a different approach. For example, 0.012 is the difference
value between an Odoo decision by AHP and FAHP. The final answer of which scale set is
accurate rather other, this case study proved is ‘Neutrosophic-set is the most accurate, therefore,
Neutrosophic-AHP is more accurate and consistence rather than AHP and fuzzy-AHP'.

5.2 Effect of using sub-criteria on decision's accuracy:

Priority Criteria and decision consistency between criteria’s levels:

Basically, Criteria weights for criterion based its sub-criteria are calculated by average
weights of sub-criteria, the next table previews difference value that main criteria get before
and after estimating weights of its sub. (The importance of criteria is calculated by the
average of its sub-criteria. The importance of criterion that has only two sub-criteria does not
give a real value as it is seen in table 3).

Table 3 weights of criteria that have sub-criteria (factors)

Criteria Weight Weight Weight Weight Weight score Weight score

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
Neutrosophic-AHP based on multi-criteria for adopting ERPS
 Neutrosophic Sets and Systems, Vol. 41, 2021 79

that have score by score by score by score by by by

sub criteria AHP AHP FAHP FAHP Neutrosophic- Neutrosophic-
(without (with sub- (without (with AHP AHP
sub- criteria) sub- sub) (without sub) (with sub)
criteria) criteria)
Support
different
18% 50% 17% 50% 15% 50%
technical
platform
Vendor
21% 20% 20% 20% 14% 20%
package
Low total
9% 17% 9% 16% 9% 17%
cost
Support
different 3% 50% 3% 50% 6% 50%
language
In comparison criteria’s rank and its importance, decision score between using one
level of criteria and two levels of them (sub-criteria), to see the number of criteria’s level effect
on decision’s quality, below tables 4 and 5 also figures 6:9 show that how factors of criterion
adjust weight criteria and its consistency. Tables 4 and 5 preview how the importance of
criteria is changed when sub-criteria (factors) are used in decision model. That shows the
effect of sub-criteria on criterion's weight and therefore decision. Table 4 lists the criteria with
its weight and rank between whole proposed criteria. The weight's criterion regards its
weight. While table 5 shows how same criterion's importance is different when used factors
for it. This difference reflects of alternatives' weights and final decisions

Table 4 importance and rank of 10 criteria

AHP FAHP Neutrosophic-AHP

Criteria
importance Rank importance Rank importance Rank
Trust vendor 17% 3 18% 2 14% 2
Support different Technical platform 18% 2 17% 3 15% 1
Vendor package 21% 1 20% 1 14% 2
Low total costs 9% 5 9% 5 9% 5
Upper management support 8% 6 8% 6 9% 5
accuracy 8% 6 9% 5 10% 4
Availability 10% 4 10% 4 11% 3
Risk management and security 3% 7 4% 7 6% 6
Support different language 3% 7 3% 8 6% 6
Database independency 2% 8 3% 8 5% 7

Table 5 importance of criteria that have sub-criteria for AHP, FAHP and Neutrosophic-AHP

AHP FAHP Neutrosophic-AHP

Applying Applying Applying Applying Applying Applying
Criteria and its sub-criteria model model model model model model
without with without with without with
factors factors factors factors factors factors
Support different Technical
18% 50% 17% 50% 15% 50%
platform

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 80

• Infrastructure
88% 87% 67%
platform
• Operating system 13% 22% 33%
Vendor package 21% 20% 20% 20% 14% 20%
• Continuous
26% 22% 24%
deployment
• Recovery 31% 40% 25%
• Training staff 19% 11% 17%
• Maintenance 11% 11% 15%
• Continuous
14% 16% 19%
integration
Low total cost 9% 17% 9% 16% 9% 17%
• Ownership licenses 25% 31% 23%
• Services 4% 2% 11%
• Implementation 9% 7% 13%
• Consultancy 8% 8% 12%
• deployment 20% 20% 22%
• Customization 34% 30% 19%
Support different language 3% 50% 3% 50% 6% 50%
• Arabic 90% 97% 50%
• English 10% 3% 50%

Database independency
Support different language
Risk management and security
Availability
Accuracy
Upper management support
Low Total costs
Vendor package
Support different Technical platform
trust vendor

0% 5% 10% 15% 20% 25%

neutrosophic AHP FAHP AHP

Figure 6 Criteria's Importance

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 81

English
Support different language
Availability
Upper management support
deployment
implementation
ownership licences
continous integration
training staff
continous deployment
operating system
Support different Technical platform
Criteria
0% 20% 40% 60% 80% 100% 120%

nutrosophic FAHP AHP

Figure 7 Criteria and sub-criteria importance

10
8
6
4
2
0

AHP FAHP neutrosophic AHP

Figure 8 Criteria's Rank for model in section 4.1(criteria only)

10
8
6
4
2
0

Ahp FAHP neutrosophic AHP

Figure 9 Criteria's Rank for model in section 4.2 (criteria and factors)

Consistency index confirms on the consistency of criteria and further on the decision,
where it is the index of the consistency of judgments across all pairwise comparisons. The

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 82

consistency of main criterion that has sub-criteria is less than consistency of criteria without
its sub as listed in table 3.

Table 3 consistency of main criteria with and without its sub-criteria (factors)

Criteria that have sub criteria consistency by consistency by AHP

AHP (with factors)
(without factors)
Support different technical platform 13.19 2
Vendor package 12.88 4.96
Low total cost 11.12 6.02
Support different language 10.68 2
The other consistency of criteria that have not sub criteria are the same and are listed in table
4

Table 4 consistency of criteria that have not sub criteria

Sub-criteria Consistency Sub-criteria Consistency criteria Consistency

by AHP by AHP by AHP
Infrastructure 1 Service/support 1.005 Trusted vendor 11.9
platform
Operating system 1 Implementation 0.691 upper management 11.26
support
Continuous 1.08 Consultancy 1.24 Accuracy 11.39
deployment
Recovery 0.88 Deployment 1.06 Availability 11.91
Training staff 1.24 Customization 0.88 Risk management and 11.48
security
Maintenance 0.95 Arabic 1 Database 11.36
independency
Continuous 0.79 English 1
integration
Ownership licenses 1.12
The selecting ERP system decision based on 10 criteria regards to approximate rank
of decision based on 25 criteria (10 criteria and 15 sub-criteria). Decision score based on these
criteria for each method is listed in below table 5 and in following figures 10and 11.

Table 5 decision score with three scale sets

AHP FAHP
Neutrosophic- Neutrosophic-AHP
systems AHP (with FAHP (with
AHP (with factors)
factors) factors)
Odoo 63% 60% 54% 54% 56% 55%
EBS 27% 40% 46% 46% 44% 45%

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 83

Decision for Odoo ERPS Decision for EBS ERPS

10 criteria 10 criteria & 10 criteria 10 criteria &

15factors 15factors

AHP FAHP Neutosophic-AHP AHP FAHP Neutosophic-AHP

Figure 10 decisions for two alternatives systems based on two models

Figure 11 rank decision of Odoo and EBS selection with and without sub-criteria

6. Conclusion

The comparison chart allows enterprises to take an in-depth look at whether different
software packages can meet their technical and functional requirements. Comparison Report
allows buyers of business software to assess functions, features, capabilities, downside of the
software solutions, but it does not help in decision making. On analysis stage, the SWOT
analysis and comparisons may be not enough for detect which system is suitable as in case
study, but it creates flog and confusion environment. In this inconsistency decision the Multi
criteria decision making (MCDM) is solved. This paper applies three methods of it; AHP,
FAHP and Neutrosophic-AHP, firstly, with 10 criteria and secondly, with 25 criteria (adding
15 sub criteria). Three approaches ranked two alternatives ERPS. The paper provides a

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and
Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 84

comparative analysis for AHP, FAHP and Neutrosophic-AHP. Although many researches
handle criteria of evaluating ERP but purchasing ERP almost is not found. The paper
proposes criteria of adopting ERPS. Furthermore, the paper studies consistency of these
criteria.

The paper studies accuracy of decision with AHP, FAHP, and Neutrosophic-AHP.
This study compares making decision of adopting ERPS by these three based on 10 criteria,
an based on 10 criteria and 15 sub-criteria. This study also analyzes criteria and factors by
calculating their weights based on two alternatives' properties and characteristics. The paper
also studies the accuracy of decision by comparing the consistency of using multi-criteria and
criteria for decision model.

The paper proves that Neutrosophic-AHP is the most accuracy rather than AHP and
FAHP. Also it shows effect of using criteria and its factors in decision's accuracy. The third
contribution, the comparative analysis that is addressed in paper tries to fill gap between
industrial and academic fields by real empirical application.

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Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 87

Appendix A

Table A SWOT analysis for Odoo and EBS

Odoo Oracle e-business suite

Strength Weakness Strength Weakness

• Flexibility to tailor the • Documentation needs to • Its company has more than • because its effected role in
system for enterprises needs improve. 130,000 employees and technical market, Oracle has
developers working with had to face many lawsuits and
• The free version of it, • Odoo does not has business
Oracle controversies which affected
consider an announcement analytics, product design,
• Oracle Company (owner) has its brand image
and increase availability in SCM, and asset management market dominance in many • competition means limited
the ERP market, marketing Commercial version is not for technical products such as growth in market share
for the commercial version. small enterprises Oracle Database, Enterprise • its user interface is not friendly
• High modular: easy to add Manager, Fusion Middleware, • not user-friendly enough than
more module servers, workstations, storage some other platforms
etc. particularly for small
• Customize created modules.
• Has the ability to integrate businesses
• Lower cost
with different modules. • The default tax module and
• Open source • Is an extremely powerful, sales modules found on EBS is
• Free educational version robust, that meet the needs of often not adequate, leading
• Easy to integrate with virtually any business companies to have their own
external systems • Support their products with custom modules built.
update, continues release • There are also many modules
• Commercial edition in SaaS
• It offers services like SAAS, for the platform, that work,
version
PAAS, consulting, financing but do not work as well as
• Has 900+ partners over 1176 etc. they do on other systems
countries with • Oracle has its presence in 100+
4000000+users. countries that share in EBS
using over them.

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and Neutrosophic-AHP based on multi-criteria for adopting ERPS
Neutrosophic Sets and Systems, Vol. 41, 2021 88

Opportunities Threats Opportunities Threats

• Continuous developing • Strong Competition from • Because Oracle is a trusted • There are strong top
thanks to open source commercial ERP vendors vendor in many technology as competitors such as: SAP,
nature and partners. such as Oracle, SAP etc. database, that will be reflected Microsoft, HP Hewlett-
on EBS's reputation. Packard and IBM.
• Cooperation with • Competition from open
• More brand visibility and • Competition from Open
governmental organizations source ERP vendors announcement can highlight source vendors such as Odoo.
helps it to grow its business. EBS • Because EBS is spread over the
• Large enterprises such as • Cooperation with world, market instability may
Toyota and Hyundai turned governmental organizations reduce its profits.
to using Odoo is a • (PC, Mobile, VM, Cloud) and • Increasing the competition
grow-up of data analysis may be decrease EBS's market
motivation to cooperate
science dominance
with more.
• Odoo can work towards
tapping the huge internet,
different infrastructures (PC,
Mobile, VM, Cloud) and
grow-up of data analysis
science
• Many add on, modules,
features add easily without
additional cost
• Its popularity increase

Received: Jan 7, 2021. Accepted: March 4, 2021.

Amany A.Slamaa, Haitham A. El-Ghareeb and Ahmed Aboelfetouh, Comparative analysis of AHP, FAHP and Neutrosophic-AHP based on multi-criteria for adopting ERPS
ISAHP Article: A Style Guide for Individual Papers To Be Submitted to the International
Symposium of the Analytic Hierarchy Process 2022, Web Conference.

FUZZY EXTENSIONS OF AHP AND ANP: A STATE OF THE ART

LITERATURE REVIEW
Sezi Çevik Onar1, Başar Öztayşi1, Selçuk Çebi2, Cengiz Kahraman1,
Istanbul Technical University, Department of Industrial Engineering, 34367 Maçka, Beşiktaş, Istanbul, Turkiye
1
2
Yildiz Technical University, Department of Industrial Engineering, 34349 Yildiz, Beşiktaş, Istanbul, Turkiye

ABSTRACT

Analytical hierarchy process and analytical network processes have been widely used in
the literature. Both AHP and ANP have been modified by using fuzzy sets. Especially,
extensions of fuzzy sets have been recently used for modifying classical AHP & ANP. In
this study, we provide a brief literature review on the usage of AHP & ANP, fuzzy AHP &
ANP. We utilize Scopus database for the research.

Keywords: AHP, ANP, fuzzy AHP, fuzzy ANP, extensions of fuzzy sets

1. Introduction
Fuzzy sets introduced by Zadeh (1965) enables dealing with uncertainty caused by
imprecision, ambiguity and vagueness. Especially, while dealing with human judgements,
the hesitancy and subjectivity in the human decision-making processes can be represented
with fuzzy sets. The different types of fuzziness has been represented by using extensions
of fuzzy sets such as Type 2 fuzzy sets (Zadeh, 1975), Intuitionistic fuzzy sets (Atanassov
1986), Hesitant fuzzy sets (Torra, 2010), Pythagorean fuzzy sets (Yager, 2013), q-rung
orthopair fuzzy sets (Yager, 2017), Picture fuzzy sets (Coung, 2015) and Spherical fuzzy
sets (Kahraman and Kutlu Gündoğdu,2019).
Fuzzy sets are very useful for representing subjective judgements in multicriteria decision
making processes. Analytical Hierarchy Process (AHP) and Analytical Network Process
(ANP) are the most used multi-criteria decision-making processes. Both AHP and ANP
enables representing human language. Yet, when the decision makers are hesitant on the
decision process and there are great differences among scales, AHP and ANP methods can
be used with fuzzy sets. In the literature, both fuzzy AHP and fuzzy ANP methods have
been modified by using fuzzy extensions. In this study, we focused on usage of fuzzy AHP
and ANP methodologies in the literature. We used the Scopus database for this research
and compare the usage of AHP, ANP with fuzzy AHP and fuzzy ANP usage.
The organization of this paper is as follows. In the second section, we give a brief review
on the usage of AHP & ANP and fuzzy AHP & ANP in the literature. In the third section,
we use summarize extensions of fuzzy AHP and fuzzy ANP studies. In the last section we
conclude and give further suggestions.
2. Literature review on fuzzy AHP & ANP
In order to see the usage of AHP&ANP and fuzzy AHP&ANP we conduct a literature
review using Scopus database. Keywords “AHP” or “ANP” and not “fuzzy”; “fuzzy” and
“AHP” or “ANP” are used for this research. The number of papers using AHP and fuzzy
AHP are shown in Fig. 1.

International Symposium on the 1 WEB CONFERENCE

Analytic Hierarchy Process DEC. 15 – DEC. 18, 2022
ISAHP Article: A Style Guide for Paper Proposals To Be Submitted to the International Symposium
on the Analytic Hierarchy Process 2022, Web Conference.

Fig. 1: AHP, ANP, fuzzy AHP and fuzzy ANP papers in the literature
Fig.1 shows us that AHP & ANP methods have been widely used in the literature, whereas
the usage of fuzzy AHP and fuzzy ANP is limited. AHP and fuzzy AHP both have been
used more frequently when they are compared with ANP. Table 1. shows the publications
that frequently publish AHP&ANP and fuzzy AHP&ANP.

Table 1. The publications that frequently publish AHP&ANP and fuzzy AHP&ANP
The publications that frequently publish AHP & ANP The publications that frequently publish fuzzy AHP & ANP
Sustainability Switzerland Applied Mechanics And Materials
Advanced Materials Research Expert Systems With Applications
Applied Mechanics And Materials Advanced Materials Research
Journal Of Physics Conference Series Advances In Intelligent Systems And Computing
Lecture Notes In Computer Science Including Subseries
Lecture Notes In Artificial Intelligence And Lecture Notes
In Bioinformatics Sustainability Switzerland

Iop Conference Series Materials Science And Engineering Journal Of Intelligent And Fuzzy Systems
Journal Of Neurophysiology Mathematical Problems In Engineering
Advances In Intelligent Systems And Computing Journal Of Cleaner Production
Lecture Notes In Computer Science Including Subseries
Lecture Notes In Artificial Intelligence And Lecture Notes In
European Journal Of Operational Research Bioinformatics
Lecture Notes In Electrical Engineering Iop Conference Series Materials Science And Engineering
Journal Of Cleaner Production Lecture Notes In Electrical Engineering
Journal Of Physiology Applied Soft Computing Journal
Expert Systems With Applications IEEE Access
Environmental Earth Sciences Lecture Notes In Networks And Systems
Communications In Computer And Information Science Soft Computing
Energies Environmental Science And Pollution Research
Water Switzerland International Journal Of Production Research
Mathematical Problems In Engineering Communications In Computer And Information Science
Arabian Journal Of Geosciences Computers And Industrial Engineering
Procedia Engineering Environmental Earth Sciences

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ISAHP Article: A Style Guide for Paper Proposals To Be Submitted to the International Symposium
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Applied Sciences Switzerland International Journal Of Advanced Manufacturing Technology

Energy Journal Of Multiple Valued Logic And Soft Computing
Journal Of Multi Criteria Decision Analysis Mathematics
Lecture Notes In Mechanical Engineering Arabian Journal Of Geosciences
Natural Hazards Energies
International Journal Of The Analytic Hierarchy Process Technological And Economic Development Of Economy
Environmental Science And Pollution Research Symmetry
Brain Research Decision Science Letters
International Journal Of Advanced Manufacturing
Technology Energy
Journal Of Neuroscience Information Sciences

When we look at Table 1, we see that both AHP &ANP and fuzzy AHP & ANP papers
have been published in various fields including energy, sustainability and medical sciences.
Yet, fuzzy AHP and ANP have also been published in the computing papers where new
versions of fuzzy AHP & ANP are the focus of the study.

3. Literature review on fuzzy extensions of AHP and ANP

In the literature, several studies utilize the extensions of fuzzy sets to modify AHP and
ANP. Cevik Onar et al. (2014) use interval type-2 fuzzy AHP for a strategic decision
process. Otay et al. (2017) evaluate the healthcare institutions using intuitionistic fuzzy
AHP. Bolturk et al. use hesitant fuzzy AHP for warehouse location selection in
humanitarian logistics. Kahraman et al. (2018) utilize hesitant fuzzy linguistic AHP for
B2C marketplace prioritization. Cevik Onar et al. (2020) evaluation legal debt collection
services by using Hesitant Pythagorean (Intuitionistic Type 2) fuzzy AHP. Oztaysi et al.
(2020) use spherical fuzzy AHP for location-based advertisement selection. Figure 2 shows
the studies that uses most popular fuzzy extensions for modifying AHP and ANP methods.

Fig 2: Number of AHP &ANP papers which use fuzzy extensions

4. Conclusion and Further Suggestions

In this study, we develop a brief perception on the usage of AHP & ANP, fuzzy AHP &
ANP, extensions of fuzzy AHP & ANP. Both AHP & ANP and fuzzy AHP & ANP
methodologies are widely used in the literature and the usage is still increasing in various
areas. Although the methodology and computation of classical AHP & ANP is rather
International Symposium on the 3 WEB CONFERENCE
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ISAHP Article: A Style Guide for Paper Proposals To Be Submitted to the International Symposium
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similar, there are many new fuzzy AHP & ANP methodologies in the literature. Especially
extensions of fuzzy sets have been used for this objective.

5. Key References

Atanassov K. (1986) Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20, pp. 87-96 .
Boltürk, E., Cevik Onar, S., Oztaysi, B., Kahraman C, K Goztepe (2016) Multi-attribute
warehouse location selection in humanitarian logistics using hesitant fuzzy AHP,
International Journal of the Analytic Hierarchy Process 8 (2), 271-298
Cevik Onar S., Oztaysi B., Kahraman C. (2020) Evaluation of legal debt collection
services by using Hesitant Pythagorean (Intuitionistic Type 2) fuzzy AHP, Journal of
Intelligent & Fuzzy Systems 38 (1), 883-894
Cevik Onar, S., Oztaysi, B., Kahraman C. (2014) Strategic decision selection using
hesitant fuzzy TOPSIS and interval type-2 fuzzy AHP: a case study, International Journal
of Computational intelligence systems 7 (5), 1002-1021
Cuong B. (2014), Picture fuzzy sets, Journal of Computer Science and Cybernetics, 30 (4)
(2014) 409–420.
Kahraman C, Cevik Onar, S., Oztaysi, B., 2018, B2C marketplace prioritization using
hesitant fuzzy linguistic AHP, International Journal of Fuzzy Systems 20 (7), 2202-2215
Kutlu Gündoğdu F., Kahraman C.(2019), Spherical fuzzy sets and spherical fuzzy TOPSIS
method, Journal of Intelligent & Fuzzy Systems, 36 (1) 337-352.
Onar S.C., Oztaysi B., Kahraman C. (2020) Evaluation of legal debt collection services by
using Hesitant Pythagorean (Intuitionistic Type 2) fuzzy AHP, Journal of Intelligent &
Fuzzy Systems 38 (1), 883-894
Otay, I. Oztaysi, B., Cevik Onar, S., Kahraman C (2017) Multi-expert performance
evaluation of healthcare institutions using an integrated intuitionistic fuzzy AHP&DEA
methodology Knowledge-Based Systems 133, 90-106
Oztaysi B., Onar S.C., Gündogdu F.K., Kahraman C. (2020), Location Based
Advertisement Selection using Spherical Fuzzy AHP-VIKOR, Journal of Multiple-Valued
Logic & Soft Computing 35
Torra V. (2010), Hesitant fuzzy sets, International Journal of Intelligent Systems, 25 (6)
529-539.
Yager R. (2013), Pythagorean fuzzy subsets, in Proceedings of the 2013 Joint IFSA World
Congress and NAFIPS Annual Meeting, IFSA/NAFIPS 2013, (2013).
Yager R. (2017), Generalized orthopair fuzzy sets, IEEE Transactions on Fuzzy Systems,
25 (5),1222-1230.
Zadeh, L.A. (1965) Fuzzy sets, Information and Control, 8(3), 338-353,
Zadeh, L.A. (1975) “The concept of a linguistic variable and its application to approximate
reasoning, Parts 1, 2, and 3,” Information Sciences, 1975, 8:199-249, 8:301-357, 9: 43-80.

International Symposium on the 4 WEB CONFERENCE

Analytic Hierarchy Process DEC. 15 – DEC. 18, 2022
Global Journal of Pure and Applied Mathematics.
ISSN 0973-1768 Volume 13, Number 6 (2017), pp. 1619-1630
© Research India Publications
http://www.ripublication.com

A Study on Fuzzy AHP method and its applications in

a “tie-breaking procedure”

1Iftikhar, 2Musheer Ahmad and 3Anwar Shahzad Siddiqui

1,2
Department of Applied Sciences and Humanities
3
Department of Electrical Engineering
Faculty of Engineering and Technology
Jamia Millia Islamia, New Delhi-110025, India.

Abstract

The situations in which two or more participants in a competition are equally

placed, known as tie-situations. To break the tie situations, the tie break
procedures or tiebreakers are developed for finding the ordering relation or
ranking among the participants. In this paper, a new methodology or approach
is proposed for dealing with the tie-situation, which is based on fuzzy
analytical hierarchy process (Fuzzy AHP) with use of triangular fuzzy
numbers for the pairwise comparison matrices. Then the extent analysis
method (EAM) [7] is used for determining the fuzzy synthetic extent values
and applying the method of comparison of fuzzy numbers for calculating the
normalized weight vectors. Finally, the final score for each student can
obtained. The working of proposed approach is illustrated with the help of a
numerical example.

Keywords: Fuzzy AHP; Triangular fuzzy numbers; Extent analysis method;

Synthetic extent values; Pairwise comparison matrices.

2010 Mathematics Subject Classification: 62C86, 90B50

1620 Iftikhar, Musheer Ahmad and Anwar Shahzad Siddiqui

1. INTRODUCTION

The Analytical Hierarchy Process (AHP) is one of the methods of multi-criteria

decision making (MCDM) developed by Saaty (1980). AHP is a structured technique
for organizing and analyzing complex decisions or issues which involves subjective
judgments. In other words, an AHP is a traditional powerful decision making
technique in order to determining priorities among different criteria, comparing the
decision alternatives for each criterion and determining an overall ranking of the
decision alternatives. The main advantages of AHP are handling multiple criteria,
easy to understand and effectively dealing with both qualitative and quantitative data.
In the real world, most of the information or data obtained from experts included
uncertainty and vagueness because of the incomplete information, impreciseness of
human judgments and uncertainty of decision environment. The combine effect of
fuzzy set theory and analytical hierarchy process gives fuzzy analytical hierarchy
process (Fuzzy AHP) as a more powerful methodology for multi-criteria decision
making (MCDM). Hence, it can be concluded that Fuzzy AHP will find more
applications than conventional AHP in the near future. There are many scientific
approaches for deriving the weights (crisp or fuzzy) from fuzzy pairwise comparison
matrices. Since fuzzy weights are not as easy to compute as crisp weights, then the
majority of Fuzzy AHP applications use a simple extent analysis method proposed by
Chang [7]. Likewise an AHP, fuzzy AHP provides a hierarchical structure, facilitates
the decompositions and pairwise comparisons, reduces the inconsistency and
generates the priority vectors. Also, a fuzzy AHP can solve and support spatial
reasoning problems in a number of different context such as: locating convenience
stores and other facilities (Kuo et al., 1999, 2002; Partovi, 2006), hospital site
selection (Chi and Kuo, 2001; Witlox, 2003; H. Vahidnia and A. Alesheikh, 2009),
screening potential landfill sites (Charnpratheep et al., 1997), supplier selection
(Kahraman et al., 2003) and local park planning (Zucca et al., 2008). In the present
work, the Fuzzy AHP method will be employed for breaking the tie situation and
deciding the rank among the students, when they have obtained the same marks in a
competitive examination. This paper is organized as follows: The basic concepts or
preliminaries of fuzzy set theory and Fuzzy AHP method are presented in Section 2.
Section 3 deals with the method of fuzzy numbers for pairwise comparisons. In
Section 4, an idea is proposed for determining the priority vectors. In section 5 a
numerical example in solved for illustrating the working process of proposed
methodology. The results and conclusions are stated in Section 6.
A Study on Fuzzy AHP method and its applications in a “tie-breaking procedure” 1621

2. PRELIMINARIES

This section contains some basic definitions of fuzzy set theory, classical AHP and
Fuzzy AHP.

2.1. Fuzzy numbers

Definition 1. Let 𝑀 ∈ F(R) be called a fuzzy number, if the following two conditions
are satisfied

(1) There exists 𝑥0 ∈ 𝑅 such that 𝜇𝑀 (𝑥0 ) = 1.

(2) For any 0 ≤ α ≤ 1, 𝐴𝛼 = [𝑥, 𝜇𝐴𝛼 (𝑥) ≥ 𝛼] is a closed interval.

where F(R) represents a family of all fuzzy sets and R is the set of real numbers.

Definition 2. A fuzzy number M on R is said to be a triangular fuzzy number if its

membership function 𝜇𝑀 (𝑥): 𝑅 → [0,1] is defined as follows:
𝑥−𝑙
,𝑙 ≤ 𝑥 ≤ 𝑚
𝑚−𝑙
𝜇𝑀 ( 𝑥) = {−𝑥+𝑢 ,𝑚 ≤ 𝑥 ≤ 𝑢 (1)
𝑢−𝑚
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

where l and u stand for the lower and upper value of the support of M respectively,
and m represent the modal value. The triangular fuzzy numbers can be denoted by
order triplet (l, m, u) of real numbers or regular numbers. The support of M is the set
of elements{𝑥 ∈ 𝑅\𝑙 < 𝑥 < 𝑢}.

Definition 3. Consider any two triangular fuzzy numbers 𝑀1 = (𝑙1 , 𝑚1 , 𝑢1 ) and 𝑀2 =

(𝑙2 , 𝑚2 , 𝑢2 ) then the following arithmetic operations can be defined as follows:

(1) (𝑙1 , 𝑚1 , 𝑢1 ) ⊕ (𝑙2 , 𝑚2 , 𝑢2 ) = (𝑙1 + 𝑙2 , 𝑚1 + 𝑚2 , 𝑢1 + 𝑢2 ).

(2) (𝑙1 , 𝑚1 , 𝑢1 ) ⊗ (𝑙2 , 𝑚2 , 𝑢2 ) = (𝑙1 𝑙2 , 𝑚1 𝑚2 , 𝑢1 𝑢2 ).
(3) 𝑘(𝑙1 , 𝑚1 , 𝑢1 ) = (𝑘𝑙1 , 𝑘𝑚1 , 𝑘𝑢1 ), 𝑘 > 0, 𝑘 ∈ 𝑅.
1 1 1
(4) (𝑙1 , 𝑚1 , 𝑢1 )−1 = (𝑢 , 𝑚 , 𝑙 ) , 𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 𝑙1 ≠ 0, 𝑚1 ≠ 0, 𝑢1 ≠ 0.
1 1 1
1622 Iftikhar, Musheer Ahmad and Anwar Shahzad Siddiqui

2.2. Classical AHP method

Definition 4. AHP is a multi-criteria decision making tool in order to determine the

priorities among different decision criteria, comparing decision alternatives for each
criterion and obtaining an overall ranking of the decision alternatives. The final
outcomes of an AHP are to decide best among the decision alternatives. The method
for AHP consists of the following four steps (See Zahedi, 1986 [19]).

(1) Decomposing the decision problem into a hierarchy.

(2) Obtaining the judgmental matrix by making pairwise comparisons.
(3) Evaluating the local weights and consistency of the comparisons.
(4) Aggregation of local weights to obtain scores and ranking the alternatives.

2.3. Fuzzy AHP method

Definition 5. The classical AHP is insufficient for dealing with fuzziness and
uncertainty in multi-criteria decision making (MCDM), because of incomplete
information, impreciseness of human judgments and fuzzy environment. Hence, the
fuzzy AHP technique can be viewed as an advanced analytical method developed
from the classical AHP. The method for fuzzy AHP consists of the following six
steps:

(1) Development of the problem hierarchy.

(2) Obtaining the fuzzy comparison matrices.
(3) Calculation of fuzzy synthetic extents.
(4) Comparison of fuzzy synthetic extents
(5) Evaluation of the minimum degree of possibilities.
(6) Normalization of weight vectors.

2.4. Fuzzy synthetic extent values

Definition 6. Let 𝑋 = {𝑥1 , 𝑥2 , … , 𝑥𝑛 } be an object set and 𝑈 = {𝑢1 , 𝑢2 , … , 𝑢𝑚 } be a

goal set. Then using the method of extent analysis, each object is taken and performs
extent analysis for each goal respectively. Therefore, we have m extent analysis
values for each object with the following notations:
1 2 𝑚
𝑀𝑔𝑖 , 𝑀𝑔𝑖 , … , 𝑀𝑔𝑖 , 𝑖 = 1, 2, … , 𝑛

𝑗
where all the 𝑀𝑔𝑖 (𝑗 = 1, 2, … , 𝑚) are triangular fuzzy numbers.
A Study on Fuzzy AHP method and its applications in a “tie-breaking procedure” 1623

1 2 𝑚
Definition 7. Let 𝑀𝑔𝑖 , 𝑀𝑔𝑖 , … , 𝑀𝑔𝑖 be values of extent analysis of the 𝑖 𝑡ℎ object for m
goals. Then the value of fuzzy synthetic extent with respect to 𝑖 𝑡ℎ object can be
determined by using the algebraic operations on triangular fuzzy numbers as follows:

𝑗 𝑗 −1
𝑆𝑖 = ∑𝑚 𝑛 𝑚
𝑗=1 𝑀𝑔𝑖 ⊗[∑𝑖=1 ∑𝑗=1 𝑀𝑔𝑖 ] (2)

3. CHANG’S EXTENT ANALYSIS METHOD

The Chang’s extent analysis on Fuzzy AHP is based on degree of possibilities of each
criterion. Firstly, triangular fuzzy numbers are taken into consideration for the
pairwise comparison scale of Fuzzy AHP. Afterwards, the following steps of Chang’s
analysis are used in order to complete the whole procedure

Step1. The fuzzy synthetic extent values for 𝑖 𝑡ℎ object can be computed using
𝑗 𝑗 −1
equation (2), which involves computation of ∑𝑚 𝑛 𝑚
𝑗=1 𝑀𝑔𝑖 and [∑𝑖=1 ∑𝑗=1 𝑀𝑔𝑖 ] .

Step2. The degree of possibility of 𝑀2 greater than equal to 𝑀1 is defined as

follows:

𝑉(𝑀2 ≥ 𝑀1 ) = max[min( 𝜇𝑀1 (𝑥), 𝜇𝑀2 (𝑦) )] (3)

𝑦≥𝑥

where x and y are the values on the axis of membership function of each criterion.
This expression can be equivalently written as follows:

1, 𝑖𝑓𝑚2 ≥ 𝑚1
𝑉(𝑀2 ≥ 𝑀1 ) = { 0, 𝑖𝑓 𝑙1 ≥ 𝑢2 (4)
𝑙1 −𝑢2
(𝑚2 −𝑢2 )−(𝑚1 −𝑙1 )
, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Step3. The degree of possibility for a convex fuzzy number 𝑀 to be greater than k
convex fuzzy numbers 𝑀𝑖 (i=1, 2, 3, …, k) can be defined as follows:

𝑉(𝑀 ≥ 𝑀1 , 𝑀2 , … , 𝑀𝑘 ) = 𝑉[(𝑀 ≥ 𝑀1 )⋀(𝑀 ≥ 𝑀2 )⋀ … ⋀(𝑀 ≥ 𝑀𝑘 )]

= min 𝑉(𝑀 ≥ 𝑀𝑖 ) , 𝑖 = 1,2, … , 𝑘

(5)

Step4. Assume that 𝑑′ (𝐴𝑖 ) = min 𝑉(𝑆𝑖 ≥ 𝑆𝑘 ) for 𝑘 = 1,2, … , 𝑛; 𝑘 ≠ 𝑖. Then the
weight vector is given by
𝑇
𝑊 ′ = (𝑑′ (𝐴1 ), 𝑑 ′ (𝐴2 ), … , 𝑑 ′ (𝐴𝑛 )) (6)
1624 Iftikhar, Musheer Ahmad and Anwar Shahzad Siddiqui

where 𝐴𝑖 (𝑖 = 1,2, … , 𝑛 ) are n elements.

Step5. Then via normalization process, we have obtained the following normalized
weight vectors
𝑇
𝑊 = (𝑑(A1 ), 𝑑(A2 ), … , 𝑑(An )) (7)

4. NUMERICAL EXAMPLE

Suppose that at a university in a competitive examination, the three students obtained

the same marks. We will call them𝑆𝑇1 , 𝑆𝑇2 and𝑆𝑇3 . A committee has formed for
finding the ordering relation or deciding the rank among students. The committee has
three members and they have identified the following decision criteria:

𝐷𝐶1 -Academic performance.

𝐷𝐶2 - Self confidence.

𝐷𝐶3 -Ability to deal with complex problems.

𝐷𝐶4 -Human maturity.

First level of decision criteria

According to the step 2 of fuzzy AHP, the fuzzy pairwise comparison matrix Ɍ is
constructed (See Table 1)

Table 1: The fuzzy pairwise comparison matrix Ɍ of decision criteria

𝐷𝐶1 𝐷𝐶2 𝐷𝐶3 𝐷𝐶4 𝑊𝐶

𝐷𝐶1 (1, 1, 1) (0.9, 1.2, 1.5) (0.6, 1, 1.4) (0.35, 0.45, 0.55) 0.17

𝐷𝐶2 (0.5, 0.8, 1.1) (1, 1, 1) (2.49, 2.99, 3.49) (0.8, 1.3, 1.8) 0.32

𝐷𝐶3 (0.7, 1.1, 1.5) (0.23, 0.3, 0.37) (1, 1, 1) (0.32, 0.49, 0.66) 0.46

𝐷𝐶4 (2.4, 2.8, 3.2) (0.4, 0.7, 1) (1.7, 2.1, 2.5) (1, 1, 1) 0.41
A Study on Fuzzy AHP method and its applications in a “tie-breaking procedure” 1625

By using formula (7), we can obtained the following fuzzy synthetic extent values

1 1 1
𝑆1 = (2.85, 3.65, 4.45)( , , ) = (0.123, 0.20, 0.31)
23.07 18.23 14.39
1 1 1
𝑆2 = (4.79, 5.09, 7.39)(23.07 , 18.23 , 14.39) = (0.21, 0.28, 0.51)

1 1 1
𝑆3 = (2.25, 2.89, 3.47)(23.07 , 18.23 , 14.39) = (0.1, 0.16 ,0.24 )

1 1 1
𝑆4 = (4.5, 6.6, 7.7)( , , ) = (0.19, 0.36, 0.53)
23.07 18.23 14.39

The degree of possibility for comparison of any two fuzzy synthetic extent values is
defined as follows:

0.21 − 0.31
𝑉(𝑆1 ≥ 𝑆2 ) = = 0.55
(0.20 − 0.31) − (0.28 − 0.21)

𝑉(𝑆1 ≥ 𝑆3 ) = 1

0.19 − 0.31
𝑉(𝑆1 ≥ 𝑆4 ) = = 0.43
(0.20 − 0.31) − (0.36 − 0.19)

𝑉(𝑆2 ≥ 𝑆1 ) = 1 , 𝑉(𝑆2 ≥ 𝑆3 ) = 1

0.19 − 0.51
𝑉(𝑆2 ≥ 𝑆4 ) = = 0.8
(0.28 − 0.51) − (0.36 − 0.19)

0.123 − 0.24
𝑉(𝑆3 ≥ 𝑆1 ) = = 0.74
(0.16 − 0.24) − (0.20 − 0.123)

0.21 − 0.24
𝑉(𝑆3 ≥ 𝑆2 ) = = 0.2
(0.16 − 0.24) − (0.28 − 0.21)

0.19 − 0.24
𝑉(𝑆3 ≥ 𝑆4 ) = = 0.2
(0.16 − 0.24) − (0.36 − 0.19)

𝑉(𝑆4 ≥ 𝑆1 ) = 1, 𝑉(𝑆4 ≥ 𝑆2 ) = 1, 𝑉(𝑆4 ≥ 𝑆3 ) = 1

1626 Iftikhar, Musheer Ahmad and Anwar Shahzad Siddiqui

Using these values the minimum degree of possibilities are calculated as follows:

𝑑 ′ (DC1 ) = 𝑉(𝑆1 ≥ 𝑆2 , 𝑆3 , 𝑆4 ) = 𝑚𝑖𝑛(0.55,1,0.43) = 0.43

𝑑 ′ (DC2 ) = 𝑉(𝑆2 ≥ 𝑆1 , 𝑆3 , 𝑆4 ) = 𝑚𝑖𝑛(1, 1, 0.8) = 0.8

𝑑 ′ (DC3 ) = 𝑉(𝑆3 ≥ 𝑆1 , 𝑆2 , 𝑆4 ) = 𝑚𝑖𝑛(0.74, 0.2, 0.2) = 0.2

𝑑 ′ (𝐷C4 ) = 𝑉(𝑆4 ≥ 𝑆1 , 𝑆2 , 𝑆3 ) = 𝑚𝑖𝑛( 1, 1, 1) = 1

Therefore, the weight vectors can be generated as:

𝑇
𝑊 ′ = (𝑑 ′ (DC1 ), 𝑑′ (DC2 ), 𝑑′ (𝐷C3 )) = (0.43, 0.8, 0.2, 1)𝑇

Via normalization, the normalized weight vectors for the decision criteriaDC1 , DC2 ,
DC3 and DC4 are calculated as follows:

𝑊′
𝑊= 𝑛 = (0.17,0.32,0.46,0.41)𝑇
∑𝑖=1 𝑑′ (DCi )

Second level of decision criteria

At the second level, the committee compares students 𝑆𝑇1 , 𝑆𝑇2 and 𝑆𝑇3 for each
criteria separately and formed the fuzzy comparison matricesɌ1 , Ɍ2 , Ɍ3 and Ɍ4 as
listed below(See Tables 2-5)

Table 2: The fuzzy pairwise comparison matrix Ɍ1 of alternatives under decision

criteria-DC1

Criteria-𝐷C1 𝑆𝑇1 𝑆𝑇2 𝑆𝑇3 𝑊𝐷𝐶1

𝑆𝑇1 (1, 1, 1) (0.6, 1, 1.4) (0.55, 0.75, 1.2) 0.28

𝑆𝑇2 (0.6, 1, 1.4) (1, 1, 1) (0.45, 0.55, 0.65) 0.21
𝑆𝑇3 (0.9, 1.32, 1.84) (1.4, 2, 2.6 ) (1, 1, 1) 0.5
A Study on Fuzzy AHP method and its applications in a “tie-breaking procedure” 1627

Table 3: The fuzzy pairwise comparison matrix Ɍ2 for the alternatives under the
decision criteria-DC2

Criteria-DC2 𝑆𝑇1 𝑆𝑇2 𝑆𝑇3

𝑆𝑇1 (1, 1, 1) (2.8, 3, 3.2) (1.8, 2.2, 2.6)
𝑆𝑇2 (2.5, 3, 3.5) (1, 1, 1) (0.8, 1, 1.2)
𝑆𝑇3 (0.4, 0.5, 0.6) (0.8, 1, 1.2) (1, 1, 1)

In Table 3, there are some elements such that 𝑙𝑖 − 𝑢𝑗 > 0, then the elements of the
given matrix must be normalized in order to find the fuzzy synthetic extent values,
minimum degree of possibilities and determining the normalized weight vectors.

Table𝟑′ : The normalized fuzzy pairwise comparison matrix R′ 2 for the alternatives
under decision criteria- DC2

Criteria-DC2 𝑆𝑇1 𝑆𝑇2 𝑆𝑇3 𝑊𝐷𝐶2

𝑆𝑇1 (0.33, 0.33, 0.34) (0.31, 0.33, 0.36) (0.27, 0.33, 0.40) 0.33
𝑆𝑇2 (0.27, 0.34, 0.39) (0.33, 0.33, 0.34) (0.26, 0.33, 0.41) 0.35
𝑆𝑇3 (0.2, 0.3, 0.5) (0.26, 0.33, 0.41) (0.33, 0.33, 0.34) 0.32

Table 4: The fuzzy pairwise comparison matrix Ɍ3 for the alternatives under the
decision criteria-DC3

Criteria-DC3 𝑆𝑇1 𝑆𝑇2 𝑆𝑇3

𝑆𝑇1 (1, 1, 1) (2.1, 2.6, 3.1) (2.7, 3.1, 3.5)
𝑆𝑇2 (0.3, 1.1, 1.4) (1, 1, 1) (0.6, 1.2, 1.8)
𝑆𝑇3 (0.65, 0.8, 0.95) (0.63, 1, 1.4) (1, 1, 1)

Similarly, there are some elements in Table 4 such that 𝑙𝑖 − 𝑢𝑗 > 0, then the elements
of the given matrix must be normalized in order to find the fuzzy synthetic extent
values, minimum degree of possibilities and determining the normalized weight
vectors.
1628 Iftikhar, Musheer Ahmad and Anwar Shahzad Siddiqui

Table𝟒′ : The normalized fuzzy pairwise comparison matrix R′ 3 for the alternatives
under the decision criteria-DC3

Criteria-𝐷C3 𝑆𝑇1 𝑆𝑇2 𝑆𝑇3 𝑊𝐷𝐶3

𝑆𝑇1 (0.33, 0.33, 0.34) (0.27, 0.33, 0.4) (0.29, 0.33, 0.38) 0.32
𝑆𝑇2 (0.11, 0.39, 0.5) (0.33, 0.33, 0.34) (0.16, 0.34, 0.5) 0.35
𝑆𝑇3 (0.27, 0.33, 0.4) (0.2, 0.34, 0.46) (0.33, 0.33, 0.34) 0.33

Table 5: The fuzzy pairwise comparison matrix Ɍ4 for the alternatives under the
decision criteria-DC4

Criteria-𝐷C4 𝑆𝑇1 𝑆𝑇2 𝑆𝑇3 𝑊𝐷𝐶4

𝑆𝑇1 (1, 1, 1) (0.9, 1.1, 1.3) (0.95, 1.25, 1.55) 0.34
𝑆𝑇2 (0.55, 0.85, 1.5) (1, 1, 1) (1.7, 2, 2.3) 0.43
𝑆𝑇3 (0.91, 1.25, 1.54) (0.41, 0.52, 0.67) (1, 1, 1) 0.22

Third level of decision criteria

At the third level, the final scores of all the students are obtained by taking the sum of
product of weights per candidate and weights of the corresponding criteria. The
results are shown in the Tables 6 and 7.

Table 6

Criterion\Alternatives 𝑆𝑇1 𝑆𝑇2 𝑆𝑇3

𝐷𝐶1 0.28 0.21 0.50
𝐷𝐶2 0.33 0.35 0.32
𝐷𝐶3 0.32 0.35 0.33
𝐷𝐶4 0.34 0.43 0.22

Table 5

𝑆𝑇1 𝑆𝑇2 𝑆𝑇3

Final Scores 0.44 0.48 0.43
A Study on Fuzzy AHP method and its applications in a “tie-breaking procedure” 1629

5. RESULTS AND CONCLUSIONS

In this work, the Fuzzy AHP method is used for breaking the tie situation and
deciding the rank among the students, when they have obtained the same marks in a
competitive examination. This method of ranking (or ordering relation) between the
students is same as in [5]. According to the obtained final scores (see Table 5), it is
concluded that student 𝑆𝑇2 have obtained rank 1, whereas students 𝑆𝑇1 and 𝑆𝑇3 have
rank 2 and 3, respectively.

6. ACKNOWLEDGEMENT

First author wishes his sincere thanks to CSIR-UGC India, for providing financial
support under Junior Research Fellowship Scheme.

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[1] Liu B, Xu S, Development of the theory and methodology of the Analytic

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[3] R.E. Bellman, L.A. Zadeh, Decision making in fuzzy environment,
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[4] 4 D.Y. Chang, Applications of the extent analysis method on fuzzy AHP,
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[5] P.J.M. Van Laarhoven, W. Pedrycz, A fuzzy extension of Saaty’s priority
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[8] K. J. Zhu and D. Y. Jing, A discussion on extent analysis method and
applications of fuzzy AHP, European Journal of Operational Research,
116(1999)450–456.
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[9] R.V. Rao, D. Singh, Analytic Hierarchy Process (AHP) for the performance
evaluation of technical institutions, The Indian journal of technical education,
25(2002) No.4.
[10] K.B. Reddy, N.H. Ayachit and M.K. Venkatesha, A theoretical method for
performance evaluation of technical institutions - Analytic Hierarchy Process
approach, The Indian journal of technical education, 27(2004) No.1.
[11] J.R. Grandzol, Improving the Faculty Selection Process in Higher Education:
A Case for the Analytic Hierarchy Process, Institutional Research Application,
6 (2005) 1-12
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search the criterion in the evaluation of best technical institutions: A Case
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(2010)2499-2510.
[13] Dipendra Nath Gosh, Analytic Hierarchy process & TOPSIS Method to
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International Journal of Approximate Reasoning 49 (2008) 451–465.
[15] L. Wang, J. Chu, J. Wu, Selection of optimum maintenance strategies based
on a fuzzy analytic hierarchy process, International Journal of Production
Economics 107 (1) (2007) 151–163.
[16] Y.M. Wang, T.M.S. Elhag, Z.S. Hua, A modified fuzzy logarithmic least
squares method for fuzzy analytic hierarchy process, Fuzzy Sets and Systems
157 (23) (2006) 3055–3071.
[17] M. Dagdeviren, I. Yuksel, A fuzzy analytic network process (ANP) model for
measurement of the sectoral competition level (SCL), Expert Systems with
Applications 37 (2010) 1005–1014.
[18] L. Mikhailov, Deriving priorities from fuzzy pairwise comparison judgments,
Fuzzy Sets and Systems 134 (2003) 365–385.
[19] F. Zahedi, The Analytic Hierarchy Process: A Survey of the Method and its
Applications, 16 (1986) 96-108.
[20] T. L. Saaty, The analytic hierarchy process: planning, priority setting, resource
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[21] D. Bouyssou, T. Marchant, M. Pirlot and P. Perny, Evaluation Models: A
Critical Perspective, Kluwer, Boston, (2000).
IJAHP Article: Khan, Ali/Analytical Hierarchy Process (AHP) and Analytic Network Process
methods and their applications: a twenty year review from 2000-2019

ANALYTICAL HIERARCHY PROCESS (AHP) AND ANALYTIC

NETWORK PROCESS METHODS AND THEIR
APPLICATIONS: A TWENTY YEAR REVIEW FROM 2000-2019

Amin Ullah Khan

Ph.D. Scholar at Department of Economics and Law
University of Macerata, Italy
&
Master’s in Engineering Management, Department of Management Science
Ghulam Ishaq Khan Institute of Engineering Sciences & Technology, Topi
Amin.llh@gmail.com

Yousaf Ali Ph.D.

Assistant Professor Department of Management Science
Ghulam Ishaq Khan Institute of Engineering Sciences & Technology Topi, Swabi,
KPK, Pakistan
yousafkhan@giki.edu.pk

ABSTRACT

This research aims to analyze a literature review of publications that have

incorporated the Analytical Hierarchy Process (AHP) and Analytic Network Process
(ANP) methods. The AHP and ANP methods have contributed to decision-making in
complex situations in recent years and possess widespread applications. Such
applications are spread over the years with publications in various major areas such
as engineering/technology/applied sciences, social sciences, health sciences, and
environmental studies. These two methods provide multiple solutions to researchers
in these fields, which is why they are being considered in the current study. For this
purpose, data was collected from 920 research papers after a vigorous literature
review using different search engines. This paper aims to classify the publications on
AHP and ANP methods from the years 2000 to 2019 to identify recognized journals
based on their indexes. Furthermore, another objective of this study is to compare
total publications by year, publications by field by year, and lastly, observe the
distribution by country of the studies. This paper concludes that the highest number
of publications are from Turkey, and the highest number of publications used AHP
method applications in every category. Most of the publications belonged to the
technical fields, followed by social sciences. The study concluded that the AHP
method is more widely preferred by researchers in almost every field and application
because it tends to produce more accurate results than the ANP.

Keywords: decision science; AHP; ANP; applications; literature review

1. Introduction
In the current world, technological advancement has had a positive impact on our
society. With the latest advancements, various fields of study have emerged that have
the possibility to create huge improvements and new developments in the future
(Almannai, Marom, & Sutton, 2016). In the past, there were fewer fields of study,

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methods and their applications: a twenty year review from 2000-2019

such as conventional engineering programs or a general physician in medicine

because things were more straightforward (Sax, et al., 2016). As time has progressed,
various fields have emerged that require demanding research topics and research
methods to cope with complex problems. Such complex situations require solutions
that can provide long-term answers to researchers, and enable them to formulate
conclusions and policies based on the results (Laukkanen, Itkonen, & Lassenius,
2017). Such complex situations create multifacted decision-making scenarios that
need to be dealt with by various experts in the concerned fields. Such decision-
making scenarios require various multi-criteria decision-making (MCDM) techniques
that can handle complex situations and provide logical answers. These analytical
solutions can pave the way for policymakers to formulate their decisions (Kabak,
Burmaoglu, & Kazancoglu, 2012).

MCDM is a tool that is both qualitative and quantitative. It helps evaluate complex
problems and helps decision-makers reach a conclusive decision (Mardani, Jusoh, &
Zavadskas, 2015). It also helps formulate a mathematical tool that can support the
decision and the policymaker’s evaluation of the functioning criteria. Similarly, the
MCDM tool efficiently provides a promising framework based on multiple criteria
evaluation (Wątróbski et al., 2019). The alternatives that are deemed the best are
selected based on proper criteria analysis through various tools (Chen, et al., 2011).
This helps choose a suitable alternative in the form of technology, supplier, or
location, etc. (Nallusamy, Kumar, Balakannan, & Chakraborty, 2016). Furthermore,
MCDM involves both engineering and managerial levels and is considered a dynamic
and complex tool in decision analysis scenarios (Opricovic & Tzeng, 2004).

MCDM techniques are well suited for solving complex problems and are used by
experts in complex decision situations. Different forms of MCDM tools vary from
selecting alternatives based on multiple criteria to relying only on the attributes or
criteria for decision analysis. Some of the MCDM methods are as follows: Analytic
Hierarchy Process (AHP), Analytic Network Process (ANP), Aggregated Indices
Randomization Method (AIRM), Base-criterion method (BCM), Choosing By
Advantages (CBA), Data Envelopment Analysis (DEA), ELECTRE, Goal
Programming (GP), Grey Relational Analysis (GRA), Measuring Attractiveness by a
categorical Based Evaluation Technique (MACBETH), Simple Multi-Attribute
Rating Technique (SMART), New Approach to Appraisal (NATA), PROMETHEE,
Stochastic Multicriteria Acceptability Analysis (SMAA), Technique for the Order of
Prioritization by Similarity to Ideal Solution (TOPSIS), Value Analysis (VA),
VIKOR and Weighted Product Model (WPM), to name a few (Zavadskas & Turskis,
2011, Yang, et al., 2008). These methods address different needs in the form of
alternative selection based on distinct criteria. Similarly, some experts even consider
solving complex situations by only analyzing different criteria. All of the methods
can be applied in different instances according to the purpose they might fulfill for a
specific problem or issue (Chui-Hua, Tzeng, & Lee, 2012). In order to highlight the
different uses of these methods, this paper only considers the AHP and ANP
approaches and reviews their usage from 2000 to 2019. This review is based on the
application of these two methodologies in the four following fields:
engineering/technology/applied sciences, social sciences, health sciences, and
environmental studies.

The Analytical Hierarchy Process (AHP) has been a favorite tool of research experts
from various fields such as engineering, technology, manufacturing, production,
social sciences, etc. It has proved to be a reliable and efficient technique. Experts

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methods and their applications: a twenty year review from 2000-2019

have applied it with various other methodologies to obtain more beneficial results
(Davies, 2001). Professor Thomas L. Saaty developed the AHP in the 1970s to
support researchers who were analyzing complex decision problems (Golden, Wasil,
& Harker, 1989). The AHP is based on a pairwise comparison of the elements in each
level of the hierarchy. Furthermore, it analyzes the alternatives at the lowest level of
the hierarchy to select the best alternative (Saaty and Shang, 2011). In this way,
experts can convert subjective judgments to objective measures (Sipahi & Timor,
2010). Further, to study the AHP method and the areas it has been utilized in, this
paper will review all of the articles published in recognized journals from 2000 to
2019.

The Analytic Network Process (ANP) is currently in the development stage. As the
world progresses, its uses will increase as further improvisations are made. Professor
Thomas L. Saaty also developed the ANP in 1996 (Saaty, 2001) which is considered
a more general form of the AHP. The ANP helps solve more complex situations,
relationships, and interdependencies and even provides feedback among the elements
in the hierarchy. ANP applications can also be found in various fields such as
engineering, social sciences, and environmental studies and provide a more in-depth
focus on the risk and uncertainty (Sipahi & Timor, 2010).

The purpose of reviewing the AHP and ANP methods in this study is to identify the
publications that have employed these two methodologies separately or with other
tools in prominent journals. Furthermore, this study's main purpose is to review the
studies that were published in prominent journals using AHP and ANP
methodologies from 2000 to 2019. The main information that the study seeks to
discover includes: (1) Determining the total number of publications where each tool
is discussed; (2) Determining the total number of publications where each tool is
discussed per year; (3) Determining the total number of publications where each tool
is used in four different sectors, i.e., engineering/technology/applied sciences, social
sciences, health care, and environmental studies; (4) Identifying and determining the
different journal indexes that publish journals that have papers related to each tool
and (5) Determining the total number of published articles in each country in
descending order (using the country of the first author). Further sections of this paper
comprise the literature review, followed by the methodology, results, discussion, and
conclusion.

2. Literature review
Multi-criteria decision-making techniques enable researchers and experts to make
decisions about qualitative and quantitative scenarios that leave no room for doubt
about the experts' decisions that were based on the comprehensive analysis carried
out on vigorously collected data (Bonissone, Subbu, & Lizzi, 2009). Different
MCDM techniques offer different solutions based on their applications and according
to a specific situation's required solution. Some of the most common MCDM
techniques that are applied in current research studies include ELECTRE (Roy,
1968), Grey Relational Analysis (GRA) (Deng, 1989), PROMETHEE (Brans &
Vincke, 1985), Technique for the Order of Prioritization by Similarity to Ideal
Solution (TOPSIS) (Hwang & Yoon, 1995), VIKOR (Opricovic & Tzeng, 2004),
AHP and ANP.

MCDM techniques help make decisions in a complicated decision-making situation.

They help resolve complex scenarios based on multiple different criteria and

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methods and their applications: a twenty year review from 2000-2019

attributes and choose the best and most efficient alternative. Such techniques have
had many applications in different research areas and are applied according to the
specific requirements of each study. One such technique, the ELECTRE method has
different applications in the fields of web-based applications (Yanie, et al., 2018),
mobile applications (Aggarwal, Grover, & Ahuja, 2019), supplier selection (Ozturk,
Pekel, & Elevli, 2018), and many more. Similarly, the Grey Relational Analysis
method also has various applications in different situations. Such applications include
the case of energy sources evaluation (Ayag & Samanlioglu, 2019), electrochemical
discharge machining optimization (Garg, Singh, & Singh, 2019), and ERP package
evaluation (Ayag & Yucekaya, 2019). Furthermore, another famous MCDM tool is
the PROMETHEE technique which has been recently applied in the areas of material
selection (Gul, Celik, Gumus, & Guneri, 2018), medical imaging (Ozsahin, Sharif,
Ozsahin, & Uzun, 2019), and the urban regeneration process (Bottero, D'Alpaos, &
Oppio, 2018). Some of the most famous techniques such as TOPSIS and VIKOR
have vigorous applications and are being used worldwide. Some of the most recent
applications of TOPSIS can be found in the fields of technology (Aloini, Dulmin,
Mininno, Pellegrini, & Farina, 2018), ISO quality management systems (Gokpinar,
Tansel, & Yurdakul, 2019), and the agriculture sector (Seyedmohammadi,
Sarmadian, Jafarzadeh, Ghorbani, & Shahbazi, 2018). Similarly, VIKOR also has
applications in major areas such as waste management (Gundogdu, Kahraman, &
Karasan, 2019), financial failure analysis (Apan, Oztel, & Islamoglu, 2018), and
hospital care (Chen T.-Y. , 2018).

The most important methodologies that will be reviewed in this paper are the AHP
and ANP. Thomas L. Saaty developed the AHP in the early 1970s, and it has been
widely implemented in numerous studies since then. The AHP is considered one of
the most widely used MCDM methods and is a preference of researchers in complex
decision-making (Yang, et al., 2019). The AHP’s purpose is to analyze complex
scenarios and support experts in their efforts to make the best decision based on their
obtained priorities. Similarly, the AHP also helps manage the consistency of the data
and identify inconsistencies. Inconsistent data results in faulty and inauthentic
conclusions (Wang, Yue, Gao, & Chen, 2018). The AHP’s applications can be found
in various decision-making studies in many different fields. One study conducted by
Zohoori, Vahedi, Meo, & Sorrentino (2016) targeted the area of wind farm
applications using the improved AHP method and deduced solutions for the
suggested applications. Furthermore, another study highlighted the issue of landfills
for a site in Iraq by using AHP and GIS applications, proving the adaptability of AHP
when used with other methodologies (Chabuk, et al., 2017). Similarly, the AHP’s
applications can also be found in the construction industry. One study aimed to
provide augmented solutions for the industry to make them feasible in the long term
(Darko, et al., 2019). Furthermore, it has been applied in 3D technology for cultural
heritage applications (Angelo, Stefano, Fratocchi, & Marzola, 2018). The AHP
technique's applications have also been extended for use in maintenance areas of
production focusing on the automotive industry (Shinde & Prasad, 2018). Similarly,
the AHP has been used in plant site selection for solar PV (photovoltaic) focusing on
efficient transmission lines in urban cities (Garni & Awasthi, 2017). The AHP has
also been implemented to improve recommended projects in an electricity generating
company (Ezzabadi, Saryazdi, & Mostafeipour, 2015). Lastly, the AHP is not limited
to technological applications. For example, one study employed the AHP for store
location selection in Turkey (Koc & Burhan, 2015).

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methods and their applications: a twenty year review from 2000-2019

The ANP was also developed by Thomas L. Saaty (Saaty T. L., 2004). The ANP
formulates a specific problem into a network instead of converting it into a hierarchy
process as in the AHP. The purpose of the ANP is to select the best alternative based
on multiple decision criteria. Such a decision is carried out by pair comparison of the
weights of the components which leads to the selection of an alternative in a decision-
making scenario (Ayag & Ozdemir, 2009). One application of the ANP is in the
Internet of Things (IoT) for security features in the specified field. The ANP method
helped evaluate security features and arrangements for the IoT industry (Hinduja &
Pandey, 2020). Similarly, another study employed the ANP in European countries for
the implementation of information and communication technologies (ICT) (Becker,
Becker, Sulikowski, & Zdziebko, 2018). Another study highlighted the hurdles that
SMEs might face in industry 4.0 application implementation using the ANP
methodology (Sevinc, Gur, & Eren, 2018). Furthermore, the ANP also has
applications in the area of sustainability and decision-making scenarios (Shen &
Tzeng, 2018). Lastly, Zegordi, Nik, & Nazari (2012) employed fuzzy ANP and fuzzy
TOPSIS for risk assessment in a power plant project. The hybrid methodologies were
applied to study the factors that can be risky in the functioning of the power plant.

This study aims to review all of the publications involving AHP/ANP in

internationally recognized journals based on four different categories. The aim is to
highlight the applications of the AHP and ANP techniques in these four fields from
2000 to 2019. Based on the review of these papers, we will determine which
technique is more trustworthy for analysis. That goal and the research questions
defined in the introduction formulate the novelty of this study.

3. Methodology
This paper's data collection consisted of a vigorous literature review from papers that
were published in recognized international journals. The data was extracted using the
four different search engines mentioned below:

 Researchgate
 Science Direct
 Google Scholar
 Microsoft Academic

The recognized journals were selected based on the following indexes:

 Science Citation Index Expanded (SCIE)

 Social Sciences Citation Index (SSCI)
 Emerging Sources Citation Index (ESCI) and
 Scopus

The journal index is defined as the uniqueness allotted to the journals based on
authenticity in their respective fields, i.e., engineering, social sciences, emerging
sciences, and Scopus database (Mongeon & Paul-Hus, 2016). The methodology of
this study is shown in Figure 1.

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methods and their applications: a twenty year review from 2000-2019

Divide the
Literature review Divide the
Formlulation of publicatons based
from search publicatons based
publications on year-wise
engines for AHP on overall
database distrubtion for
& ANP tools publications
both tools

Divide the
Divide the
Divide the publicatons publicatons based
publicatons based on
based on country-wise on year-wise
year-wise distribution
distribution for each distrubtion of
of journal indexes for
tool fields for each
each tool
tool

Figure 1 The procedural hierarchy for the study

The research papers were then divided based on the two methodologies, i.e., AHP
and ANP, from 2000 to 2019. The papers were arranged according to four main
fields, i.e., engineering/technology/applied sciences, social sciences, health studies,
and environmental studies. These papers were obtained using a vigorous literature
review and analyzed using methodological decision analysis. Then, they were
arranged according to the subject or field category and the authors’ countries were
highlighted. In papers where the author’s country name was not known, the journal’s
origin country was used. University-based journals, Masters and Ph.D. theses, and
papers that were not published in English were excluded. A total of 343 papers using
the ANP and 577 papers using the AHP fit the study's requirements. A total of 920
research papers were filtered from almost 16,400 research papers using the AHP and
ANP methods and were arranged according to the research questions in the results
and discussion section.

4. Results and discussion

The data for the publications related to the AHP and ANP methods were collected
after a detailed literature review using search engines. The purpose was to gather the
information related to the publications about these two methods depending on the
fields of study such as engineering/technology/applied sciences, social sciences,
medical studies, and environmental studies. A few of the prominent journals found to
be using these tools after an analysis of the literature review are mentioned in Table
1.

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methods and their applications: a twenty year review from 2000-2019

Table 1
Prominent journals with articles using AHP and ANP tools

Computers & Industrial Engineering Journal of the Operational Research

Society
Mathematical and Computer Modelling Journal of Intelligent & Fuzzy Systems
Expert Systems with Applications International Journal of Production Research
Applied Soft Computing Energy
Omega International Journal of Production
Economics
Production Planning & Control Renewable and Sustainable Energy Reviews
Sustainability Information Sciences
Natural Hazards Journal of Cleaner Production
European Journal of Operational Research Waste Management
Tourism Management IEEE Transactions of Fuzzy Systems
International Journal of Systems Science: Supply Chain Forum: An International
Operations & Logistics Journal

Cogent Engineering Journal of Control and Decision

International Journal of Management Science and International Journal of the Analytic
Engineering Management Hierarchy Process

These journals had the highest number of publications where researchers had adopted
the AHP and ANP methods for analysis. Some of the journals that had a higher
number of publications related to AHP and ANP in different research fields are
depicted in Table 2.

Table 2
Fields of research highlighted in AHP and ANP studies

Engineering Manufacturing
Civil Works Strategies
Economic Quality
Construction E-Invoicing
Agriculture Supply Chain
Finance Health Care
Forestry Environment
Earthquakes Hazards Natural Disasters
Food Safety
Geographical Sustainability
Water Pipeline Systems
Purchasing Automobiles
Information and Technology Research and Development
Human Error Assessment Hydrogen Energy Technology
Banking Policy Making
History Software
Maritime Industry Mathematics
Navigation Organic
Profit and Loss Management
Green Initiatives Tourism

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methods and their applications: a twenty year review from 2000-2019

Transportation Waste Management

Landslides Entropy

Table 2 shows the significant areas of research that were assessed using these two
methods as applications. Furthermore, the research papers were divided into four
categories, and different forms of data were extracted such as the author’s country,
journal’s index, and the year they were published. The papers were collected from the
years 2000 to 2019, and only the articles published in internationally recognized
journals were selected and evaluated.

4.1 Total publications

The total number of research papers that were published using the AHP and ANP
techniques was approximately 12,900 for the AHP and 3,500 for the ANP between
2000 and 2019. From these research papers, there were 577 for the AHP and 343 for
the ANP that fulfilled this study’s requirements, i.e., the papers were published in
recognized journals. The number of total publications is depicted graphically in
Figure 2.

BREAKDOWN OF AHP & ANP METHODS

TOTAL: 920 PAPERS

600 577

400 343

200
0
AHP ANP

Figure 2 Total number of publications for AHP and ANP from 2000-2019

4.2 Yearly distribution of AHP and ANP publications

The total number of papers published in recognized journals can be further divided
into yearly distribution of publications for both methods. Figure 3 shows the trends
for each year.

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methods and their applications: a twenty year review from 2000-2019

AHP & ANP Publications/year (2000-2019)

50 46
43
4041
40 35 33 34 3532 34 35 35
27 28 29 27 2829
30 25 24 24 26 24 26
18 17
20 14 15 16 15 13
12
9 11
10 7 6
2 4
1 0
0
20002001200220032004200520062007200820092010201120122013201420152016201720182019

AHP ANP

Figure 3 Yearly breakdown of AHP and ANP publications

Figure 3 shows that the publications by year started at a slow pace in the early 2000s,
with the numbers increasing after 2010 for both methods. The ANP method had no
publications in recognized journals in 2002, and similarly, the AHP method had the
lowest number of publications in the year 2000. The highest number of publications
was 46 in 2019 and 41 in 2018 for the AHP and ANP methodologies, respectively.

4.3 Comparison by field

The next phase of this study determined the number of publications by category for
each technique. The purpose was to identify the total number of publications in each
category for both methods. The categories were formulated after a detailed literature
review and included engineering/technology/applied sciences, social sciences, health
studies, and environmental studies. The first step was to determine the overall
comparison of the publications in each category for both the AHP and ANP methods.
The general comparison by field is depicted in Figure 4.

Publication distribution by field

300
245
250 217
200
137 125
150
98
100 77
50 17 4
0
Engineering/Technology Social Sciences Health Studies Environmental Studies

AHP ANP

Figure 4 Overall comparison by field for AHP and ANP

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methods and their applications: a twenty year review from 2000-2019

As shown in Figure 4, engineering/technology/applied sciences had the highest

number of publications when compared to the other categories for both the AHP and
ANP. Engineering had the highest number of publications, i.e., 245 for the AHP and
137 for the ANP. Similarly, the social sciences category had a higher number of
publications for the AHP, i.e., 217 as compared to 125 for the ANP. The AHP and
ANP methods did not have too many applications in the health category as shown by
the lowest number of publications for both methods in this category, i.e., 17 for the
AHP and only 4 for the ANP. Lastly, the AHP had the most publications in the
environmental studies category with 98 publications, while the ANP had 77 in this
category. Therefore it can be concluded that both methodologies possess a more
significant number of applications in the engineering/technology/applied sciences
sector than in any other field. The high number of publications for both methods
shows the validity of the techniques in terms of deducing technical results. For the
next phase of this study, the author’s separated the articles by category into yearly
publications for both techniques for comparison purposes and mentioned all of the
relevant publications by topic and author.

4.3.1 Engineering/technology/applied sciences

Engineering/technology/applied cciences had numerous applications for the AHP and
ANP methods in different engineering and technological advancements. The studies
related to the formulation of new hybrid techniques were also included in this
category, which shows the wider scope of this area. This wider scope is evidenced by
the higher number of publications in this category, i.e., 245 for the AHP and 137 for
the ANP method. However, these figures do not give the complete details about the
trends of the yearly publication for the AHP and ANP in this category. This requires
an annual comparison of publications, which is depicted in Figure 5.

Engineering/Technology/Applied Sciences
19 19
20 18
17
16
15
14 14
15 13 13 13 13 13
12 12 12
11 11 11 11
10 10 10 10
9
10 8
7 7 7 7
5
4
5 3 3 3
2
0 0 0 0
0
20002001200220032004200520062007200820092010201120122013201420152016201720182019

AHP ANP

Figure 5 Yearly comparison for engineering/technology/applied sciences for AHP &

ANP

Figure 5 shows that the average number of publications per year for the AHP is 12,
and 7 for the ANP. The figure shows that the number of publications was low in the
early 2000s for the ANP, but doubled by 2010. The highest number of publications in
a year for the AHP was 19 in 2018 and 18 for the ANP in 2018. These numbers show
that the AHP was the top choice for researchers in this category for authentic results
when compared to the ANP technique.

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methods and their applications: a twenty year review from 2000-2019

After the comparison by year, the research studies done in this category using the
AHP and ANP need to be mentioned. The areas that these two methods covered as
applications are mentioned in Table 2. The research studies for this category are
highlighted according to their journal names, research titles, and author names in
Table 3 for the ANP and Table 4 for the AHP in Appendix A.

4.3.2 Social sciences

Social sciences had the second-highest number of publications using the AHP and
ANP methodologies. The research areas highlighted in this category included human
resource management, supply chain, management, and social issues. The distribution
by year for the AHP and ANP publications in this category shows that the highest
number of papers published in a year was 19 in 2012 and 2019 for the AHP and 13 in
2018 for the ANP. The details are shown in Figure 6.

Social Sciences
19 19
20
16
15
14 14 14
15 13
12 12
11 11
10 10 10 10 10
9 9 9 9 9
10 8 8
7 7
6
5 5 5 5
4 4 4
5
2 2 2 2
1
0
0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

AHP ANP

Figure 6 Distribution by year for social sciences publications for the AHP & ANP

These numbers are also evidence that the AHP was a more authentic and preferable
choice for researchers than the ANP. Tables 5 and 6 show the research publication
details in terms of area, authors, and journals for the ANP and AHP, respectively in
Appendix B.

4.3.3 Health studies

The cateogory of health studies includes the least amount of applications of the AHP
and ANP methods. The few areas of health that were studied focused mainly on
hospitals and their management, and a few studies related to diseases. Figure 7 shows
the distribution by year for health or medical courses from 2000 to 2019 for the AHP
and ANP.

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methods and their applications: a twenty year review from 2000-2019

Health Studies
3
2 2 2 2 2
2
1 1 1 1 1 1 11 1 11
1
00 00 00 00 0 00 0 0 0 0 0 0 0 0 00 0 0 0
0
20002001200220032004200520062007200820092010201120122013201420152016201720182019

AHP ANP

Figure 7 Comparison by year for health studies for the AHP & ANP

Figure 7 shows that the highest number of publications in a year was two for the AHP
and one for the ANP. The total number of publications from 2000-2019 was 17 for
the AHP and 4 for the ANP, which was the fewest of all of the categories.
Furthermore, the publications for both of the methodologies are mentioned in Table 7
for the ANP and Table 8 for the AHP. The publications are divided again on the basis
of area, journal name, and author names in Appendix C.

4.3.4 Environmental studies

Environmental studies had the third-highest number of publications among all of the
categories. Environmental applications are currently highlighted more and more in
studies as the world's environmental situation deteriorates. The studies that are being
highlighted using the AHP and ANP methods include landslides, environmental
emissions, resources, transportation, etc. The distribution by year for environmental
studies is shown in Figure 8. The figure highlights that the AHP method was the most
used technique when compared to the ANP. The highest number of publications in a
year for the AHP was 11 in both 2013 and 2019, whereas, for the ANP, it was 10 in
2017 and 2018. The total number of publications was 98 for the AHP and 77 for the
ANP method. This again shows that the AHP was the preferred technique in this
category.

Environmental Studies
15
11 11
10 10
9 9
10 88
7 7 77
6 6 6
5 5
4 4 4 4 4
5 3 3 33 3
2 2
1 1 1 1
0 00 0 0 0 0
0
20002001200220032004200520062007200820092010201120122013201420152016201720182019

AHP ANP

Figure 8 Comparison by year for environmental sciences publications for the AHP &
ANP

Furthermore, the publications in this category were distributed by area, journal name,
and author name in Tables 9 and 10 for the ANP and AHP, respectively in Appendix

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methods and their applications: a twenty year review from 2000-2019

D. Only some of the papers are cited in the Appendix because of the large number of
papers and space constraints.

4.4 Journal index

The next step involved assessing the indexing of the internationally recognized
journals in which the papers related to the AHP and ANP were published. The journal
indexes were extracted from data obtained from the journals’ websites and a database
website known as Clarivate Analytics. This database helps browse journals by name,
category and ISSN number (Clarivate, 2019). These research journal indexes were
also categorized into four major fields using the AHP and ANP techniques.

4.4.1 Engineering/technology/applied sciences

The index that mainly dominated the journal publications was the SCIE index,
followed by Scopus. The majority of the publications related to the AHP and ANP
were in SCIE indexed journals in this category, with 217 and 124 publications
respectively. The second highest number of publications were in the SCOPUS index
with 18 papers using the AHP and four using the ANP method. The SSCI indexed
publications included 11 for the AHP and five for the ANP. Lastly, the emerging
category of journals (ESCI) had two publications related to the AHP and four related
to the ANP. Therefore, SCIE journals were the main focus for researchers, and again,
the preferred technique was the AHP. The details are shown in Figure 9.

Engineering Indexes
SCOPUS 4
18

ESCI 4
2

SSCI 5
11

SCIE 124
217

0 50 100 150 200 250

ANP AHP

Figure 9 Journal indexes for engineering/technology/applied sciences for the AHP &
ANP

4.4.2 Social sciences

Social sciences had the second-highest number of total publications in this study for
the AHP and ANP. Figure 10 shows that the SCIE index dominated with 158
publications related to the AHP and 88 related to the ANP. The SSCI index had the
second-highest indexed journals with 34 publications using the AHP and 27 using the
ANP. The SCOPUS index had 25 publications using the AHP and seven publications
using the ANP method. Furthermore, the AHP method had two publications, and the
ANP method had six publications in ESCI indexed journals. The AHP methodology
was the preferred method for experts for analysis in this specific category.

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methods and their applications: a twenty year review from 2000-2019

Social Sciences Indexes

SCOPUS 25 7
ESCI 26
SSCI 34 27
SCIE 158 88

AHP ANP

Figure 10 Journal indexes for social sciences for theAHP & ANP

4.4.3 Health sciences

The health sciences category had the lowest number of publications among all of the
major categories that incorporated the AHP and ANP techniques. The index metrics
are displayed in Figure 11 which shows that SCIE indexed journals had the highest
number of publications, i.e., 13 for the AHP and one for the ANP. Furthermore, SSCI
indexed journals had two publications using the AHP and two using the ANP.
Similarly, SCOPUS indexed journals had two publications using the AHP and one
using the ANP. There were no publications in ESCI indexed journals, most likely
because the number of publications in the health category was exceptionally small
and researchers preferred more established journals. The details are depicted in
Figure 11.

Health Studies Indexes

15 13

10

5
2 2 2
1 1
0 0
0
SCIE SSCI ESCI SCOPUS

AHP ANP

Figure 11 Journal indexes for health sciences for the AHP & ANP

4.4.4 Environmental studies

Environmental studies comprise the fourth category evaluated in the current research.
Figure 12 shows that the SCIE indexed journals had the most publications related to
these fields with 90 publications using the AHP and 66 using the ANP method. The
rest of the indexes did not have a significant number of publications as compared to
the SCIE. There were seven publications for the AHP and 10 for the ANP in the SSCI
indexed journals. There were no publications related to AHP in the ESCI index, and
only one study associated with the ANP. Lastly, the SCOPUS indexed journals had
one publication that incorporated the AHP, while there were no publications included
in this index that used the ANP method. Therefore, the AHP technique had the
highest number of publications in this category as well.

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methods and their applications: a twenty year review from 2000-2019

Environmental Studies Indexes

SCOPUS 0
1
ESCI 1
0
SSCI 10
7
SCIE 66
90
0 10 20 30 40 50 60 70 80 90 100

ANP AHP

Figure 12 Journal indexes for environmental studies for the AHP & ANP

4.5 Distribution by country

The most important research question that this study aimed to determine was the
concentration of publications by country. In other words, to determine which
countries have contributed the most to the research in the four major fields of study
through implementation of the AHP and ANP techniques. In order to do so, data
related to the author's country of origin were collected from the databases of journal
biographies. Authors whose countries were not mentioned or had no information at
all were listed under the country of the journal. The data was collected using search
engines and was extracted separately based on distribution by country. The objective
was to determine the countries that have contributed the most to the use of these two
techniques. The distribution by country was divided based on the method, showing
the number of publications in a country in descending order.

4.5.1 AHP application, distribution by country

There were 577 total publications in recognized journals from 2000 to 2019 that
employed the AHP method. The first countries that incorporated the AHP method in
their studies were Italy, China, and Finland in 2000. The distribution by country is
represented in Figure 13, along with representation on the map based on a country's
publications in Figure 14.

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methods and their applications: a twenty year review from 2000-2019

AHP PUBLICATIONS
AHP Publications
82
68
48
46
43
38
27
21
18
16
15
14
13
11
9
6
6
5
5
5
5
5
4
4
4
3
3
3
3
3
3
3
3
3
3
3
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
Figure 13 Distribution by country for AHP publications

Figure 14 Map for the AHP publications concentrated in various countries

Figures 13 and 14 show that the highest number of publications using the AHP were
in Turkey with 82 research studies, followed by China with 68 and India with 48
publications. The number of publications is arranged in descending order in Figure
13. The lowest number of publications can be seen in countries like Switzerland, the
Czech Republic, and Kenya (1).

4.5.2 ANP method, distribution by country

There were 343 total ANP publications in recognized journals from 2000 to 2019.
The number of publications using the ANP was very small compared to the AHP.
The first country that employed the ANP method in its studies was South Korea in

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methods and their applications: a twenty year review from 2000-2019

2000. The distribution by country for the ANP technique is depicted in Figure 15 and
a map-based representation is shown in Figure 16.

ANP Publications
70
60 61
55
50 50
40 40
30
20 19 18
10 11 10 9 9
6 6 5 3 3 3
0 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Figure 15 Distribution by country for ANP publications

Figure 16 Map for ANP publications concentrated in various countries

This figure shows that Turkey again had the highest number of publications, i.e., 61,
followed by Taiwan with 55 publications and China with 50 publications. The figure
displays the number of publications in descending order by country. The lowest
number of publications in a country was one in countries such as Hong Kong,
Sweden, and Nigeria.

4.6 Comparison of the AHP and ANP methodologies

The data extracted about the AHP and ANP was mainly used to determine which
technique had wider exposure and applications. The study explored these techniques
based on the overall number of publications, publications by field, metrics of journal
indexes, and distribution by country. From the above results, it can be concluded that

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methods and their applications: a twenty year review from 2000-2019

the AHP is the superior methodology when compared to the ANP in terms of
applications, preference by the experts, and use in almost every major research field.
Similarly, based on the publications and journals the articles were published in, the
AHP method was more authentic, that is, there were more publications using that
method in ISI indexed journals, the web of science, and even SCOPUS. Therefore, it
can be safely stated that the AHP method produces more superior, authentic and
efficient results than the ANP technique.

5. Conclusions
Various fields are emerging through improvisation and rapid changes which makes
them extremely complicated. Researchers related to these new fields and the older
classic fields are always looking to formulate a method to incorporate analysis into a
study. The objective of this study was to conduct a detailed review of famous
MCDM methodologies, the AHP and ANP, from 2000 to 2019. The data were
collected through various search engines, and 577 papers using the AHP and 343
papers using the ANP were found that had been published in recognized journals, 920
papers in total. Then, the data were categorized in various ways depending on the
requirements of the study. The overall requirements of the study included the
following: determining the total number of publications for each technique as well as
their distribution by year, distribution of the publications by year based on each
category for both the AHP and ANP methods, distribution by year of the publications
based on their journal indexes, and the distribution by country based on the author’s
country origin.

After the data analysis, it was concluded that the AHP has dominated the last 20 years
in terms of number of publications in all of the major categories, i.e.,
engineering/technology/applied sciences, social sciences, health studies and
environmental studies. The highest number of publications for the AHP shows that
researchers highly trust this technique. The category with the highest number of
publications was the engineering/technology/applied sciences category. This result is
evidence that the highest number of publications were in SCIE indexed journals that
are more focused on publishing technical content. Lastly, the country that had the
most significant number of publications for both methodologies was Turkey. Turkey
has employed both methods in almost every sector, showing that Turkey is growing
at a very fast pace.

The study also concluded that the AHP was the top choice for analysis when
compared to the ANP based on the number of applications in every category. This
shows that the AHP produces more authentic and reliable results and has been mostly
preferred by researchers in the last 20 years. The study can be extended in the future
by studying more techniques for the same 20 years and analyzing them based on their
categories, countries, and journal indexes.

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methods and their applications: a twenty year review from 2000-2019

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Nishizawa, K. (2000). Bi-directional nearness in a network by AHP (Analytic

Hierarchy Process) and ANP (Analytic Network Process). RAIRO-Operations
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Ohta, K., Kobashi, G., Takano, S., Kagaya, S., Yamada, H., Minkami, H., &
Yamamura, E. (2007). Analysis of the geographical accessibility of neurosurgical
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Omasa, T., Kishimoto, M., Kawase, M., & Yagi, K. (2004). An attempt at decision
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Opricovic, S., & Tzeng, G.-H. (2004). Compromise solution by MCDM methods: A
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Ortiz, M. A., Felizzola, H. A., & Isaza, S. N. (2015). A contrast between DEMATEL-
ANP and ANP methods for six sigma project selection: a case study in healthcare
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Ozsahin, I., Sharif, T., Ozsahin, D. U., & Uzun, B. (2019). Evaluation of solid-state
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Ozturk, H., Pekel, E., & Elevli, B. (2018). Using ANP and ELECTRE Methods for
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methods and their applications: a twenty year review from 2000-2019

Pal, D. K., Ravi, B., & Bhargava, L. S. (2007). Rapid tooling route selection for metal
casting using QFD–ANP methodology. International Journal of Computer Integrated
Manufacturing, 20(4), 338-354. doi: https://doi.org/10.1080/09511920600883229

Pecchia, L., Martin, J. L., Ragozzino, A., & Vanzanella, C. (2013). User needs
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Ravi, V., Shankar, R., & Tiwari, M. K. (2005). Analyzing alternatives in reverse
logistics for end-of-life computers: ANP and balanced scorecard approach.
Computers & industrial engineering, 48(2), 327-356. doi:
https://doi.org/10.1016/j.cie.2005.01.017

Ravi, V., Shankar, R., & Tiwari, M. K. (2008). Selection of a reverse logistics project
for end-of-life computers: ANP and goal programing approach. International Journal
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Roy, B. (1968). Classement et choix en présence de points de vue multiples. Revue

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Saaty, T. L. (2001). Decision making with dependence and feedback: The Analytic
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Saaty, T. L. (2004). Decision making—the analytic hierarchy and network processes

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Saaty, T. L. (2004). Fundamentals of the analytic network process—Dependence and

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Saaty, T. L. (2005). Making and validating complex decisions with the AHP/ANP.
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methods and their applications: a twenty year review from 2000-2019

Saaty, T. L. (2007). Time dependent decision-making; dynamic priorities in the

AHP/ANP: Generalizing from points to functions and from real to complex variables.
Mathematical and Computer Modelling, 46(7-8), 860-891. doi:
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Sax, L. J., Kanny, M. A., Jacobs, J. A., Whang, H., Weintraub, D. S., & Hroch, A.
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Sekitani, K., & Takahashi, I. (2005). A new approach of revising unstable data in
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Shinde, D. D., & Prasad, R. (2018). Application of AHP for ranking of total
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Shyur, H.-J. (2006). COTS evaluation using modified TOPSIS and ANP. Applied
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Simunich, B. (2007). In the fall of 2002, the ANP had shown a better way to deal
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https://doi.org/10.1016/j.mcm.2007.03.002

Singh, A., & Prasher, A. (2019). Measuring healthcare service quality from patients’
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Sinuany-Stern, Z., Mehrez, A., & Hadad, Y. (2000). An AHP/DEA methodology for
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methods and their applications: a twenty year review from 2000-2019

Sipahi, S., & Timor, M. (2010). The analytic hierarchy process and analytic network
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Solnes, J. (2003). Environmental quality indexing of large industrial development

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Su, X. Y., Hipel, K. W., & Kilgour, D. M. (2005). Comparison of the analytic
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Science and Systems Engineering, 14(3), 308-325. doi:
https://doi.org/10.1007/s11518-006-0196-5

Tam, M. C., & Tummala, V. R. (2001). An application of the AHP in vendor

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https://doi.org/10.1016/s0305-0483(00)00039-6

Tesfamariam, D., & Lindberg, B. (2005). Aggregate analysis of manufacturing

systems using system dynamics and ANP. Computers & Industrial Engineering,
49(1), 98-117. doi: https://doi.org/10.1016/j.cie.2005.05.001

Tesfamariam, S., & Sadiq, R. (2006). Risk-based environmental decision-making

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Tosun, O. K., Gungor, A., & Topcu, Y. l. (2008). ANP application for evaluating
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Tsai, W.-H., & Chou, W.-C. (2009). Selecting management systems for sustainable
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https://doi.org/10.1016/j.eswa.2007.11.058

Tummala, V. R., & Ling, H. (2000). A note on the sampling distribution of the
information content of the priority vector of a consistent pairwise comparison
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Vahidnia, M. H., Alesheikh, A. A., & Alimohammadi, A. (2009). Hospital site

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Van der Honert, R. C. (2001). Decisional power in group decision making: a note on
the allocation of group members' weights in the multiplicative AHP and SMART.
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https://doi.org/10.1023/a:1011201501379

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methods and their applications: a twenty year review from 2000-2019

Wang, J., Fan, K., & Wang, W. (2010). Integration of fuzzy AHP and FPP with
TOPSIS methodology for aeroengine health assessment. Expert Systems with
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Wang, M., Yue, X., Gao, C., & Chen, Y. (2018). Feature selection ensemble for
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Wedley, W. C., Choo, E. U., & Schoner, B. (2001). Magnitude adjustment for AHP
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Wey, W.-M., & Wu, K.-Y. (2007). Using ANP priorities with goal programming in
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Wijnmalen, D. J. (2007). Analysis of benefits, opportunities, costs, and risks (BOCR)

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Wolfslehner, B., Vacik, H., & Lexer, M. J. (2005). Application of the analytic
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Wu, W.-W. (2008). Choosing knowledge management strategies by using a

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Yang, J., Shen, L., Jin, X., Hou, L., Shang, S., & Zhang, Y. (2019). Evaluating the
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2000-2019

Appendix A
ENGINEERING/TECHNOLOGY/APPLIED SCIENCES

Table 3
Research publications in engineering/technology/applied science category for ANP-2000 to 2019

ANP
Authors Research Title Journal Name
Measuring long-term performance of a manufacturing firm using the Analytic
(Yurdakul, 2003) International Journal of Production Research
Network Process (ANP) approach.
(Leung, Hui, & Zheng, 2003) Analysis of compatibility between interdependent matrices in ANP Journal of the Operational Research Society
(Karsak, Sozer, & Alptekin, Product planning in quality function deployment using a combined analytic
Computers & industrial engineering
2003) network process and goal programming approach
Model and Algorithms of Supply and Demand Coordination Performance
(Zhi-xiang, 2004) Computer Integrated Manufacturing Systems
Measurement Based on ANP Theory [J]
(Ravi, Shankar, & Tiwari, Analyzing alternatives in reverse logistics for end-of-life computers: ANP and
Computers & industrial engineering,
2005) balanced scorecard approach.
(Mohanty, Agarwal,
A fuzzy ANP-based approach to R&D project selection: a case study International Journal of Production Research
Choudhury, & Tiwari, 2005)
(Chung, Lee, & Pearn,
Product mix optimization for
Product mix optimization for semiconductor manufacturing based on AHP and The International Journal of Advanced
semiconductor
ANP analysis Manufacturing Technology
manufacturing based on AHP
and ANP analysis, 2005)
(Tesfamariam & Lindberg,
Aggregate analysis of manufacturing systems using system dynamics and ANP Computers & Industrial Engineering
2005)
(Erdogmus, Kapanoglu, &
Koc, Evaluating high-tech
Evaluating high-tech alternatives by using analytic network process with BOCR
alternatives by using analytic Evaluation and Program Planning
and multi actors
network process with BOCR
and multiactors, 2005)
(Ertay, Buyukozkan, Quality function deployment implementation based on analytic network process
Journal of Intelligent & Fuzzy Systems
Kahraman, & Ruan, 2005) with linguistic data: An application in automotive industry
Comparison of the analytic network process and the graph model for conflict Journal of Systems Science and Systems
(Su, Hipel, & Kilgour, 2005)
resolution Engineering
The International Journal of Advanced
(Lu & Hsiao, 2006) ANP-GP approach for product variety design
Manufacturing Technology
(Kahraman, Ertay, & A fuzzy optimization model for QFD planning process using analytic network
European Journal of Operational Research
Buyukozkan, 2006) approach

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2000-2019

Evaluation of connection types in design for disassembly (DFD) using analytic

(Gungor, 2006) Computers & Industrial Engineering
network process
(Ayag & Ozdemir, An
intelligent approach to ERP
An intelligent approach to ERP software selection through fuzzy ANP International Journal of Production Research
software selection through
fuzzy ANP, 2007)
(Saaty T. L., Time dependent
decision-making; dynamic
priorities in the AHP/ANP: Time-dependent decision-making; dynamic priorities in the AHP/ANP:
Mathematical and Computer Modelling
Generalizing from points to Generalizing from points to functions and from real to complex variables
functions and from real to
complex variables, 2007)
(Cheng & Li, Application of
ANP in process models: An
Application of ANP in process models: An example of strategic partnering Building and environment
example of strategic
partnering, 2007)
Analysis of benefits, opportunities, costs, and risks (BOCR) with the AHP–ANP:
(Wijnmalen, 2007) Mathematical and computer modelling
A critical validation
Using ANP priorities with goal programming in resource allocation in
(Wey & Wu, 2007) Mathematical and computer modelling
transportation
(Pal, Ravi, & Bhargava, International Journal of Computer Integrated
Rapid tooling route selection for metal casting using QFD–ANP methodology
2007) Manufacturing
Parallels between the analytic hierarchy and network processes (AHP/ANP) and
(Garuti & Spencer, 2007) Mathematical and Computer Modelling
fractal geometry
(Lin, Chiu, & Tsai, The study
of applying ANP model to
The study of applying ANP model to assess dispatching rules for wafer fabrication Expert Systems with Applications
assess dispatching rules for
wafer fabrication, 2008)
(Ravi, Shankar, & Tiwari, Selection of a reverse logistics project for end-of-life computers: ANP and goal
International Journal of Production Research
2008) programing approach
(Tosun, Gungor, & Topcu,
ANP application for evaluating Turkish mobile communication operators Journal of Global Optimization
2008)
(Lee H. , Kim, Cho, & Park, An ANP-based technology network for identification of core technologies: A case
Expert Systems with Applications
2009) of telecommunication technologies
Yang, Chang-Lin, Shan-Ping
Manufacturing evaluation system based on AHP/ANP approach for wafer
Chuang, and Rong-Hwa expert Systems with Applications
fabricating industry
Huang
Pi-Fang, Hsu Evaluation of Advertising Spokespersons via the ANP-GRA Selection Model Journal of Grey System
Yüksel, İhsan, and Metin Using the fuzzy analytic network process (ANP) for Balanced Scorecard (BSC):
Expert Systems with Applications
Dağdeviren A case study for a manufacturing firm
Aragonés-Beltrán, P., F.
Chaparro-González, J. P. An ANP-based approach for the selection of photovoltaic solar power plant
Renewable and sustainable energy reviews
Pastor-Ferrando, and F. investment projects
Rodríguez-Pozo

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2000-2019

An ANP approach for R&D project evaluation based on interdependencies

Jung, Uk, and D. W. Seo Decision Support Systems
between research objectives and evaluation criteria
Lee, Hakyeon, Chulhyun Evaluation and management of new service concepts: An ANP-based portfolio
Computers & Industrial Engineering
Kim, and Yongtae Park approach
Yazgan, Harun Resit, Semra Selection of dispatching rules in FMS: ANP model based on BOCR with Choquet The International Journal of Advanced
Boran, and Kerim Goztepe integral Manufacturing Technology
Luo, Zhi-meng, Jian-Zhong
A TFN–ANP based approach to evaluate Virtual Research Center comprehensive
Zhou, Li-ping Zheng, Li Mo, Expert Systems with Applications
performance
and Yao-Yao He
Kasirian, M. Navid, and Application of AHP and ANP in supplier selection process-a case in an International journal of management science and
Rosnah Mohd Yusuff automotive company Engineering Management
Caballero-Luque, Antonio,
Pablo Aragonés-Beltrán, International Journal of Information Technology &
Analysis of the alignment of company goals to web content using ANP
Mónica García-Melón, and Decision Making
Carlos Dema-Pérez
Liao, Sen-Kuei, Kuei-Lun
Optimal selection of program suppliers for TV companies using an analytic
Chang, and Tzeng-Wei Asia-Pacific Journal of Operational Research
network process (ANP) approach
Tseng
Gumus, Alev Taskin, and Sea vessel type selection via an integrated VAHP–ANP methodology for high-
Expert Systems with Applications
Gokhan Yilmaz speed public transportation in Bosphorus
Mohan, K. Krishna, Ajit ANP-based software reliability prediction using PoCs and subsequent
International Journal of Systems Assurance
Srividya, and Ajit Kumar employment of orthogonal defect classification measurements for risk mitigation
Engineering and Management
Verma during prototype studies
Hsu, Chia-Wei, Allen H. Hu,
Using the FDM and ANP to construct a sustainability balanced scorecard for the
Cherng-Ying Chiou, and Ta- Expert Systems with Applications
semiconductor industry
Che Chen
An interpretation of the AHP global priority as the eigenvector solution of an International Journal of the Analytic Hierarchy
Lipovetsky, Stan
ANP supermatrix Process
Liou, James JH, Gwo-
A hybrid ANP model in fuzzy environments for strategic alliance partner selection
Hshiung Tzeng, Chieh-Yuan Applied Soft Computing
in the airline industry
Tsai, and Chao-Che Hsu
Kim, Chulhyun, Hakyeon
Identifying core technologies based on technological cross-impacts: An
Lee, Hyeonju Seol, and Expert Systems with Applications
association rule mining (ARM) and analytic network process (ANP) approach
Changyong Lee
Paramasivam, V., V. Senthil, Decision making in equipment selection: an integrated approach with digraph and The International Journal of Advanced
and N. Rajam Ramasamy matrix approach, AHP and ANP Manufacturing Technology
The International Journal of Advanced
Yazgan, Harun Resit Selection of dispatching rules with fuzzy ANP approach
Manufacturing Technology
Yang, Chang-Lin, Ching
Lien Huang, and Shan-Ping Outsourcing evaluation system based on AHP/ANP approach for LED industry Journal of Statistics and Management Systems
Chuang
Sevkli, Mehmet, Asil
Development of a fuzzy ANP based SWOT analysis for the airline industry in
Oztekin, Ozgur Uysal, Expert Systems with Applications
Turkey
Gökhan Torlak, Ali

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2000-2019

Turkyilmaz, and Dursun

Delen
Zaim, Selim, Ali Turkyılmaz,
Mehmet F. Acar, Umar Al- Maintenance strategy selection using AHP and ANP algorithms: a case study Journal of Quality in Maintenance Engineering
Turki, and Omer F. Demirel.
Atmaca, Ediz, and Hasan
Evaluation of power plants in Turkey using Analytic Network Process (ANP) Energy
Burak Basar
Ayağ, Zeki, and Rifat Gürcan Evaluating machine tool alternatives through modified TOPSIS and alpha-cut
International Journal of Production Economics
Özdemir based fuzzy ANP
Kang, He-Yau, Amy HI Lee,
A fuzzy ANP model for supplier selection as applied to IC packaging Journal of Intelligent Manufacturing
and C-Y. Yang
Hsu, Tsuen-Ho, Li-Chu
A hybrid ANP evaluation model for electronic service quality Applied Soft Computing
Hung, and Jia-Wei Tang
A multi-criteria decision-making methodology on the selection of facility The International Journal of Advanced
Özdağoğlu, Aşkın
location: fuzzy ANP Manufacturing Technology
Research and applications of AHP/ANP and MCDA for decision making in INTERNATIONAL JOURNAL OF PRODUCTION
De Felice, Fabio
manufacturing RESEARCH
Ordoobadi, Sharon M Application of ANP methodology in evaluation of advanced technologies Journal of Manufacturing Technology Management
Vahdani, Behnam, Hasan
Hadipour, and Reza Soft computing based on interval-valued fuzzy ANP-A novel methodology Journal of Intelligent Manufacturing
Tavakkoli-Moghaddam
Ozaki, Toshimasa, Mei-Chen
Lo, Eizo Kinoshita, and Decision-making for the best selection of suppliers by using minor ANP Journal of Intelligent Manufacturing
Gwo-Hshiung Tzeng
Zolfani, Sarfaraz H., Nahid
Selecting the best multi-role artist of rock bands of Iran 2000s by applying ANP Economic Computation and Economic Cybernetics
Rezaeiniya, and J.
and TOPSIS grey Studies and Research
Saparauskas
Goztepe, Kerim, and Semra A decision support system for supplier selection using fuzzy analytic network
Scientific Research and Essays
Boran process (Fuzzy ANP) and artificial neural network integration
Sabri, Soheil, Ahmad Nazri
Conceptual design for an integrated geosimulation and analytic network process
Muhammad M. Ludin, and Applied Spatial Analysis and Policy
(ANP) in gentrification appraisal
Chin Siong Ho
Tavana, Madjid, Ehsan
Momeni, Nahid Rezaeiniya,
A novel hybrid social media platform selection model using fuzzy ANP and
Seyed Mostafa Expert Systems with Applications
COPRAS-G
Mirhedayatian, and
Hamidreza Rezaeiniya
Eshtehardian, Ehsan, Parviz
Using ANP and AHP for the supplier selection in the construction and civil
Ghodousi, and Azadeh KSCE Journal of Civil Engineering
engineering companies; case study of Iranian company
Bejanpour
Liang, Xingyu, Xiuxiu Sun,
Using the analytic network process (ANP) to determine method of waste energy
Gequn Shu, Kang Sun, Xu Energy Conversion and Management
recovery from engine
Wang, and Xinlei Wang
Tavana, Madjid, Faramak A hybrid fuzzy group ANP–TOPSIS framework for assessment of e-government Information & Management

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 IJAHP Article: Khan, Ali/Analytical Hierarchy Process (AHP) and Analytic Network Process methods and their applications: a twenty year review from
2000-2019

Zandi, and Michael N. readiness from a CiRM perspective

Katehakis
Multi-criteria inventory classification by using a fuzzy analytic network process
Kiriş, Şafak Informatica
(ANP) approach
Hsiao, Shih-Wen, Ya-Chuan
Ko, Chi-Hung Lo, and Shih- An ISM, DEI, and ANP based approach for product family development Advanced Engineering Informatics
Ho Chen
Keramati, Abbas, and Mona Website success comparison in the context of e-recruitment: An analytic network
Applied Soft Computing
Salehi process (ANP) approach
Chen, Zhen, Arham B.
Journal of Construction Engineering and
Abdullah, Chimay J. ANP experiment for demolition plan evaluation
Management
Anumba, and Heng Li
Zhou, Jian-Lan, Bai Zhe- Safety assessment of high-risk operations in hydroelectric-project based on
Mathematical Problems in Engineering
Hua, and Zhi-Yu Sun accidents analysis, SEM, and ANP
Chen, Hsing Hung, and Hao A fuzzy ANP model integrated with benefits, opportunities, costs, and risks to
Mathematical Problems in Engineering
Gu prioritize intelligent power grid systems
A novel hybrid evaluation model for the performance of ERP project based on
Hui-Ru, Zhao, and Li Na-na Mathematical Problems in Engineering
ANP and improved matter-element extension model
Ting, Chih-Wen, Jyun-Wei
Combining DEMATEL with ANP to modify multidimensional scaling in
Huang, Ding-Shan Wang, African Journal of Business Management
identifying the similarities of e-shopping stores
and Gwo-Hshiung Tzeng
Aragonés-Beltrán, Pablo,
Fidel Chaparro-González, An AHP (Analytic Hierarchy Process)/ANP (Analytic Network Process)-based
Juan-Pascual Pastor- multi-criteria decision approach for the selection of solar-thermal power plant Energy
Ferrando, and Andrea Pla- investment projects
Rubio
Van Horenbeek, Adriaan, Development of a maintenance performance measurement framework—using the
Omega
and Liliane Pintelon analytic network process (ANP) for maintenance performance indicator selection
Zaim, Selim, Mehmet Sevkli,
Hatice Camgöz-Akdağ,
Use of ANP weighted crisp and fuzzy QFD for product development Expert Systems with Applications
Omer F. Demirel, A. Yesim
Yayla, and Dursun Delen
Yeh, Tsu-Ming, and Yu- Factors in determining wind farm location: Integrating GQM, fuzzy DEMATEL,
Renewable Energy
Lang Huang and ANP
Shahabi, Reza Shakoor,
Mohammad Hossein Basiri, An ANP–SWOT approach for interdependency analysis and prioritizing the Iran‫ ׳‬s
Resources Policy
Mahdi Rashidi Kahag, and steel scrap industry strategies
Samad Ahangar Zonouzi
Wu, Che-I., Hsu-Yang Kung,
An intelligent slope disaster prediction and monitoring system based on WSN and
Chi-Hua Chen, and Li-Chia Expert Systems with Applications
ANP
Kuo
Li, Kewen, Yu Zhang, and
Weight analysis based on ANP and QFD in software quality evaluation Applied Mathematics & Information Sciences
Wenying Liu
Demirtaş, Nurgül, Şenim Selecting e-purse smart card technology via fuzzy AHP and ANP Journal of Applied Mathematics

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 IJAHP Article: Khan, Ali/Analytical Hierarchy Process (AHP) and Analytic Network Process methods and their applications: a twenty year review from
2000-2019

Özgürler, Mesut Özgürler,

and Ali Fuat Güneri
Pan, R., W. Zhang, S. Yang, A state entropy model integrated with BSC and ANP for supplier evaluation and
International Journal of Simulation Modelling
and Y. Xiao selection
Jeong, Hwa-Young, Jong
An ANP-based practical quality model for a secure embedded system with sensor International Journal of Distributed Sensor
Hyuk Park, and Young-Sik
network Networks
Jeong
Uygun, Özer, Hasan
An integrated DEMATEL and Fuzzy ANP techniques for evaluation and selection
Kaçamak, and Ünal Atakan Computers & Industrial Engineering
of outsourcing provider for a telecommunication company
Kahraman
Mostafa, Sherif, Tariq
Abdelhamid, Nicholas Decision support model using ANP to align leagile strategies to off-site International Journal of the Analytic Hierarchy
Chileshe, and Jantanee manufacturing in Australia Process
Dumrak
Chemweno, Peter, Liliane
Pintelon, Adriaan Van Development of a risk assessment selection methodology for asset maintenance
International Journal of Production Economics
Horenbeek, and Peter decision making: An analytic network process (ANP) approach
Muchiri
Lee, Sora, Youngjung Geum,
Evaluating new concepts of PSS based on the customer value: Application of
Sungjoo Lee, and Yongtae Expert systems with Applications
ANP and niche theory
Park
Nilashi, Mehrbakhsh, Rozana
Zakaria, Othman Ibrahim,
MCPCM: a DEMATEL-ANP-based multi-criteria decision-making approach to
Muhd Zaimi Abd Majid, Arabian Journal for Science and Engineering
evaluate the critical success factors in construction projects
Rosli Mohamad Zin, and
Mohammadali Farahmand
Wang, Xin, Zhengjiang Liu, A rating based fuzzy analytic network process (F-ANP) model for evaluation of
Ocean Engineering
and Yao Cai ship maneuverability
Aliakbari Nouri, Fahimeh,
A hybrid MCDM approach based on fuzzy ANP and fuzzy TOPSIS for
Saber Khalili Esbouei, and Informatica
technology selection
Jurgita Antucheviciene
Kumru, Mesut, and Pınar
A fuzzy ANP model for the selection of 3D coordinate-measuring machine Journal of Intelligent Manufacturing
Yıldız Kumru
Chen, Wen-Chin, Hui-Pin
An Efficient Model for NPD Performance Evaluation Using DEMATEL and
Chang, Kuan-Ming Lin, and Energies
Fuzzy ANP—Applied to the TFT-LCD Touch Panel Industry in Taiwan
Neng-Hao Kan
Tang-Nguyen, Hanh, and The SWOT-ANP decision framework for the enterprise's cloud computing
Information
Young-Chan Lee strategy
Jin, Lisheng, Keyong Li,
Yuying Jiang, Huacai Xian, Classifying Secondary Task Driving Safety Using Method of F-ANP Advances in Mechanical Engineering
and Linlin Gao
A combined MCDM model based on DEMATEL and ANP for the selection of
Chen, I-Shuo airline service quality improvement criteria: A study based on the Taiwanese Journal of Air Transport Management
airline industry

International Journal of the 408 Vol. 12 Issue 3 2020

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 IJAHP Article: Khan, Ali/Analytical Hierarchy Process (AHP) and Analytic Network Process methods and their applications: a twenty year review from
2000-2019

Mei, Ying, Jiawei Ye, and Entropy-weighted ANP fuzzy comprehensive evaluation of interim product
Computers & Industrial Engineering
Zhigang Zeng production schemes in one-of-a-kind production
Ramkumar, M., Tobias
Risk assessment of outsourcing e-procurement services: integrating SWOT
Schoenherr, and Mamata Production Planning & Control
analysis with a modified ANP-based fuzzy inference system.
Jenamani
Ozdemir, Yavuz, and Aircraft selection using Fuzzy ANP and the generalized Choquet Integral method:
Journal of Intelligent & Fuzzy Systems
Huseyin Basligil The Turkish Airlines case
Al-Refaie, A., E. Sy, I. Integration of SWOT and ANP for effective strategic planning in the cosmetic Advances in Production Engineering &
Rawabdeh, and W. Alaween industry Management
Samanlioglu, Funda, and Fuzzy ANP-based PROMETHEE II approach for evaluation of machine tool
Journal of Intelligent & Fuzzy Systems
Zeki Ayağ alternatives
Oztaysi, Basar, Tuncay
Journal of Multiple-Valued Logic & Soft
Gurbuz, Esra Albayrak, and Target Marketing Strategy Determination for Shopping Malls Using Fuzzy ANP
Computing
Cengiz Kahraman
Wang, Xiaojia, Chenggong
Li, Jennifer Shang, Changhui Strategic choices of China’s new energy vehicle industry: An analysis based on
Energies
Yang, Bingli Zhang, and ANP and SWOT
Xinsheng Ke
Shariati, Shahram,
Masoumeh Abedi, Alieh
Saedi, Abdolreza Yazdani-
Critical factors of the application of nanotechnology in construction industry by
Chamzini, Jolanta Journal of Civil Engineering and Management
using ANP technique under fuzzy intuitionistic environment
Tamošaitienė, Jonas
Šaparauskas, and Stanislav
Stupak
Cheng, Chia-Hua, James A consistent fuzzy preference relation based ANP model for R&D project
Sustainability
Liou, and Chui-Yu Chiu selection
Toosi, SL Razavi, and J. M. Prioritizing watersheds using a novel hybrid decision model based on fuzzy
Water resources management
V. Samani DEMATEL, fuzzy ANP and fuzzy VIKOR
Kabak, Mehmet, and Metin A hybrid approach based on ANP and grey relational analysis for machine
Tehnički vjesnik
Dagdeviren selection
Özdemir, Ali, and Fatih An Integrated Fuzzy DEMATEL and Fuzzy ANP Based Balanced Scorecard Journal of Multiple-Valued Logic & Soft
Tüysüz Approach: Application in Turkish Higher Education Institutions Computing
Li, Kunlun, and Jun Wang Multi-objective Optimization for cloud task scheduling based on the ANP model Chinese Journal of Electronics
Ervural, Beyzanur Cayir,
Selim Zaim, Omer F.
An ANP and fuzzy TOPSIS-based SWOT analysis for Turkey’s energy planning Renewable and Sustainable Energy Reviews
Demirel, Zeynep Aydin, and
Dursun Delen
Azizi, Majid, and APPLYING ANP TO ANALYZE THE ROLE OF DESIGN IN THE International Journal of the Analytic Hierarchy
Gholamreza Mehdikhanloo FURNITURE INDUSTRY Process
Hemmati, Narges, Masoud
Rahiminezhad Galankashi,
Maintenance policy selection: a fuzzy-ANP approach Journal of Manufacturing Technology Management
Din Mohammad Imani, and
Hiwa Farughi

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2000-2019

Ebrahimi, M., M. Aramesh, Innovative ANP model to prioritization of PV/T systems based on cost and
Renewable Energy
and Y. Khanjari efficiency approaches: With a case study for Asia
Sayyadi, Reza, and Anjali An integrated approach based on system dynamics and ANP for evaluating International Journal of Systems Science:
Awasthi sustainable transportation policies Operations & Logistics
Ganji, SR Seyedalizadeh,
Vehicle safety analysis based on a hybrid approach integrating DEMATEL, ANP
Amir Abbas Rassafi, and Ali KSCE Journal of Civil Engineering
and ER
Abdi Kordani
Hasnain, Muhammad,
Best value contractor selection in road construction projects: ANP-based decision
Muhammad Jamaluddin International Journal of Civil Engineering
support system
Thaheem, and Fahim Ullah
Bongo, Miriam F., Kissy
Mae S. Alimpangog, Jennifer An application of DEMATEL-ANP and PROMETHEE II approach for air traffic
F. Loar, Jason A. controllers’ workload stress problem: A case of Mactan Civil Aviation Authority Journal of Air Transport Management
Montefalcon, and Lanndon of the Philippines
A. Ocampo
Wu, Yunna, Buyuan Zhang,
Site selection decision framework using fuzzy ANP-VIKOR for large commercial
Chuanbo Xu, and Sustainable cities and society
rooftop PV system based on sustainability perspective
Lingwenying Li
Application of ANP to the selection of shipping registry: the case of Taiwanese
Chou, Chien-chang International Journal of Industrial Ergonomics
maritime industry
Li, Xuerui, Suihuai Yu, and Optimal selection of manufacturing services in cloud manufacturing: A novel
Journal of Intelligent & Fuzzy Systems
Jianjie Chu hybrid MCDM approach based on rough ANP and rough TOPSIS
Liu, Guiwen, Saina Zheng,
An ANP-SWOT approach for ESCOs industry strategies in Chinese building
Pengpeng Xu, and Taozhi Renewable and Sustainable Energy Reviews
sectors
Zhuang
Yazgan, Ebru, and Ayşe Prioritisation of factors contributing to human error for airworthiness management
Aircraft Engineering and Aerospace Technology
Kucuk Yilmaz strategy with ANP
Erginel, Nihal, Meryem
Evaluation methods for completed Six Sigma projects through an interval type-2
Uluskan, Gamze Küçük, and Journal of Intelligent & Fuzzy Systems
fuzzy ANP
Merve Altintaş
Li, Lianhui, and Hongguang A green supplier assessment method for manufacturing enterprises based on rough
Information
Wang ANP and evidence theory
Tang, Gongbin, Yifan Chen,
The development of hydraulic oils for the new fuel-efficient hydraulic hybrid
Feng Xiao, Shanshan Zhang, Industrial Lubrication and Tribology
vehicles with ANP method
and Fuchuan Huang
Yang, Jing, Changhui Yang,
Exploring Promotion Effect for FIT Policy of Solar PV Power Generation Based
Yiming Song, and Xiaojia Mathematical Problems in Engineering
on Integrated ANP: Entropy Model
Wang
Khan, Muhammad Aamir,
Ahmad Ali, Muhammad Analysis of power plants in China Pakistan economic corridor (CPEC): An
Journal of Renewable and Sustainable Energy
Iftikhar ul Husnain, and application of analytic network process (ANP)
Muhammad Zakaria
Karaşan, Ali, and Cengiz A novel intuitionistic fuzzy DEMATEL–ANP–TOPSIS integrated methodology
Journal of Intelligent & Fuzzy Systems
Kahraman for freight village location selection

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2000-2019

Fargnoli, Mario, and Nicolas A practical ANP-QFD methodology for dealing with requirements’ inner
Computers & Industrial Engineering
Haber dependency in PSS development
Mahdiyar, Amir, Sanaz
Tabatabaee, Serdar Durdyev,
Syuhaida Ismail, Arham
A prototype decision support system for green roof type selection: A cybernetic Table 4.
Sustainable cities and society
fuzzy ANP method
Abdullah, and Wan Nurul
Mardiah Wan Mohd Rani
Kazemi-Beydokhti, M., R.
Ali Abbaspour, M. Determination of the physical domain for air quality monitoring stations using the
Environmental monitoring and assessment
Kheradmandi, and A. ANP-OWA method in GIS
Bozorgi-Amiri
Tan, Zhongfu, Qingkun Tan,
Liwei Ju, Shenbo Yang, Trend Analysis and Comprehensive Evaluation of Green Production Principal
Discrete Dynamics in Nature and Society
Huangfu Cheng, and Jiale Component of Thermal Power Unit Based on ANP-MEEM Model
Ma
Seyedmohammadi, Javad,
Fereydoon Sarmadian, Ali Integration of ANP and Fuzzy set techniques for land suitability assessment based
Archives of Agronomy and Soil Science
Asghar Jafarzadeh, and on remote sensing and GIS for irrigated maize cultivation
Richard W. McDowell
Hu, Yaoguang, Shasha Xiao,
An ANP-multi-criterion-based methodology to construct maintenance networks
Jingqian Wen, and Jinliang Computers and electronics in agriculture
for agricultural machinery cluster in a balanced scorecard context
Li
Ligardo-Herrera, Ivan,
Application of the ANP to the prioritization of project stakeholders in the context
Tomás Gómez-Navarro, and Central European Journal of Operations Research
of responsible research and innovation
Hannia Gonzalez-Urango
Poudeh, Hossein Dehghani,
Mohsen Cheshmberah, Determining and prioritizing the factors influencing the outsourcing of Complex
Hassan Torabi, Mohammad Product Systems R&D projects employing ANP and grey-DEMATEL method Technology in Society
Hossein Karimi Gavareshki, (case study: Aviation Industries Organization, Iran)
and Reza Hosnavi
Yucelgazi, Fikri, and İbrahim An ANP Model for Risk Assessment in Large-Scale Transport Infrastructure
Arabian Journal for Science and Engineering
Yitmen Projects
Choi, Cheol-Rim, and Hwa- Quality evaluation for multimedia contents of e-learning systems using the ANP
Multimedia Tools and Applications
Young Jeong approach on high-speed network
Karimi, Marziyeh, Amir An application of fuzzy-logic and grey-relational ANP-based SWOT in the Knowledge-Based Systems
Hossein Niknamfar, and ceramic and tile industry
Seyed Taghi Akhavan Niaki

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2000-2019

Table 4
Research publications in engineering/technology/applied science category for AHP-2000 to 2019
AHP

Authors Research Title Journal Name

(Cagno, Caron, Mancini, & Using AHP in determining the prior distributions on gas pipeline failures in a Reliability Engineering & System Safety
Ruggeri, 2000) robust Bayesian approach
(Tummala & Ling, 2000) A note on the sampling distribution of the information content of the priority vector Journal of the Operational Research Society
of a consistent pairwise comparison judgment matrix of AHP
(Tam & Tummala, 2001) An application of the AHP in vendor selection of a telecommunications system Omega

(Byun, 2001) The AHP approach for selecting an automobile purchase model Information & Management

(Badri, 2001) A combined AHP–GP model for quality control systems International Journal of Production Economics

(Yusuff, Yee, & Hashmi, 2001) A preliminary study on the potential use of the analytical hierarchical process Robotics and Computer-Integrated
(AHP) to predict advanced manufacturing technology (AMT) implementation Manufacturing
(Fahmy, 2001) Reliability evaluation in distributed computing environments using the AHP Computer Networks

(Kwong & Bai, 2002) A fuzzy AHP approach to the determination of importance weights of customer Journal of intelligent manufacturing
requirements in quality function deployment
(Lai, Wong, & Cheung, 2002) Group decision making in a multiple criteria environment: A case using the AHP in European Journal of Operational Research
software selection
(Kuo, Chi, & Kao, 2002) A decision support system for selecting convenience store location through Computers in industry
integration of fuzzy AHP and artificial neural network
(Beynon, DS/AHP method: A DS/AHP method: A mathematical analysis, including an understanding of European Journal of Operational Research
mathematical analysis, uncertainty
including an understanding of
uncertainty, 2002)
(Lipovetsky & Conklin, 2002) Robust estimation of priorities in the AHP European Journal of Operational Research

(Chin, Pun, Xu, & Chan, 2002) An AHP based study of critical factors for TQM implementation in Shanghai Technovation
manufacturing industries
(Beynon, An analysis of An analysis of distributions of priority values from alternative comparison scales European Journal of Operational Research
distributions of priority values within AHP
from alternative comparison
scales within AHP, 2002)
(Monitto, Pappalardo, & Tolio, A new fuzzy AHP method for the evaluation of automated manufacturing systems CIRP Annals
2002)
Forgionne, Guisseppi A., Rajiv An AHP analysis of quality in AI and DSS journals Omega
Kohli, and Darniet Jennings
Mohamadghasemi, A., and A. A decision support system for selecting convenience store location through Computers in industry
Hadi-Vencheh integration of fuzzy AHP and artificial neural network

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2000-2019

Thirumalaivasan, D., M. AHP-DRASTIC: software for specific aquifer vulnerability assessment using Environmental Modelling & Software
Karmegam, and K. Venugopal DRASTIC model and GIS
Abdi, Mohammad Reza, and A design strategy for reconfigurable manufacturing systems (RMSs) using International Journal of production research
Ashraf W. Labib analytical hierarchical process (AHP): a case study
Laininen, Pertti, and Raimo P. Analyzing AHP-matrices by regression European Journal of Operational Research
Hämäläinen
Stam, Antonie, and A. Pedro On multiplicative priority rating methods for the AHP European Journal of Operational Research
Duarte Silva
Scale transitivity in the AHP Journal of the Operational Research Society
Ji, Ping, and Renyan Jiang
Shee, Daniel Y., Gwo-Hshiung AHP, fuzzy measure and fuzzy integral approaches for the appraisal of information Journal of Global Information Technology
Tzeng, and Tzung-I. Tang service providers in Taiwan Management
Ong, S. K., M. J. Sun, and A. A fuzzy set AHP-based DFM tool for rotational parts Journal of Materials Processing Technology
Y. C. Nee
Fogliatto, Flavio S., and Susan An AHP-based procedure for sensory data collection and analysis in quality and Food Quality and Preference
L. Albin reliability applications
A method for solving LSM problems of small size in the AHP Central European Journal of Operations
Bozóki, Sándor Research
Yang, Z. Y., Y. H. Chen, and Using AHP and fuzzy sets to determine the build orientation in layer-based International Journal of Computer Integrated
W. S. Sze machining Manufacturing
Macharis, Cathy, Johan PROMETHEE and AHP: The design of operational synergies in multicriteria European Journal of Operational Research
Springael, Klaas De Brucker, analysis.: Strengthening PROMETHEE with ideas of AHP
and Alain Verbeke
Lirn, T. C., H. A. Thanopoulou, An application of AHP on transhipment port selection: a global perspective Maritime Economics & Logistics
Malcolm James Beynon, and
Anthony Kenneth Charles
Beresford
Shrestha, Ram K., Janaki RR Exploring the potential for silvopasture adoption in south-central Florida: an Agricultural Systems
Alavalapati, and Robert S. application of SWOT–AHP method
Kalmbacher
Albayrak, Esra, and Yasemin Using analytic hierarchy process (AHP) to improve human performance: An Journal of Intelligent Manufacturing
Claire Erensal application of multiple criteria decision-making problem
Escobar, María Teresa, Juan A note on AHP group consistency for the row geometric mean priorization European Journal of Operational Research
Aguarón, and José María procedure
Moreno-Jiménez
AHP as a strategic decision-making tool to justify machine tool selection Journal of Materials Processing Technology
Yurdakul, Mustafa
Sugihara, Kazutomi, Hiroaki Interval priorities in AHP by interval regression analysis European Journal of Operational Research
Ishii, and Hideo Tanaka
Kwiesielewicz, Miroslaw, and Inconsistent and contradictory judgements in pairwise comparison method in the Computers & Operations Research
Ewa Van Uden AHP
Enea, Mario, and Tommaso Project selection by constrained fuzzy AHP Fuzzy optimization and decision making
Piazza

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2000-2019

Group prioritization in the AHP by fuzzy preference programming method Computers & operations research
Mikhailov, Ludmil
Gass, Saul I., and Tamás Singular value decomposition in AHP European Journal of Operational Research
Rapcsák
Yurdakul, Mustafa, and Yusuf AHP approach in the credit evaluation of the manufacturing firms in Turkey International Journal of Production Economics
Tansel Ic
An AHP/DEA method for measurement of the efficiency of R&D management International Transactions in Operational
Feng, Y. J., H. Lu, and K. Bi activities in universities Research
Ishizaka, Alessio, and Markus An expert module to improve the consistency of AHP matrices International Transactions in Operational
Lusti Research
A practical method for improving consistency of judgement matrix in the AHP Journal of systems science and complexity
Zeshui, X. U
Ginevičius, Romualdas, Determining of technological effectiveness of building systems by AHP method Technological and Economic Development of
Valentinas Podvezko, and Economy
Algirdas Andruškevičius
Bhattacharya, Arijit, Bijan Integrating AHP with QFD for robot selection under requirement perspective International Journal of production research
Sarkar*, and Sanat Kumar
Mukherjee
Salmeron, Jose L., and Ines An AHP-based methodology to rank critical success factors of executive Computer Standards & Interfaces
Herrero information systems
Use of AHP in decision-making for flexible manufacturing systems Journal of Manufacturing Technology
Bayazit, Ozden Management
A fuzzy AHP-based simulation approach to concept evaluation in a NPD IIE transactions
Ayağ, Zeki environment
Yurdakul*, Mustafa, and Y. Development of a performance measurement model for manufacturing companies International Journal of production research
Tansel Ic using the AHP and TOPSIS approaches
Understanding local ignorance and non-specificity within the DS/AHP method of European Journal of Operational Research
Beynon, Malcolm J multi-criteria decision making
Majumdar, A., B. Sarkar, and Determination of quality value of cotton fibre using hybrid AHP-TOPSIS method Journal of the Textile Institute
P. K. Majumdar of multi-criteria decision-making
Liu, Chih-Ming, Hen-Shen A performance evaluation model based on AHP and DEA Journal of the Chinese Institute of Industrial
Hsu, Shen-Tsu Wang, and Hai- Engineers
Kun Lee
Bozóki, Sandor, and Robert H. Solving the Least Squares Method problem in the AHP for 3 x 3 and 4 x 4 matrices Central European Journal of Operations
Lewis Research
Variant process planning of castings using AHP-based nearest neighbour algorithm International Journal of production research
Chougule, R. G., and B. Ravi for case retrieval
MarÍa, JosÉ, Moreno JimÉnez, A spreadsheet module for consistent consensus building in AHP-group decision Group Decision and Negotiation
Juan AguarÓn Joven, AgustÍn making
Raluy Pirla, and Alberto TurÓn
Lanuza
Lee, Younghwa, and Kenneth Investigating the effect of website quality on e-business success: An analytic Decision support systems
A. Kozar hierarchy process (AHP) approach

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Ayağ, Zeki, and Rifat Gürcan A fuzzy AHP approach to evaluating machine tool alternatives Journal of intelligent manufacturing
Özdemir
Applying the analytical hierarchy process (AHP) approach to convention site Journal of Travel Research
Chen, Ching-Fu selection
Bertolini, Massimo, and A combined goal programming—AHP approach to maintenance selection problem Reliability Engineering & System Safety
Maurizio Bevilacqua
Aull-Hyde, Rhonda, Sevgi An experiment on the consistency of aggregated comparison matrices in AHP European Journal of Operational Research
Erdogan, and Joshua M. Duke
Fu, Hsin-Pin, Yung-Ching Ho, Factors affecting the adoption of electronic marketplaces: A fuzzy AHP analysis International Journal of Operations &
Roger CY Chen, Tien-Hsiang Production Management
Chang, and Pei-Hsiang Chien
Hanumaiah, Naga, B. Ravi, and Rapid hard tooling process selection using QFD-AHP methodology Journal of Manufacturing Technology
N. P. Mukherjee Management
Braglia, Marcello, Gionata AHP-based evaluation of CMMS software Journal of Manufacturing Technology
Carmignani, Marco Frosolini, Management
and Andrea Grassi
Ung, S. T., V. Williams, H. S. Human error assessment and management in port operations using fuzzy AHP Marine Technology Society Journal
Chen, S. Bonsall, and J. Wang
Multi-criteria decision-making approach with incomplete certain information based Journal of Systems Engineering and Electronics
Wang, Jianqiang on ternary AHP
Beskese, Ahmet, and F. TUNÇ Prioritization of relational capital measurement indicators using fuzzy AHP Applied Artificial Intelligence
BOZBURA
Sharma, B. C., and O. P. RUL assessment of lube oil using AHP and vector projection approach Industrial Lubrication and Tribology
Gandhi
Damigos, D., and D. Developing fuzzy AHP system to evaluate rehabilitation alternatives of asbestos Mineral Processing and Extractive Metallurgy
Kaliampakos industrial complex
Chang, Che-Wei, Cheng-Ru An application of AHP and sensitivity analysis for selecting the best slicing Computers & Industrial Engineering
Wu, Chin-Tsai Lin, and Huang- machine
Chu Chen
Gerdsri, Nathasit, and Dundar Applying the Analytic Hierarchy Process (AHP) to build a strategic framework for Mathematical and Computer Modelling
F. Kocaoglu technology road mapping
Chiu, Yu-Jing, and Yuh-Wen Using AHP in patent valuation Mathematical and Computer Modelling
Chen
Kang, He-Yau, and Amy HI Priority mix planning for semiconductor fabrication by fuzzy AHP ranking Expert Systems with Applications
Lee
Çimren, Emrah, Bülent Çatay, Development of a machine tool selection system using AHP The International Journal of Advanced
and Erhan Budak Manufacturing Technology
Measuring the efficiency of production units by AHP models Mathematical and Computer Modelling
Jablonsky, Josef
Kreng, Victor B., and Chao-Yi Evaluation of knowledge portal development tools using a fuzzy AHP approach: European Journal of Operational Research
Wu The case of Taiwanese stone industry
A hybrid approach to machine-tool selection through AHP and simulation International journal of production research
Ayağ, Z

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Detecting and adjusting ordinal and cardinal inconsistencies through a graphical Computers & Operations Research
Li, Han-Lin, and Li-Ching Ma and optimal approach in AHP models
Statistical analyses on time complexity and rank consistency between singular Mathematical and Computer Modelling
Mamat, Nur Jumaadzan Zaleha, value decomposition and the duality approach in AHP: A case study of faculty
and Jacob Karikottu Daniel member selection
Lee, Amy HI, Wen-Chin Chen, A fuzzy AHP and BSC approach for evaluating performance of IT department in Expert Systems with Applications
and Ching-Jan Chang the manufacturing industry in Taiwan
Lin, Ming-Chyuan, Chen- Using AHP and TOPSIS approaches in customer-driven product design process Computers in industry
Cheng Wang, Ming-Shi Chen,
and C. Alec Chang
Decision making in equipment selection: an integrated approach with AHP and Journal of intelligent manufacturing
Dağdeviren, Metin PROMETHEE
e Costa, Carlos A. Bana, and A critical analysis of the eigenvalue method used to derive priorities in AHP European Journal of Operational Research
Jean-Claude Vansnick
Durán, Orlando, and José Computer-aided machine-tool selection based on a Fuzzy-AHP approach Expert Systems with Applications
Aguilo
Fuzzy AHP approach for selecting the suitable bridge construction method Automation in construction
Pan, Nang-Fei
Wong, Johnny KW, and Heng Application of the analytic hierarchy process (AHP) in multi-criteria analysis of the Building and Environment
Li selection of intelligent building systems
Zayed, Tarek, Mohamed Amer, Assessing risk and uncertainty inherent in Chinese highway projects using AHP International journal of project management
and Jiayin Pan
Wang, Ying-Ming, Jun Liu, An integrated AHP–DEA methodology for bridge risk assessment Computers & Industrial Engineering
and Taha MS Elhag
Cakir, Ozan, and Mustafa S. A web-based decision support system for multi-criteria inventory classification Expert Systems with Applications
Canbolat using fuzzy AHP methodology
Dong, Yucheng, Yinfeng Xu, A comparative study of the numerical scales and the prioritization methods in AHP European Journal of Operational Research
Hongyi Li, and Min Dai
Azadeh, Ali, S. F. Ghaderi, and Integration of DEA and AHP with computer simulation for railway system Applied Mathematics and Computation
H. Izadbakhsh improvement and optimization
Chen, Mei-Fang, Gwo-Hshiung Combining fuzzy AHP with MDS in identifying the preference similarity of Applied Soft Computing
Tzeng, and Cherng G. Ding alternatives
Lee, Seong Kon, Gento Mogi, The competitiveness of Korea as a developer of hydrogen energy technology: the Energy policy
and Jong Wook Kim AHP approach
Chin, Kwai-Sang, Dong-ling Group-based ER–AHP system for product project screening Expert Systems with Applications
Xu, Jian-Bo Yang, and James
Ping-Kit Lam
Chang, Che-Wei, Cheng-Ru Using expert technology to select unstable slicing machine to control wafer slicing Expert Systems with Applications
Wu, and Huang-Chu Chen quality via fuzzy AHP
Melon, Monica Garcia, Pablo An AHP-based evaluation procedure for Innovative Educational Projects: A face- Omega
Aragonés Beltran, and M. to-face vs. computer-mediated case study
Carmen González Cruz
Dağdeviren, Metin, Serkan Weapon selection using the AHP and TOPSIS methods under fuzzy environment Expert Systems with Applications
Yavuz, and Nevzat Kılınç

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Words from the AHP Creator International Journal of the Analytic Hierarchy
Saaty, Thomas L Process
Fuzzy AHP-based decision support system for selecting ERP systems in textile Expert Systems with Applications
Cebeci, Ufuk industry by using balanced scorecard
Celik, Metin, I. Deha Er, and Application of fuzzy extended AHP methodology on shipping registry selection: Expert Systems with Applications
A. Fahri Ozok The case of Turkish maritime industry
Tseng, Ming-Lang, Yuan-Hsu Fuzzy AHP-based study of cleaner production implementation in Taiwan PWB Journal of Cleaner Production
Lin, and Anthony SF Chiu manufacturer
Li, Yanlai, Jiafu Tang, An integrated method of rough set, Kano’s model and AHP for rating customer Expert Systems with Applications
Xinggang Luo, and Jie Xu requirements’ final importance
Li, Te-Sheng, and Hsing-Hsin RETRACTED: Applying TRIZ and Fuzzy AHP to develop innovative design for Expert Systems with Applications
Huang automated manufacturing systems
Perini, Anna, Filippo Ricca, Tool-supported requirements prioritization: Comparing the AHP and CBRank Information and Software Technology
and Angelo Susi methods
Sharma, Sanjay, and Narayan Selection of a pull production control policy under different demand situations for a Computers & Operations Research
Agrawal manufacturing system by AHP-algorithm
Karaarslan, Nevin, and Emin An application for modular capability-based ERP software selection using AHP The International Journal of Advanced
Gundogar method Manufacturing Technology
Lozano, Sebastián, and Gabriel Multi-objective target setting in data envelopment analysis using AHP Computers & Operations Research
Villa
Aguilar-Lasserre, Alberto A., An AHP-based decision-making tool for the solution of multiproduct batch plant Computers & Operations Research
Marco A. Bautista Bautista, design problem under imprecise demand
Antonin Ponsich, and Magno
A. González Huerta
An online credit evaluation method based on AHP and SPA Communications in Nonlinear Science and
Xu, Yingtao, and Ying Zhang Numerical Simulation
Project selection for oil-fields development by using the AHP and fuzzy TOPSIS Expert Systems with Applications
Amiri, Morteza Pakdin methods
An interpretation of the AHP eigenvector solution for the layperson International Journal of the Analytic Hierarchy
Lipovetsky, Stan Process
Torfi, Fatemeh, Reza Zanjirani Fuzzy AHP to determine the relative weights of evaluation criteria and Fuzzy Applied Soft Computing
Farahani, and Shabnam TOPSIS to rank the alternatives
Rezapour
Chamodrakas, Ioannis, D. Supplier selection in electronic marketplaces using satisficing and fuzzy AHP Expert Systems with Applications
Batis, and Drakoulis Martakos
Hsu, Yu-Lung, Cheng-Haw The application of Fuzzy Delphi Method and Fuzzy AHP in lubricant regenerative Expert Systems with Applications
Lee, and Victor B. Kreng technology selection
An application of fuzzy AHP for evaluating course website quality Computers & Education
Lin, Hsiu-Fen
Nepal, Bimal, Om P. Yadav, A fuzzy-AHP approach to prioritization of CS attributes in target planning for Expert Systems with Applications
and Alper Murat automotive product development
Vidal, Ludovic-Alexandre, Applying AHP to select drugs to be produced by anticipation in a chemotherapy Expert Systems with Applications
Evren Sahin, Nicolas Martelli, compounding unit
Malik Berhoune, and Brigitte

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Bonan

Lee, Seong Kon, Gento Mogi, Econometric analysis of the R&D performance in the national hydrogen energy International journal of hydrogen energy
Sang Kon Lee, K. S. Hui, and technology development for measuring relative efficiency: The fuzzy AHP/DEA
Jong Wook Kim integrated model approach
Haghighi, Mahammad, Ali The impact of 3D e-readiness on e-banking development in Iran: A fuzzy AHP Expert Systems with Applications
Divandari, and Masoud analysis
Keimasi
Retracted article: Applying TRIZ and AHP to develop innovative design for The International Journal of Advanced
Li, Tesheng automated assembly systems Manufacturing Technology
Kuo, R. J., L. Y. Lee, and Developing a supplier selection system through integrating fuzzy AHP and fuzzy Production Planning and Control
Tung-Lai Hu DEA: a case study on an auto lighting system company in Taiwan
Tudes, Sule, and Nazan Duygu Preparation of land use planning model using GIS-based on AHP: case study Bulletin of engineering geology and the
Yigiter Adana-Turkey environment
Yu, Xiaobing, Shunsheng Guo, Rank B2C e-commerce websites in e-alliance based on AHP and fuzzy TOPSIS Expert Systems with Applications
Jun Guo, and Xiaorong Huang
About one approach to AHP/ANP stability measurement International Journal of the Analytic Hierarchy
Tsyganok, Vitaliy V Process
An interpretation of the AHP global priority as the eigenvector solution of an ANP International Journal of the Analytic Hierarchy
Lipovetsky, Stan supermatrix Process
Peng, Yi, Gang Kou, Guoxun Ensemble of software defect predictors: an AHP-based evaluation method International Journal of Information
Wang, Wenshuai Wu, and Technology & Decision Making
Yong Shi
Performance measurement model for Turkish aviation firms using the rough-AHP Expert Systems with Applications
Aydogan, Emel Kızılkaya and TOPSIS methods under fuzzy environment
Dehghanian, Payman, Mahmud Critical component identification in reliability-centered asset management of power IEEE Systems Journal
Fotuhi-Firuzabad, Saeed distribution systems via fuzzy AHP
Bagheri-Shouraki, and Ali
Asghar Razi Kazemi
Tavana, Madjid, and Adel A group AHP-TOPSIS framework for human spaceflight mission planning at Expert Systems with Applications
Hatami-Marbini NASA
Computer-aided maintenance management systems selection based on a fuzzy Advances in Engineering Software
Durán, Orlando AHP approach
Lee, SeongKon, Gento Mogi, Prioritizing the weights of hydrogen energy technologies in the sector of the International journal of hydrogen energy
SangKon Lee, and JongWook hydrogen economy by using a fuzzy AHP approach
Kim
Bernardon, Daniel Pinheiro, AHP decision-making algorithm to allocate remotely controlled switches in IEEE Transactions on Power Delivery
Mauricio Sperandio, Vinícius distribution networks
Jacques Garcia, Luciane Neves
Canha, Alzenira da Rosa
Abaide, and Eric Fernando
Boeck Daza
Benítez, Joaquín, Xitlali Balancing consistency and expert judgment in AHP Mathematical and Computer Modelling
Delgado-Galván, J. A.

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Gutiérrez, and Joaquín

Izquierdo
Wu, Qiang, Yuanzhang Liu, Prediction of floor water inrush: the application of GIS-based AHP vulnerable Rock Mechanics and Rock Engineering
Donghai Liu, and Wanfang index method to Donghuantuo coal mine, China
Zhou
Kutlu, Ahmet Can, and Fuzzy failure modes and effects analysis by using fuzzy TOPSIS-based fuzzy AHP Expert Systems with Applications
Mehmet Ekmekçioğlu
Girard, Luigi Fusco, Maria Analytic hierarchy process (AHP) and geographical information systems (GIS): an International Journal of the Analytic Hierarchy
Cerreta, and Pasquale De Toro integrated spatial assessment for planning strategic choices Process
Büyüközkan, Gülçin, and A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic Expert Systems with Applications
Gizem Çifçi service quality in healthcare industry
Choudhary, Devendra, and A STEEP-fuzzy AHP-TOPSIS framework for evaluation and selection of thermal Energy
Ravi Shankar power plant location: A case study from India
Chou, Ying-Chyi, Chia-Chi Evaluating the criteria for human resource for science and technology (HRST) Applied Soft Computing
Sun, and Hsin-Yi Yen based on an integrated fuzzy AHP and fuzzy DEMATEL approach
Javanbarg, Mohammad Bagher, Fuzzy AHP-based multicriteria decision making systems using particle swarm Expert Systems with Applications
Charles Scawthorn, Junji optimization
Kiyono, and Babak
Shahbodaghkhan
Taha, Zahari, and Sarkawt A hybrid fuzzy AHP-PROMETHEE decision support system for machine tool Journal of Intelligent Manufacturing
Rostam selection in flexible manufacturing cell
Lee, Sangjae, Wanki Kim, Using AHP to determine intangible priority factors for technology transfer adoption Expert Systems with Applications
Young Min Kim, and Kyong
Joo Oh
Chan, Hing Kai, Xiaojun An extended fuzzy-AHP approach for the evaluation of green product designs IEEE Transactions on Engineering Management
Wang, Gareth Reginald
Terence White, and Nick Yip
GIS-based solar farms site selection using analytic hierarchy process (AHP) in Renewable and Sustainable Energy Reviews
Uyan, Mevlut Karapinar region, Konya/Turkey
Development of a new technology product evaluation model for assessing Expert Systems with Applications
Cho, Jaemin, and Jaeho Lee commercialization opportunities using Delphi method and fuzzy AHP approach
Nikou, Shahrokh, and József Evaluation of mobile services and substantial adoption factors with Analytic Telecommunications Policy
Mezei Hierarchy Process (AHP)
Chen, Yun, Jia Yu, and The spatial framework for weight sensitivity analysis in AHP-based multi-criteria Environmental modelling & software
Shahbaz Khan decision making
Caputo, Antonio C., Pacifico AHP-based methodology for selecting safety devices of industrial machinery Safety science
M. Pelagagge, and Paolo Salini
The integrated framework for analysis of electricity supply chain using an International Journal of Electrical Power &
integrated SWOT-fuzzy TOPSIS methodology combined with AHP: The case of Energy Systems
Bas, Esra Turkey
A fuzzy analytic hierarchy process (AHP)/data envelopment analysis (DEA) hybrid Renewable and Sustainable Energy Reviews
Lee, Seong Kon, Gento Mogi, model for efficiently allocating energy R&D resources: In the case of energy
and K. S. Hui technologies against high oil prices

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Yang, Xiaojun, Liaoliao Yan, How to handle uncertainties in AHP: The Cloud Delphi hierarchical analysis Information Sciences
and Luan Zeng
Mousavi, S. Meysam, R. Multi-criteria decision making for plant location selection: an integrated Delphi– Arabian Journal for Science and Engineering
Tavakkoli-Moghaddam, M. AHP–PROMETHEE methodology
Heydar, and S. Ebrahimnejad
Wu, Jian, Hai-bin Huang, and Research on AHP with interval-valued intuitionistic fuzzy sets and its application Applied Mathematical Modelling
Qing-Wei Cao in multi-criteria decision-making problems
Hadi-Vencheh, A., and A. An integrated AHP–NLP methodology for facility layout design Journal of Manufacturing Systems
Mohamadghasemi
Deng, Xinyang, Yong Hu, Supplier selection using AHP methodology extended by D numbers Expert Systems with Applications
Yong Deng, and Sankaran
Mahadevan
Taylan, Osman, Abdallah O. Construction projects selection and risk assessment by fuzzy AHP and fuzzy Applied Soft Computing
Bafail, Reda MS Abdulaal, and TOPSIS methodologies
Mohammed R. Kabli
Kou, Gang, and Changsheng A cosine maximization method for the priority vector derivation in AHP European Journal of Operational Research
Lin
A decision model for information technology selection using AHP integrated Knowledge-Based Systems
Oztaysi, Basar TOPSIS-Grey: The case of content management systems
Wang, Ying, Kyung-Ae Jung, Selecting a cruise port of call location using the fuzzy-AHP method: A case study Tourism Management
Gi-tae Yeo, and Chien-Chang in East Asia
Chou
Avikal, Shwetank, P. K. A Fuzzy AHP and PROMETHEE method-based heuristic for disassembly line International Journal of production research
Mishra, and Rajeev Jain balancing problems
Vinodh, S., M. Prasanna, and Integrated Fuzzy AHP–TOPSIS for selecting the best plastic recycling method: A Applied Mathematical Modelling
N. Hari Prakash case study
Pedrycz, Witold, and Mingli A granulation of linguistic information in AHP decision-making problems Information Fusion
Song
Tan, R. R., K. B. Aviso, A. P. Fuzzy AHP approach to selection problems in process engineering involving Process Safety and Environmental Protection
Huelgas, and M. A. B. quantitative and qualitative aspects
Promentilla
Kutut, V., E. K. Zavadskas, and Assessment of priority alternatives for preservation of historic buildings using Archives of Civil and Mechanical Engineering
M. Lazauskas model based on ARAS and AHP methods
Ozgen, Dogan, and Bahadir Combining possibilistic linear programming and fuzzy AHP for solving the multi- Information Sciences
Gulsun objective capacitated multi-facility location problem
Jalao, Eugene Rex, Teresa Wu, A stochastic AHP decision-making methodology for imprecise preferences Information Sciences
and Dan Shunk
Song, Zeyang, Hongqing Zhu, Comprehensive evaluation on self-ignition risks of coal stockpiles using fuzzy Journal of Loss Prevention in the Process
Guowei Jia, and Chaonan He AHP approaches Industries
Measuring operational performance of OSH management system–A demonstration Safety science
Podgórski, Daniel of AHP-based selection of leading key performance indicators
An AHP application in the investment selection problem of small hydropower International Journal of the Analytic Hierarchy
Saracoglu, Burak Omer plants in Turkey Process

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Oyatoye, Emmanuel Olateju, Evaluating Subscribers’ preference for service attributes of mobile International Journal of the Analytic Hierarchy
Sulaimon Olanrewaju Adebiyi, telecommunication in Nigeria using analytic hierarchy process (AHP) Process
and Bilqis Bolanle Amole
An analytic hierarchy process (AHP) approach in the selection of sustainable International Journal of the Analytic Hierarchy
Ocampo, Lanndon, and Eppie manufacturing initiatives: a case in a semiconductor manufacturing firm in the Process
Clark Philippines
Ganguly, Anirban, and Donald An Integrated AHP-QFD Approach for Evaluating Competing Technological International Journal of the Analytic Hierarchy
N. Merino Processes Process
Nachtnebel, Hans Peter, and Prioritizing hydropower development using Analytical Hierarchy Process (AHP)-A International Journal of the Analytic Hierarchy
Rana Pratap Singh case study of Nepal Process
Zhu, Guo-Niu, Jie Hu, Jin Qi, An integrated AHP and VIKOR for design concept evaluation based on rough Advanced Engineering Informatics
Chao-Chen Gu, and Ying-Hong number
Peng
Turskis, Zenonas, Edmundas A hybrid model based on fuzzy AHP and fuzzy WASPAS for construction site International Journal of Computers
Kazimieras Zavadskas, Jurgita selection Communications & Control
Antucheviciene, and Natalja
Kosareva
Sivakumar, Ramakrishnan, Green vendor evaluation and selection using AHP and Taguchi loss functions in Resources Policy
Devika Kannan, and Palzha production outsourcing in mining industry
Murugesan
Hyun, Ki-Chang, Sangyoon Risk analysis using fault-tree analysis (FTA) and analytic hierarchy process (AHP) Tunnelling and Underground Space Technology
Min, Hangseok Choi, Jeongjun applicable to shield TBM tunnels
Park, and In-Mo Lee
Zaidan, A. A., B. B. Zaidan, Evaluation and selection of open-source EMR software packages based on Journal of biomedical informatics
Ahmed Al-Haiqi, Miss Laiha integrated AHP and TOPSIS
Mat Kiah, Muzammil Hussain,
and Mohamed Abdulnabi
Akkaya, Gökay, Betül An integrated fuzzy AHP and fuzzy MOORA approach to the problem of industrial Expert Systems with Applications
Turanoğlu, and Sinan Öztaş engineering sector choosing
Lai, Po‐Lin, Andrew Potter, Evaluating the efficiency performance of airports using an integrated AHP/DEA- Transport Policy
Malcolm Beynon, and Anthony AR technique
Beresford
Galvez, Daniel, Auguste Reverse logistics network design for a biogas plant: An approach based on MILP Journal of Manufacturing Systems
Rakotondranaivo, Laure Morel, optimization and Analytical Hierarchical Process (AHP)
Mauricio Camargo, and Michel
Fick
Nguyen, Huu-Tho, Siti Zawiah An integrated approach of fuzzy linguistic preference-based AHP and fuzzy PloS one
Md Dawal, Yusoff Nukman, COPRAS for machine tool evaluation
Hideki Aoyama, and Keith
Case
Notes on order preservation and consistency in AHP European Journal of Operational Research
Kułakowski, Konrad
Ezzabadi, Jamal Hosseini, Implementing Fuzzy Logic and AHP into the EFQM model for performance Applied Soft Computing
Mohammad Dehghani improvement: A case study

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Saryazdi, and Ali

Mostafaeipour
Dong, Minggao, Shouyi Li, and Approaches to group decision making with incomplete information based on power Expert Systems with Applications
Hongying Zhang geometric operators and triangular fuzzy AHP
A Group Decision Making Approach Using Interval Type-2 Fuzzy AHP for Journal of Multiple-Valued Logic & Soft
Oztaysi, Basar Enterprise Information Systems Project Selection Computing
Dweiri, Fikri, Sameer Kumar, Designing an integrated AHP based decision support system for supplier selection Expert Systems with Applications
Sharfuddin Ahmed Khan, and in automotive industry
Vipul Jain
Kubler, Sylvain, Jérémy A state-of the-art survey & testbed of Fuzzy AHP (FAHP) applications Expert Systems with Applications
Robert, William Derigent,
Alexandre Voisin, and Yves Le
Traon
Fan, Guichao, Denghua Zhong, A hybrid fuzzy evaluation method for curtain grouting efficiency assessment based Expert Systems with Applications
Fugen Yan, and Pan Yue on an AHP method extended by D numbers
Singh, Rana Pratap, and Hans Analytical hierarchy process (AHP) application for reinforcement of hydropower Renewable and Sustainable Energy Reviews
Peter Nachtnebel strategy in Nepal
Galankashi, Masoud Supplier selection in automobile industry: A mixed balanced scorecard–fuzzy AHP Alexandria Engineering Journal
Rahiminezhad, Syed Ahmad approach
Helmi, and Pooria Hashemzahi
Beşikçi, E. Bal, T. Kececi, O. An application of fuzzy-AHP to ship operational energy efficiency measures Ocean Engineering
Arslan, and O. Turan
Chaudhary, Pandav, Sachin Application of an Analytic Hierarchy Process (AHP) in the GIS interface for Socio-Economic Planning Sciences
Kumar Chhetri, Kiran Man suitable fire site selection: A case study from Kathmandu Metropolitan City, Nepal
Joshi, Basanta Man Shrestha,
and Prabin Kayastha
Elia, Valerio, Maria Grazia Evaluating the application of augmented reality devices in manufacturing from a Expert Systems with Applications
Gnoni, and Alessandra process point of view: An AHP based model
Lanzilotto
Lee, Sangwon, and Kwang- A hybrid multi-criteria decision-making model for a cloud service selection Wireless Personal Communications
Kyu Seo problem using BSC, fuzzy Delphi method and fuzzy AHP
Hanine, Mohamed, Omar Application of an integrated multi-criteria decision making AHP-TOPSIS SpringerPlus
Boutkhoum, Abdessadek methodology for ETL software selection
Tikniouine, and Tarik Agouti
Singh, Sujit, Ezutah Udoncy Strategy selection for sustainable manufacturing with integrated AHP-VIKOR The International Journal of Advanced
Olugu, Siti Nurmaya Musa, method under interval-valued fuzzy environment Manufacturing Technology
Abu Bakar Mahat, and Kuan
Yew Wong
Hosseini Firouz, Mansour, and Optimal preventive maintenance policy for electric power distribution systems Complexity
Noradin Ghadimi based on the fuzzy AHP methods
Which energy mix for the UK (United Kingdom)? An evolutive descriptive Energy
Ishizaka, Alessio, Sajid Siraj, mapping with the integrated GAIA (graphical analysis for interactive aid)–AHP
and Philippe Nemery (analytic hierarchy process) visualization tool

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Garbuzova-Schlifter, Maria, AHP-based risk analysis of energy performance contracting projects in Russia Energy policy
and Reinhard Madlener
Luzon, Bushra, and Sameh M. Evaluating supplier selection criteria for oil and gas projects in the UAE using International Journal of Construction
El-Sayegh AHP and Delphi Management
Sindhu, Sonal, Vijay Nehra, Investigation of feasibility study of solar farms deployment using hybrid AHP- Renewable and Sustainable Energy Reviews
and Sunil Luthra TOPSIS analysis: Case study of India
An algebraic representation via differential equations for pairwise comparisons of International Journal of the Analytic Hierarchy
Mizuno, Takafumi AHP Process
Li, Wenhua, Suihuai Yu, A hybrid approach based on fuzzy AHP and 2-tuple fuzzy linguistic method for Journal of Air Transport Management
Huining Pei, Chuan Zhao, and evaluation in-flight service quality
Baozhen Tian
Al Garni, Hassan Z., and Anjali Solar PV power plant site selection using a GIS-AHP based approach with Applied energy
Awasthi application in Saudi Arabia
Özcan, Evren Can, Sultan A combined goal programming–AHP approach supported with TOPSIS for Renewable and Sustainable Energy Reviews
Ünlüsoy, and Tamer Eren maintenance strategy selection in hydroelectric power plants
Bian, Tian, Jiantao Hu, and Identifying influential nodes in complex networks based on AHP Physica A: Statistical Mechanics and its
Yong Deng Applications
Raviv, Gabriel, Aviad Shapira, AHP-based analysis of the risk potential of safety incidents: Case study of cranes in Safety science
and Barak Fishbain the construction industry
Soner, Omer, Erkan Celik, and Application of AHP and VIKOR methods under interval type 2 fuzzy environment Ocean Engineering
Emre Akyuz in maritime transportation
The application of the AHP-TOPSIS for evaluating ballast water treatment systems Transportation Research Part D: Transport and
Karahalios, Hristos by ship operators Environment
Fallahpour, Alireza, Ezutah A hybrid model for supplier selection: integration of AHP and multi expression Neural Computing and Applications
Udoncy Olugu, and Siti programming (MEP)
Nurmaya Musa
Commentary on “Evaluating the criteria for human resource for science and Applied Soft Computing
Pandey, Asmita, and Amit technology (HRST) based on an integrated fuzzy AHP and fuzzy DEMATEL
Kumar approach”
Meesariganda, Bhaskara Raju, Mapping verbal AHP scale to numerical scale for cloud computing strategy Applied Soft Computing
and Alessio Ishizaka selection
Sindhu, Sonal, Vijay Nehra, Solar energy deployment for sustainable future of India: Hybrid SWOC-AHP Renewable and Sustainable Energy Reviews
and Sunil Luthra analysis
Jain, Vipul, Arun Kumar Supplier selection using fuzzy AHP and TOPSIS: a case study in the Indian Neural Computing and Applications
Sangaiah, Sumit Sakhuja, automotive industry
Nittin Thoduka, and Rahul
Aggarwal
Implementation of an online software tool for the analytic hierarchy process (AHP- International Journal of the Analytic Hierarchy
Goepel, Klaus D OS) Process
Kahraman, Cengiz, and Irem Solar PV power plant location selection using a Z-fuzzy number based AHP International Journal of the Analytic Hierarchy
Otay Process
Selection of industrial maintenance strategy: classical AHP and fuzzy AHP International Journal of the Analytic Hierarchy
Ohta, Robison applications Process

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Topcu, Ilker, Berna Unver, An AHP based prioritization model for risk evaluation factors in the automotive International Journal of the Analytic Hierarchy
Mine Isik, and Ozgur Kabak industry Process
Zhou, Xinyi, Yong Hu, Yong A DEMATEL-based completion method for incomplete pairwise comparison Annals of Operations Research
Deng, Felix TS Chan, and matrix in AHP
Alessio Ishizaka
Fattahi, Reza, and Mohammad Risk evaluation using a novel hybrid method based on FMEA extended Safety science
Khalilzadeh MULTIMOORA, and AHP methods under fuzzy environment
Abdel-Basset, Mohamed, Three-way decisions based on neutrosophic sets and AHP-QFD framework for Future Generation Computer Systems
Gunasekaran Manogaran, Mai supplier selection problem
Mohamed, and Naveen
Chilamkurti
Abdel-Basset, Mohamed, Mai Neutrosophic AHP-Delphi Group decision-making model based on trapezoidal Journal of Ambient Intelligence and Humanized
Mohamed, and Arun Kumar neutrosophic numbers Computing
Sangaiah
Sennaroglu, Bahar, and Gulsay A military airport location selection by AHP integrated PROMETHEE and VIKOR Transportation Research Part D: Transport and
Varlik Celebi methods Environment
Goyal, Raman Kumar, Sakshi The utility-based non-linear fuzzy AHP optimization model for network selection Applied Soft Computing
Kaushal, and Arun Kumar in heterogeneous wireless networks
Sangaiah
Pamučar, Dragan, Željko Integration of interval rough AHP and interval rough MABAC methods for Applied Soft Computing
Stević, and Edmundas evaluating university web pages
Kazimieras Zavadskas
Azimifard, Arezoo, Seyed Selecting sustainable supplier countries for Iran's steel industry at three levels by Resources Policy
Hamed Moosavirad, and using AHP and TOPSIS methods
Shahram Ariafar
(Ali, Butt, Sabir, Mumtaz, & Selection of suitable site in Pakistan for wind power plant installation using Journal of Control and Decision
Salman, 2018) analytic hierarchy process (AHP)
An interval type-2 fuzzy AHP and TOPSIS methods for decision-making problems Ocean Engineering
Celik, Erkan, and Emre Akyuz in maritime transportation engineering: the case of ship loader
Dožić, Slavica, Tatjana Fuzzy AHP approach to passenger aircraft type selection Journal of Air Transport Management
Lutovac, and Milica Kalić
Merrouni, Ahmed Alami, A GIS-AHP combination for the sites assessment of large-scale CSP plants with Solar Energy
Fakhreddine Elwali Elalaoui, dry and wet cooling systems. Case study: Eastern Morocco
Abdellatif Ghennioui, Ahmed
Mezrhab, and Abdelhamid
Mezrhab
Shinde, Dnyandeo Dattatraya, Application of AHP for ranking of total productive maintenance pillars Wireless Personal Communications
and Ramjee Prasad
(Ali, Rasheed, Muhammad, & Energy optimization in the wake of China Pakistan Economic Corridor (CPEC) Journal of Control and Decision
Yousaf, 2018)
Darko, Amos, Albert Ping Review of application of analytic hierarchy process (AHP) in construction International Journal of Construction
Chuen Chan, Ernest Effah Management
Ameyaw, Emmanuel Kingsford
Owusu, Erika Pärn, and David

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John Edwards

Shaygan, Amir, and Özlem A fuzzy AHP-based methodology for project prioritization and selection Soft computing
Müge Testik
Roy, Tribeni, and Ranjit Kumar Integrated fuzzy AHP and fuzzy TOPSIS methods for multi-objective optimization Soft computing
Dutta of electro-discharge machining process
Yucesan, Melih, and Gökhan Risk evaluation and prevention in hydropower plant operations: A model based on Energy policy
Kahraman Pythagorean fuzzy AHP
Abdelmaguid, Tamer F., and Halting decisions for gas pipeline construction projects using AHP: a case study Operational Research
Waleed Elrashidy
Kumar, Naresh, Tej Singh, J. S. A novel hybrid AHP-SAW approach for optimal selection of natural fiber Materials Research Express
Grewal, Amar Patnaik, and reinforced non-asbestos organic brake friction composites
Gusztáv Fekete
Ahmed, Mohd, M. N. Qureshi, Decision support model for design of high-performance concrete mixtures using Advances in Civil Engineering
Javed Mallick, Mohd Hasan, two-phase AHP-TOPSIS approach
and Mahmoud Hussain
İnce, Murat, Tuncay Yiğit, and A hybrid AHP-GA method for metadata-based learning object evaluation Neural Computing and Applications
Ali Hakan Işık
Goyal, Tanu, and Sakshi Handover optimization scheme for LTE-Advance networks based on AHP-TOPSIS Computer Communications
Kaushal and Q-learning
Amohadi, Masoud, and Optimal placement of switching and protection devices in radial distribution Turkish Journal of Electrical Engineering &
MAHMUD FOTUHI networks to enhance system reliability using the AHP-PSO method Computer Sciences
FIRUZABAD
Altuzarra, Alfredo, Pilar Homogeneous groups of actors in an AHP-local decision-making context: A Mathematics
Gargallo, José María Moreno- Bayesian analysis
Jiménez, and Manuel Salvador
Havle, Celal Alpay, and Bilal A hybrid approach based on the fuzzy AHP and HFACS framework for identifying Journal of Air Transport Management
Kılıç and analyzing gross navigation errors during transatlantic flights
Silva, Maisa M., Keith W. Strategic analysis of a regulatory conflict using Dempster-Shafer theory and AHP Journal of Systems Science and Systems
Hipel, D. Marc Kilgour, and for preference elicitation Engineering
Ana Paula CS Costa
Singh, Lakhwinder Pal, and Strategic enhancement of workplace safety in small scale manufacturing industries International Journal of the Analytic Hierarchy
Satnam Singh using AHP approach Process

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Appendix B
SOCIAL SCIENCES
Table 5
Research publications in social science category for ANP-2000 to 2019

ANP
Authors Research Title Journal Name

(Lee & Kim, 2000) Using analytic network process and goal programming for interdependent Computers & Operations Research
information system project selection
(Nishizawa, 2000) Bi-directional nearness in a network by AHP (Analytic Hierarchy Process) and ANP RAIRO-Operations Research-Recherche
(Analytic Network Process) Opérationnelle
(Sekitani & Takahashi, A A unified model and analysis for AHP and ANP Journal of the Operations Research Society of
unified model and analysis for Japan
AHP and ANP, 2001; Momoh
& Zhu, Optimal generation
scheduling based on
AHP/ANP, 2003)
(Momoh & Zhu, Optimal Optimal generation scheduling based on AHP/ANP IEEE Transactions on Systems, Man, and
generation scheduling based on Cybernetics, Part B (Cybernetics)
AHP/ANP, 2003)
(Mikhailov & Singh, 2003) Fuzzy analytic network process and its application to the development of decision IEEE Transactions on Systems, Man, and
support systems Cybernetics, Part C (Applications and
Reviews)
(Saaty T. L., Decision Decision making—the analytic hierarchy and network processes (AHP/ANP) Journal of systems science and systems
making—the analytic hierarchy engineering,
and network processes
(AHP/ANP), 2004)
(Niemira & Saaty, 2004) An analytic network process model for financial-crisis forecasting. International Journal of Forecasting

(Saaty T. L., Fundamentals of Fundamentals of the analytic network process—Dependence and feedback in Journal of Systems science and Systems
the analytic network process— decision-making with a single network engineering
Dependence and feedback in
decision-making with a single
network, 2004)
(Saaty T. L., Fundamentals of Fundamentals of the analytic network process—multiple networks with benefits, journal of systems science and systems
the analytic network process— costs, opportunities and risks engineering
multiple networks with
benefits, costs, opportunities
and risks, 2004)
(Saaty T. L., Making and Making and validating complex decisions with the AHP/ANP Journal of Systems Science and Systems

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validating complex decisions Engineering

with the AHP/ANP, 2005)
(Sekitani & Takahashi, A new A new approach of revising unstable data in ANP by Bayes theorem Journal of the Operations Research Society of
approach of revising unstable Japan
data in ANP by Bayes theorem,
2005)
(Chung, Lee, & Pearn, Analytic Analytic network process (ANP) approach for product mix planning in International journal of production economics
network process (ANP) semiconductor fabricator
approach for product mix
planning in semiconductor
fabricator, 2005)
(Huang, Tzeng, & Ong, 2005) Multidimensional data in multidimensional scaling using the analytic network Pattern Recognition Letters
process
(Coulter & Sarkis, 2005) Development of a media selection model using the analytic network process International journal of advertising

(Agarwal, Shankar, & Tiwari, Modeling the metrics of lean, agile and leagile supply chain: An ANP-based European Journal of Operational Research
2006) approach
(Shyur, 2006) COTS evaluation using modified TOPSIS and ANP Applied mathematics and computation

(Fiala, 2006) An ANP/DNP analysis of economic elements in today’s world network economy Journal of Systems Science and Systems
Engineering
(Mu, 2006) A unified framework for site selection and business forecasting using ANP Journal of systems science and systems
engineering
(Leung, Lam, & Cao, Implementing the balanced scorecard using the analytic hierarchy process & the Journal of the Operational Research Society
Implementing the balanced analytic network process
scorecard using the analytic
hierarchy process & the
analytic network process, 2006)
(Cheng & Li, Job performance Job performance evaluation for construction companies: an analytic network process Journal of Construction Engineering and
evaluation for construction approach Management
companies: an analytic network
process approach, 2006)
(Jharkharia & Shankar, 2007) Selection of logistics service provider: An analytic network process (ANP) approach Omega

(Yuksel & Dagdeviren, 2007) Using the analytic network process (ANP) in a SWOT analysis–A case study for a Information Sciences
textile firm
(Wu, 2008) Choosing knowledge management strategies by using a combined ANP and Expert Systems with Applications
DEMATEL approach
(Chen & Lee, 2008) Applying ANP approach to partner selection for strategic alliance Management Decision

(Tsai & Chou, 2009) Selecting management systems for sustainable development in SMEs: A novel Expert systems with applications
hybrid model based on DEMATEL, ANP, and ZOGP
(Guneri, Cengiz, & Seker, A fuzzy ANP approach to shipyard location selection Expert Systems with Applications
2009)

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(Lin, Tsai, Shiang, Kuo, & Research on using ANP to establish a performance assessment model for business Expert Systems with Applications
Tsai, 2009) intelligence systems
(Hallikainen, Kivijarvi, & Supporting the module sequencing decision in the ERP implementation process—An International Journal of Production
Tuominen, 2009) application of the ANP method Economics
(Chiang-Ku, Hui-Yin, & Jin- Using ANP and GRA to Evaluate the Employability of Graduates from Department Journal of Grey System
Lung, 2009) of Risk Management and Insurance
(Chen & Chen, 2010) Using a novel conjunctive MCDM approach based on DEMATEL, fuzzy ANP, and Expert Systems with Applications
TOPSIS as an innovation support system for Taiwanese higher education
Dağdeviren, Metin, and İhsan A fuzzy analytic network process (ANP) model for measurement of the sectoral Expert Systems with Applications
Yüksel competition level (SCL)
Wu, Cheng-Shiung, Chin-Tsai Optimal marketing strategy: A decision-making with ANP and TOPSIS International Journal of Production
Lin, and Chuan Lee Economics
Evaluating and selecting key performance indicators: an ANP-based model Measuring Business Excellence
Carlucci, Daniela
A novel hybrid model based on DEMATEL and ANP for selecting cost of quality Total Quality Management
Tsai, Wen-Hsien, and Wei Hsu model development
Pastor-Ferrando, Juan-Pascual, An ANP-and AHP-based approach for weighting criteria in public works bidding Journal of the Operational Research Society
Pablo Aragonés-Beltrán,
Antonio Hospitaler-Pérez, and
Mónica García-Melón
Kirytopoulos, Konstantinos, Multiple sourcing strategies and order allocation: an ANP-AUGMECON meta- Supply Chain Management: An International
Vrassidas Leopoulos, George model Journal
Mavrotas, and Dimitra
Voulgaridou
ANP-based marketing activity selection model for construction companies Construction Innovation
Polat, Gul, and Umit Donmez
Using ANP priorities with goal programming in optimally allocating marketing Construction Innovation
Polat, Gul. resources
Yang, Jiann Liang, and Gwo- An integrated MCDM technique combined with DEMATEL for a novel cluster- Expert Systems with Applications
Hshiung Tzeng weighted with ANP method
Lami, Isabella Maria, Elena Analytic network process (ANP) and visualization of spatial data: the use of International Journal of the Analytic
Masala, and Stefano Pensa dynamic maps in territorial transformation processes Hierarchy Process
A balanced scorecard approach to establish a performance evaluation and International Journal of Hospitality
Chen, Fu-Hsiang, Tsung-Shin relationship model for hot spring hotels based on a hybrid MCDM model combining Management
Hsu, and Gwo-Hshiung Tzeng DEMATEL and ANP
Ergu, Daji, Gang Kou, Yi Peng, A simple method to improve the consistency ratio of the pair-wise comparison European Journal of Operational Research
and Yong Shi matrix in ANP
Yücenur, G. Nilay, Özalp Supplier selection problem in global supply chains by AHP and ANP approaches International Journal of Advanced
Vayvay, and Nihan Çetin under fuzzy environment Manufacturing Technology
Demirel
Onut, Semih, Umut R. Selecting container port via a fuzzy ANP-based approach: A case study in the Transport Policy
Tuzkaya, and Erçin Torun Marmara Region, Turkey
Activity-based divergent supply chain planning for competitive advantage in the Expert Systems with Applications
Hung, Shih-Jieh risky global environment: A DEMATEL-ANP fuzzy goal programming approach

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Azimi, Reza, Abdolreza Ranking the strategies of mining sector through ANP and TOPSIS in a SWOT Journal of business economics and
Yazdani-Chamzini, framework management
Mohammad Majid Fouladgar,
Edmundas Kazimieras
Zavadskas, and Mohammad
Hossein Basiri
Thakkar, Jitesh J., Arun Kanda, A decision framework for supply chain planning in SMEs: A QFD-ISM-enabled Supply Chain Forum: An International Journal
and S. G. Deshmukh ANP-GP approach
Wang, Yung-Lan, and Gwo- Brand marketing for creating brand value based on a MCDM model combining Expert Systems with Applications
Hshiung Tzeng DEMATEL with ANP and VIKOR methods
Büyüközkan, Gülçin, and Evaluation of the green supply chain management practices: a fuzzy ANP approach Production Planning & Control
Gizem Çifçi
Poveda-Bautista, Rocío, Doris Setting competitiveness indicators using BSC and ANP International Journal of Production Research
C. Baptista, and Mónica
García-Melón
Yang, Hao-Wei, and Kuei-Feng Combining means-end chain and fuzzy ANP to explore customers’ decision process International Journal of Information
Chang in selecting bundles Management
Pamučar, Dragan, Boban Modification of the dynamic scale of marks in analytic hierarchy process (AHP) and Scientific Research and Essays
Đorović, Darko Božanić, and analytic network approach (ANP) through application of fuzzy approach
Goran Ćirović
Kivijärvi, Hannu, Petri Supporting IT implementation decisions with ANP—supplier scheduling for E- International Journal of Information
Hallikainen, and Esko invoicing Technology & Decision Making
Penttinen
Talebi, K., M. Ghavamipour, Innovation in Iran’s small and medium-size enterprises (SMEs): Prioritize influence African Journal of Business Management
and A. Ir factors affecting innovation of SMEs, using analytic network process (ANP) method
Integrated multi-criteria decision-making (MCDM) method combined with decision- African Journal of Business Management
Shen, Jung-Lu, and Yong-Mei making trial and evaluation laboratory (DEMATEL) and analytic network process
Liu (ANP) in food supplier selection
Yang, Yu-Ping Ou, How-Ming A VIKOR technique based on DEMATEL and ANP for information security risk Information Sciences
Shieh, and Gwo-Hshiung control assessment
Tzeng
The modern science of multicriteria decision making and its practical applications: Operations research
Saaty, Thomas L The AHP/ANP approach
Cil, Ibrahim, and Yusuf S. An ANP-based assessment model for lean enterprise transformation International Journal of Advanced
Turkan Manufacturing Technology
A Fuzzy DEMATEL-ANP Based Multi-Criteria Decision-Making Approach for Journal of Multiple-Valued Logic & Soft
Kabak, Mehmet Personnel Selection Computing
Chang, An-Yuan, Kuo-Jen Hu, An ISM-ANP approach to identifying key agile factors in launching a new product International Journal of Production Research
and Yun-Lin Hong into mass production
Zareinejad, Mohsen, Evaluation and selection of a third-party reverse logistics provider using ANP and Life Science Journal
Habibollah Javanmard, and IFG-MCDM methodology
Iran Arak
Ada, Erhan, Yigit Kazancoglu, Improving Competitiveness of Small‐and Medium‐Sized Enterprises (SMEs) in Agribusiness
and Muhittin Sagnak Agriproduct Export Business Through ANP: The Turkey Case

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Analytic network process (ANP) approach for selecting strategies influencing the African Journal of Business Management
Najafi, Asadallah productivity of knowledge women workers
Cooper, Orrin, and Qingxing Bilateral relations between China and the United States: Policy prioritization with Journal of Systems Science and Systems
Dong the ANP Engineering
Bhattacharya, Arijit, Priyabrata Green supply chain performance measurement using fuzzy ANP-based balanced Production Planning & Control
Mohapatra, Vikas Kumar, scorecard: a collaborative decision-making approach
Prasanta Kumar Dey, Malcolm
Brady, Manoj Kumar Tiwari,
and Sai S. Nudurupati
Miri, Mohsen, Manouchehr Developing ANP to rank the branches of an insurance company based on International Journal of the Analytic
Omidvari, Ahmad Sadeghi, and SERVQUAL Hierarchy Process
Hasan Haleh
Tadić, Snežana, Slobodan A novel hybrid MCDM model based on fuzzy DEMATEL, fuzzy ANP and fuzzy Expert Systems with Applications
Zečević, and Mladen Krstić VIKOR for city logistics concept selection
Wong, Wai Peng, Joshua What is the leanness level of your organisation in lean transformation Production Planning & Control
Ignatius, and Keng Lin Soh implementation? An integrated lean index using ANP approach
Theißen, Sebastian, and Stefan Strategic analysis of manufacturer-supplier partnerships: An ANP model for European Journal of Operational Research
Spinler collaborative CO2 reduction management
Boj, Jorge Juan, Raul An ANP-multi-criterion-based methodology to link intangible assets and Decision Support Systems
Rodriguez-Rodriguez, and organizational performance in a Balanced Scorecard context
Juan-Jose Alfaro-Saiz
Baykasoglu, Adil, and Zeynep A hybrid MCDM for private primary school assessment using DEMATEL based on International Journal of Computational
DU Durmusoglu ANP and fuzzy cognitive map Intelligence
Zamani, Mahmoud, Arefeh An integrated model for extending brand based on fuzzy ARAS and ANP methods Journal of Business Economics and
Rabbani, Abdolreza Yazdani- Management
Chamzini, and Zenonas Turskis
Developing an integrated ANP and intuitionistic fuzzy TOPSIS model for supplier Journal of Testing and Evaluation
Rouyendegh, Babak Daneshvar selection
Ernesto Quezada and, Luis, A method for generating strategy maps using ANP Journal of Manufacturing Technology
Pedro Ivan Palominos, Rosa E. Management
Galleguillos, and Alexis H.
Olmedo
Ergu, Daji, Gang Kou, and A modular-based supplier evaluation framework: A comprehensive data analysis of International Journal of Information
Jennifer Shang ANP structure Technology & Decision Making
Wang, Shih-Ching, and Ming- The use of a hybrid ANP-VIKOR approach for establishing the performance African Journal of Business Management
Kuen Chen evaluation model of e-business project
Kilic, Huseyin Selcuk, Selim Selecting “The Best” ERP system for SMEs using a combination of ANP and Expert Systems with Applications
Zaim, and Dursun Delen PROMETHEE methods
Aragonés-Beltrán, Pablo, Analysis of the participation of stakeholders in environmental management based on International Journal of the Analytic
Mónica García-Melón, and ANP: Application to a Spanish natural park Hierarchy Process
Vicent Estruch-Guitart
Designing a sustainable maritime supply chain: A hybrid QFD–ANP approach Transportation Research Part E: Logistics and
Lam, Jasmine Siu Lee Transportation Review

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Pourahmad, Ahmad, Ali Combination of fuzzy-AHP and DEMATEL-ANP with GIS in a new hybrid MCDM Technological and Economic Development of
Hosseini, Audrius Banaitis, model used for the selection of the best space for leisure in a blighted urban site Economy
Hossein Nasiri, Nerija
Banaitienė, and Gwo-Hshiung
Tzeng
Hu, Yaoguang, Jingqian Wen, Measuring the performance of knowledge resources using a value perspective: Journal of Knowledge Management
and Yan Yan integrating BSC and ANP
Ju, Yanbing, Aihua Wang, and Emergency alternative evaluation and selection based on ANP, DEMATEL, and TL- Natural Hazards
Tianhui You TOPSIS
Gupta, Manish, and Rakesh A fuzzy ANP based approach in the selection of the best E-Business strategy and to Information Technology and Management
Narain assess the impact of E-Procurement on organizational performance
Gölcük, İlker, and Adil An analysis of DEMATEL approaches for criteria interaction handling within ANP Expert Systems with Applications
Baykasoğlu
Selection of Reverse Logistics Service Provider (RLSP) Using Analytical Network International Journal of the Analytic
Jayant, Arvind Process (ANP): A Case Study Of An Automotive Company Hierarchy Process
Vinodh, S., TS Sai Balagi, and A hybrid MCDM approach for agile concept selection using fuzzy DEMATEL, The International Journal of Advanced
Adithya Patil fuzzy ANP and fuzzy TOPSIS Manufacturing Technology
Supeekit, Tuangyot, Tuanjai DEMATEL-modified ANP to evaluate internal hospital supply chain performance Computers & Industrial Engineering
Somboonwiwat, and Duangpun
Kritchanchai
Peker, Iskender, Birdogan Logistics center site selection by ANP/BOCR analysis: A case study of Turkey Journal of Intelligent & Fuzzy Systems
Baki, Mehmet Tanyas, and
Ilker Murat Ar
Shieh, Lon-Fon, Ching-Chiang Critical success factors in digital publishing technology using an ANP approach Technological and Economic Development of
Yeh, and Ming-Cheng Lai Economy
Kong, Feng, Wei Wei, and Jia- Rank reversal and rank preservation in ANP method Journal of Discrete Mathematical Sciences and
Hao Gong Cryptography
Liao, Chin-Nung, Chih-Hsiang Integrative model for the selection of a new product launch strategy, based on ANP, Technological and Economic Development of
Lin, and Yan-Kai Fu TOPSIS and MCGP: a case study Economy
Wan, Shu-ping, Gai-li Xu, and Supplier selection using ANP and ELECTRE II in interval 2-tuple linguistic Information Sciences
Jiu-Ying Dong environment
Pamučar, Dragan, Milan Novel approach to group multi-criteria decision making based on interval rough Expert Systems with Applications
Mihajlović, Radojko numbers: Hybrid DEMATEL-ANP-MAIRCA model
Obradović, and Predrag
Atanasković
Büyüközkan, Gülçin, Sezin A new combined IF-DEMATEL and IF-ANP approach for CRM partner evaluation International journal of production economics
Güleryüz, and Birsen Karpak
Dehdasht, Gholamreza, Rosli DEMATEL-ANP risk assessment in oil and gas construction projects Sustainability
Mohamad Zin, M. Ferwati,
Mohammed Abdullahi, Ali
Keyvanfar, and Ronald
McCaffer
Aragonés-Beltrán, Pablo, Rocío An in-depth analysis of a TTO's objectives alignment within the university strategy: Journal of Engineering and Technology
Poveda-Bautista, and Fernando An ANP-based approach Management

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Jiménez-Sáez

Tang, Hui-Wen Vivian, Critical factors for implementing a programme for international MICE professionals: Current Issues in Tourism
Kuopao Chang, Mu-Shang Yin, A hybrid MCDM model combining DEMATEL and ANP
and Ru-Shou Sheu
Zheng, Xia-Zhong, Fei Wang, A hybrid approach for evaluating faulty behavior risk of high-risk operations using Mathematical Problems in Engineering
and Jian-Lan Zhou ANP and evidence theory
Xu, Zhitao, Adel Elomri, Product-service supplier pre-evaluation with modified fuzzy ANP reducing decision International Journal of Computer Integrated
Shaligram Pokharel, and X. G. information distortion Manufacturing
Ming
Grimaldi, Michele, Vincenzo Urban plan and water infrastructures planning: A methodology based on spatial ANP Sustainability
Pellecchia, and Isidoro
Fasolino
A dynamic clustering method to improve the coherency of an ANP Super matrix Annals of Operations Research
Yavuz, Idil, and Orrin Cooper
Mostamand, Morteza, Razavi Selecting Strategies by Considering Budget Limitation: A Hybrid Algorithm of Informatica
Hajiagha, Seyed Hossein, and SWOT-DEMATEL-ANP and Binary Programming with Grey Information
Maryam Daneshvar
Abdel-Basset, Mohamed, Mai A hybrid neutrosophic group ANP-TOPSIS framework for supplier selection Symmetry
Mohamed, and Florentin problems
Smarandache
Quezada, Luis E., Héctor A. Identifying causal relationships in strategy maps using ANP and DEMATEL Computers & Industrial Engineering
López-Ospina, Pedro I.
Palominos, and Astrid M.
Oddershede
Wu, Wann-Yih, Alfiyatul The Integration between Service Value and Service Recovery in the Hospitality International Journal of Hospitality
Qomariyah, Nguyen Thi Industry: An Application of QFD and ANP Management
Truong Sa, and Yingkai Liao
Bottani, Eleonora, Piera A QFD-ANP method for supplier selection with benefits, opportunities, costs and International Journal of Information
Centobelli, Teresa Murino, and risks considerations Technology & Decision Making
Ehsan Shekarian
Modak, Mousumi, Kunal Kanti A BSC-ANP approach to organizational outsourcing decision support-A case study Journal of Business Research
Ghosh, and Khanindra Pathak
Liu, Shuo-Fang, Yang Zhang, ANP-based analysis of design strategy, customer demand, and firm performance of Journal of Interdisciplinary Mathematics
and Min Jiang the elderly motorized mobility scooter
Hellebrandt, Thomas, Ina ANP-based knowledge management solutions framework for the long-term Total Quality Management & Business
Heine, and Robert H. Schmitt complaint knowledge transfer Excellence
Chen, You-Shyang, Huan- A study for project risk management using an advanced MCDM-based DEMATEL- Journal of Ambient Intelligence and
Ming Chuang, Arun Kumar ANP approach Humanized Computing
Sangaiah, Chien-Ku Lin, and
Wen-Bin Huang
Airport Safety Risk Evaluation for Bureaucrats Using Fuzzy ANP and the Transylvanian Review
Ozdemir, Yavuz Generalized Choquet Integral Method

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2000-2019

Ranking of Performance Assessment Measures at Tehran Hotel by Combining Mathematical Problems in Engineering
Kargari, Mehrdad DEMATEL, ANP, and SERVQUAL Models under Fuzzy Condition
dos Santos, Hugo Henrique, Decision analysis in referrals of children and adolescent victims of violence: An Journal of the Operational Research Society
Regiane Máximo de Souza, and ANP approach
Aílton Souza Aragão
Chen, Tingqiang, Shuaibin Assessment of Dairy Product Safety Supervision in Sales Link: A Fuzzy-ANP Journal of Food Quality
Wang, Lei Pei, and Jining Comprehensive Evaluation Method
Wang
Modeling critical leadership competencies for junior high school principals: A Kybernetes
Tang, Hui-Wen Vivian hybrid MCDM model combining DEMATEL and ANP
Özder, Emir Hüseyin, Evrencan Staff Task-Based Shift Scheduling Solution with an ANP and Goal Programming Mathematics
Özcan, and Tamer Eren Method in a Natural Gas Combined Cycle Power Plant
Dinçer, Hasan, Serhat Yüksel, Interval type 2-based hybrid fuzzy evaluation of financial services in E7 economies Applied Soft Computing
and Luis Martínez with DEMATEL-ANP and MOORA methods
Asadabadi, Mehdi Rajabi, Are MCDM Methods Useful? A Critical Review of Analytic Hierarchy Process Cogent Engineering
Elizabeth Chang, and Morteza (AHP) and Analytic Network Process (ANP)
Saberi
Leksono, Eko Budi, Suparno Integration of a Balanced Scorecard, DEMATEL, and ANP for Measuring the Sustainability
Suparno, and Iwan Vanany Performance of a Sustainable Healthcare Supply Chain
Kiani Mavi, Reza, Hamed Ranking factors influencing strategic management of university business incubators Management Decision
Gheibdoust, Ahmad A. with ANP
Khanfar, and Neda Kiani Mavi
Salah, Souhir Ben, Wafa Ben An integrated Fuzzy ANP-MOP approach for partner selection problem and order RAIRO-Operations Research
Yahia, Omar Ayadi, and Faouzi allocation optimization: The case of virtual enterprise configuration
Masmoudi
Zhou, Xiaoyang, Liqin Wang, Emergency rescue planning under probabilistic linguistic information: An integrated International Journal of Disaster Risk
Jindong Qin, Jian Chai, and FTA-ANP method Reduction
Carlos Quiterio Gómez Muñoz
Yuan, Jiahai, Xinying Li, Investment risk assessment of coal-fired power plants in countries along the Belt and Energy
Chuanbo Xu, Changhong Zhao, Road initiative based on ANP-Entropy-TODIM method
and Yuanxin Liu
Bathaei, Ahmad, Abbas Application of Fuzzy Analytical Network Process (ANP) and VIKOR for the Symmetry
Mardani, Tomas Baležentis, Assessment of Green Agility Critical Success Factors in Dairy Companies
Siti Rahmah Awang, Dalia
Streimikiene, Goh Chin Fei,
and Norhayati Zakuan
Mimovic, Predrag Miroslav, Serbia joining the European union: an ANP model for forecasting the accessing date International Journal of the Analytic
Ana Krstic, and Jovana Savic Hierarchy Process

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Table 6
Research publications in social sciences category for AHP-2000 to 2019

AHP
Authors Research Title Journal Name

(Xu, 2000) On consistency of the weighted geometric mean complex judgement matrix in AHP European Journal of Operational Research

(Leung & Cao, On consistency On consistency and ranking of alternatives in fuzzy AHP European Journal of Operational Research
and ranking of alternatives in
fuzzy AHP, 2000)
(Sinuany-Stern, Mehrez, & An AHP/DEA methodology for ranking decision-making units International Transactions in Operational
Hadad, 2000) Research
(Millet & Saaty, 2000) On the relativity of relative measures–accommodating both rank preservation and European Journal of Operational Research
rank reversals in the AHP
(Al-Harbi, 2001) Application of the AHP in project management International journal of project management

(Wedley, Choo, & Schoner, Magnitude adjustment for AHP benefit/cost ratios European Journal of Operational Research
2001)
(Leung & Cao, On the efficacy On the efficacy of modeling multi-attribute decision problems using AHP and European Journal of Operational Research
of modeling multi-attribute Sinarchy
decision problems using AHP
and Sinarchy, 2001)
(Van der Honert, 2001) Decisional power in group decision making: a note on the allocation of group Group Decision and Negotiation
members' weights in the multiplicative AHP and SMART
(Davies, Adaptive AHP: a Adaptive AHP: a review of marketing applications with extensions European Journal of Marketing
review of marketing
applications with extensions,
2001)
(Jackson, 2001) Prioritising customers and other stakeholders using the AHP European Journal of Marketing

(Chwolka & Raith, 2001) Group preference aggregation with the AHP–implications for multiple-issue agendas European Journal of Operational Research

(Cai & Wu, 2001) Synthetic financial evaluation by a method of combining DEA with AHP International Transactions in Operational
Research
(Muller & Fairlie-Clarke, 2001) Using the AHP to determine the correlation of product issues to profit European Journal of Marketing

(Al Khalil, 2002) Selecting the appropriate project delivery method using AHP International journal of project management

(Yu, 2002) A GP-AHP method for solving group decision-making fuzzy AHP problems Computers & Operations Research

Khasnabis, Snehamay, Comparative study of two techniques of transit performance assessment: AHP and Journal of Transportation Engineering
Emadeddin Alsaidi, Libo Liu, GAT

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2000-2019

and Richard Darin Ellis

Batubara, Maruhum, Hidehiko An application of the AHP to urban residential upgrading in Jakarta Journal of Asian Architecture and Building
Tanimura, Monday Ohi Engineering
Asikhia, and Atsushi Toshimori
Decision-making with the AHP: Why is the principal eigenvector necessary European Journal of Operational Research
Saaty, Thomas L
Determining the importance weights for the customer requirements in QFD using a Iie Transactions
Kwong, Chun-Kit, and H. Bai fuzzy AHP with an extent analysis approach
Aguaron, Juan, Marıá Teresa Consistency stability intervals for a judgement in AHP decision support systems European Journal of Operational Research
Escobar, and José Marı́a
Moreno-Jiménez
Radcliffe, Larry L., and Marc J. Trust evaluation: an AHP and multi-objective programming approach Management Decision
Schniederjans
Performance of the AHP in comparison of gains and losses Mathematical and Computer Modelling
Korhonen, P., and H. Topdagi
Kahraman, Cengiz, Ufuk Multi-attribute comparison of catering service companies using fuzzy AHP: The International journal of production economics
Cebeci, and Da Ruan case of Turkey
Yang, Ching-Chow, and Bai- Key quality performance evaluation using fuzzy AHP Journal of the Chinese Institute of Industrial
Sheng Chen Engineers
Chan, Alan HS, W. Y. Kwok, Using AHP for determining priority in a safety management system Industrial Management & Data Systems
and Vincent G. Duffy
A Web-based AHP approach to standardize the process of managing service- Decision Support Systems
Sundarraj, R. P contracts
Entani, Tomoe, Hidetorno Evaluation method based on interval AHP and DEA Central European Journal of Operations
Ichihashi, and Hideo Tanaka Research
Wei, Chun-Chin, Chen-Fu An AHP-based approach to ERP system selection International journal of production economics
Chien, and Mao-Jiun J. Wang
Liu, Duen-Ren, and Ya-Yueh Integrating AHP and data mining for product recommendation based on customer Information & Management
Shih lifetime value
Ngai, Eric WT, and E. W. C. Evaluation of knowledge management tools using AHP Expert systems with applications
Chan
Mahdi, Ibrahim M., and Khaled Decision support system for selecting the proper project delivery method using International journal of project management
Alreshaid analytical hierarchy process (AHP)
A method of aggregation in DS/AHP for group decision-making with the non- Computers & Operations Research
Beynon, Malcolm J equivalent importance of individuals in the group
Shapira, Aviad, and Marat AHP-based equipment selection model for construction projects Journal of Construction Engineering and
Goldenberg Management
Mau-Crimmins, Theresa, AHP as a means for improving public participation: a pre–post experiment with Forest policy and economics
Joseph E. de Steiguer, and university students
Donald Dennis
Gaudenzi, Barbara, and Managing risks in the supply chain using the AHP method The International Journal of Logistics
Antonio Borghesi Management

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2000-2019

Bertolini, M., Marcello Braglia, Application of the AHP methodology in making a proposal for a public work International Journal of Project Management
and Gionata Carmignani contract
Ishizaka, Alessio, and Markus How to derive priorities in AHP: a comparative study Central European Journal of Operations
Lusti Research
Pi, Wei-Ning, and Chinyao Supplier evaluation and selection via Taguchi loss functions and an AHP The International Journal of Advanced
Low Manufacturing Technology
Ugboma, Chinonye, An analytic hierarchy process (AHP) approach to port selection decisions–empirical Maritime Economics & Logistics
Ogochukwu Ugboma, and evidence from Nigerian ports
Innocent C. Ogwude
Wang, Ying-Ming, and Taha An approach to avoiding rank reversal in AHP decision Support Systems
MS Elhag
Pérez, Joaquín, José L. Jimeno, Another potential shortcoming of AHP Top
and Ethel Mokotoff
The role of the DS/AHP in identifying inter-group alliances and majority rule Group Decision and Negotiation
Beynon, Malcolm J within-group decision making
Raharjo, Hendry, and Dini Evaluating relationship of consistency ratio and number of alternatives on rank Quality Engineering
Endah reversal in the AHP
Garuti, Claudio, and Mario The AHP: A multicriteria decision-making methodology for shiftwork prioritizing Journal of Systems Science and Systems
Sandoval Engineering
Chan, Felix TS, and Niraj Global supplier development considering risk factors using fuzzy extended AHP- Omega
Kumar based approach
Bozbura, F. Tunç, Ahmet Prioritization of human capital measurement indicators using fuzzy AHP Expert systems with applications
Beskese, and Cengiz Kahraman
Supplier selection problem: integrating DEA with the approaches of total cost of Supply Chain Management: an international
Ramanathan, Ramakrishnan ownership and AHP journal
Bozbura, F. Tunç, and Ahmet Prioritization of organizational capital measurement indicators using fuzzy AHP International journal of approximate
Beskese reasoning
Escobar, María Teresa, and Aggregation of individual preference structures in AHP-group decision making Group Decision and Negotiation
José Maria Moreno-Jimenéz
Korpela, Jukka, Antti Warehouse operator selection by combining AHP and DEA methodologies International journal of production economics
Lehmusvaara, and Jukka
Nisonen
Rabelo, Luis, Hamidreza Value chain analysis using hybrid simulation and AHP International journal of production economics
Eskandari, Tarek Shaalan, and
Magdy Helal
Altuzarra, Alfredo, José María A Bayesian priorization procedure for AHP-group decision making European Journal of Operational Research
Moreno-Jiménez, and Manuel
Salvador
Kahraman, Cengiz, Nihan Prioritization of e-Government strategies using a SWOT-AHP analysis: the case of European Journal of Information Systems
Cetin Demirel, and Tufan Turkey
Demirel
Carlucci, Daniela, and Knowledge assets value creation map: assessing knowledge assets value drivers Expert systems with applications
Giovanni Schiuma using AHP

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2000-2019

A multi-attribute comparison of Turkish quality consultants by fuzzy AHP International Journal of Information
Cebeci, Ufuk, and D. A. Ruan Technology & Decision Making
Abudayyeh, Osama, Saad J. Hybrid prequalification-based, innovative contracting model using AHP Journal of management in engineering
Zidan, Sherif Yehia, and
Dennis Randolph
Chen, S. C., C. C. Yang, W. T. Construction of key model for knowledge management system using AHP-QFD for Journal of Manufacturing Technology
Lin, T. M. Yeh, and Y. S. Lin semiconductor industry in Taiwan Management
Developing and implementing a selection model for bedding chain retail store Quality and Quantity
Hsu, Pi-Fang, and Bi-Yu Chen franchisee using Delphi and fuzzy AHP
Wang, Ying-Ming, Ying Luo, On the extent analysis method for fuzzy AHP and its applications European Journal of Operational Research
and Zhongsheng Hua
Chan, Felix TS, Niraj Kumar, Global supplier selection: a fuzzy-AHP approach International Journal of production research
Manoj Kumar Tiwari, Henry
CW Lau, and K. L. Choy
Huang, Chi-Cheng, Pin-Yu A fuzzy AHP application in government-sponsored R&D project selection Omega
Chu, and Yu-Hsiu Chiang
Transshipment site selection using the AHP and TOPSIS approaches under fuzzy Waste Management
Önüt, Semih, and Selin Soner environment
Dağdeviren, Metin, and İhsan Developing a fuzzy analytic hierarchy process (AHP) model for behavior-based Information sciences
Yüksel safety management
Ertuğrul, İrfan, and Nilsen Comparison of fuzzy AHP and fuzzy TOPSIS methods for facility location selection The International Journal of Advanced
Karakaşoğlu Manufacturing Technology
Wang, Tien-Chin, and Yueh- Applying fuzzy linguistic preference relations to the improvement of consistency of Information sciences
Hsiang Chen fuzzy AHP
Hua, Zhongsheng, Bengang A DS–AHP approach for multi-attribute decision-making problem with incomplete Expert systems with applications
Gong, and Xiaoyan Xu information
Lee, Grace KL, and Edwin HW The analytic hierarchy process (AHP) approach for assessment of urban renewal Social indicators research
Chan proposals
Moreno-Jiménez, J. M., J. The core of consistency in AHP-group decision making Group Decision and Negotiation
Aguarón, and M. T. Escobar
Lai, Yu-Ting, Wei-Chih Wang, AHP-and simulation-based budget determination procedure for public building Automation in Construction
and Han-Hsiang Wang construction projects
Güngör, Zülal, Gürkan A fuzzy AHP approach to personnel selection problem Applied Soft Computing
Serhadlıoğlu, and Saadettin
Erhan Kesen
Application of AHP technique Journal of Business Economics and
Podvezko, Valentinas Management
Lin, Hsiu-Fen, Hsuan-Shih Evaluation of factors influencing knowledge sharing based on a fuzzy AHP Journal of Information Science
Lee, and Da Wei Wang approach
Tseng, Ya-Fen, and Tzai-Zang Comparing appropriate decision support of human resource practices on Expert systems with applications
Lee organizational performance with DEA/AHP model
A fuzzy AHP evaluation model for buyer-supplier relationships with the International Journal of production research
Lee, Amy HI consideration of benefits, opportunities, costs and risks

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2000-2019

Hybridising human judgment, AHP, simulation and a fuzzy expert system for Expert systems with applications
Li, Shuliang, and Jim Zheng Li strategy formulation under uncertainty
Sueyoshi, Toshiyuki, Jennifer A decision support framework for internal audit prioritization in a rental car European Journal of Operational Research
Shang, and Wen-Chyuan company: A combined use between DEA and AHP
Chiang
Bhagwat, Rajat, and Milind An application of the integrated AHP-PGP model for performance measurement of Production Planning & Control
Kumar Sharma supply chain management
Arslan, Ozcan, and Osman Analytical investigation of marine casualties at the Strait of Istanbul with SWOT– Maritime Policy & Management
Turan AHP method
Ünal, Can, and Mücella G. Selection of ERP suppliers using AHP tools in the clothing industry International Journal of Clothing Science and
Güner Technology
A performance evaluation model by integrating fuzzy AHP and fuzzy TOPSIS Expert systems with applications
Sun, Chia-Chi methods
Costa, Helder Gomes, and P. S. Construction of an AHP-based model to catch criteria weights in post-occupancy International Journal of the Analytic
Correa evaluation Hierarchy Process
Dong, Yucheng, Guiqing Consensus models for AHP group decision making under row geometric mean Decision Support Systems
Zhang, Wei-Chiang Hong, and prioritization method
Yinfeng Xu
Abdelgawad, Mohamed, and Risk management in the construction industry using combined fuzzy FMEA and Journal of Construction Engineering and
Aminah Robinson Fayek fuzzy AHP Management
Jaskowski, Piotr, Slawomir Assessing contractor selection criteria weights with fuzzy AHP method application Automation in Construction
Biruk, and Robert Bucon in group decision environment
Using fuzzy AHP to develop intellectual capital evaluation model for assessing their Expert systems with applications
Lee, Shyh-Hwang performance contribution in a university
Chen, Ming-Kuen, and Shih- The critical factors of success for information service industry in developing Expert systems with applications
Ching Wang international market: Using analytic hierarchy process (AHP) approach
Chan, Felix TS, and Hing Kai An AHP model for selection of suppliers in the fast-changing fashion market The International Journal of Advanced
Chan Manufacturing Technology
Altuzarra, Alfredo, José María Consensus building in AHP-group decision making: A Bayesian approach Operations research
Moreno-Jiménez, and Manuel
Salvador
De Feo, Giovanni, and Sabino Using an innovative criteria weighting tool for stakeholders involvement to rank Waste Management
De Gisi MSW facility sites with the AHP
Şen, Ceyda Güngör, and Gökçe Evaluation and pre-allocation of operators with multiple skills: A combined fuzzy Expert systems with applications
Çınar AHP and max-min approach
Che, ZhengHua, H. S. Wang, A fuzzy AHP and DEA approach for making bank loan decisions for small and Expert systems with applications
and Chih-Ling Chuang medium enterprises in Taiwan
Application of AHP and Taguchi loss functions in supply chain Industrial Management & Data Systems
Ordoobadi, Sharon M
Chen, Ming-Kuen, and Shih- The use of a hybrid fuzzy-Delphi-AHP approach to develop global business Expert systems with applications
Ching Wang intelligence for information service firms
Kilincci, Ozcan, and Suzan Fuzzy AHP approach for supplier selection in a washing machine company Expert systems with applications
Aslı Onal

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2000-2019

Validity of the AHP/ANP: Comparing apples and oranges International Journal of the Analytic
von Solms, Sibs Hierarchy Process
Editor-in-chief Enrique mu uses AHP to help city of Pittsburgh move to the cloud International Journal of the Analytic
Mu, Enrique Hierarchy Process
Vidal, Ludovic-Alexandre, Using a Delphi process and the Analytic Hierarchy Process (AHP) to evaluate the Expert systems with applications
Franck Marle, and Jean-Claude complexity of projects
Bocquet
Pedrycz, Witold, and Mingli Analytic hierarchy process (AHP) in group decision making and its optimization IEEE Transactions on Fuzzy Systems
Song with an allocation of information granularity
Joshi, Rohit, D. K. Banwet, and A Delphi-AHP-TOPSIS based benchmarking framework for performance Expert systems with applications
Ravi Shankar improvement of a cold chain
Fuzzy AHP-based risk assessment methodology for PPP projects Journal of Construction Engineering and
Li, Jie, and Patrick XW Zou Management
Saaty, Thomas L., and Jennifer An innovative orders-of-magnitude approach to AHP-based multi-criteria decision European Journal of Operational Research
S. Shang making: Prioritizing divergent intangible humane acts
Lee, Seungbum, and Patrick SWOT and AHP hybrid model for sport marketing outsourcing using a case of Sport Management Review
Walsh intercollegiate sport
Hadi-Vencheh, A., and A. A fuzzy AHP-DEA approach for multiple criteria ABC inventory classification Expert systems with applications
Mohamadghasemi
Lin, Ming-Ian, Yuan-Duen Applying integrated DEA/AHP to evaluate the economic performance of local European Journal of Operational Research
Lee, and Tsai-Neng Ho governments in China
Isaai, Mohammad T., Aram Intelligent timetable evaluation using fuzzy AHP Expert systems with applications
Kanani, Mahshid Tootoonchi,
and Hamid R. Afzali
Ishizaka, Alessio, Dieter Influence of aggregation and measurement scale on ranking a compromise Journal of the Operational Research Society
Balkenborg, and Todd Kaplan alternative in AHP
Rostamzadeh, Reza, and Prioritizing effective 7Ms to improve production systems performance using fuzzy Expert systems with applications
Saudah Sofian AHP and fuzzy TOPSIS (case study)
Shaw, Krishnendu, Ravi Supplier selection using fuzzy AHP and fuzzy multi-objective linear programming Expert systems with applications
Shankar, Surendra S. Yadav, for developing low carbon supply chain
and Lakshman S. Thakur
Dynamic vendor selection: A fuzzy AHP approach International Journal of the Analytic
Koul, Saroj, and Rakesh Verma Hierarchy Process
Wang, Xiaojun, Hing Kai A two-stage fuzzy-AHP model for risk assessment of implementing green initiatives International journal of production economics
Chan, Rachel WY Yee, and in the fashion supply chain
Ivan Diaz-Rainey
Bruno, Giuseppe, Emilio AHP-based approaches for supplier evaluation: Problems and perspectives Journal of purchasing and supply management
Esposito, Andrea Genovese,
and Renato Passaro
Ho, William, Ting He, Carman Strategic logistics outsourcing: An integrated QFD and fuzzy AHP approach Expert systems with applications
Ka Man Lee, and Ali
Emrouznejad
Bentes, Alexandre Veronese, Multidimensional assessment of organizational performance: Integrating BSC and Journal of business research
Jorge Carneiro, Jorge Ferreira AHP

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2000-2019

da Silva, and Herbert Kimura

Dai, Jing, and Jennifer A four-phase AHP–QFD approach for supplier assessment: a sustainability International Journal of production research
Blackhurst perspective
Ishizaka, Alessio, Craig AHPSort: an AHP-based method for sorting problems International Journal of production research
Pearman, and Philippe Nemery
Falsini, Diego, Federico Fondi, A logistics provider evaluation and selection methodology based on AHP, DEA and International Journal of production research
and Massimiliano M. Schiraldi linear programming integration
Das, Manik Chandra, Bijan A framework to measure relative performance of Indian technical institutions using Socio-Economic Planning Sciences
Sarkar, and Siddhartha Ray integrated fuzzy AHP and COPRAS methodology
Zhang, Yajuan, Xinyang Deng, Assessment of E-Commerce security using AHP and evidential reasoning Expert systems with applications
Daijun Wei, and Yong Deng
Ju, Yanbing, Aihua Wang, and Evaluating emergency response capacity by fuzzy AHP and 2-tuple fuzzy linguistic Expert systems with applications
Xiaoyue Liu approach
Paksoy, Turan, Nimet Yapici Organizational strategy development in distribution channel management using Expert systems with applications
Pehlivan, and Cengiz fuzzy AHP and hierarchical fuzzy TOPSIS
Kahraman
Bulut, Emrah, Okan Duru, Use of consistency index, expert prioritization and direct numerical inputs for Expert systems with applications
Tuba Keçeci, and Shigeru generic fuzzy-AHP modeling: A process model for shipping asset management
Yoshida
Fouladgar, Mohammad Majid, Maintenance strategy selection using AHP and COPRAS under fuzzy environment International journal of strategic property
Abdolreza Yazdani-Chamzini, management
Ali Lashgari, Edmundas
Kazimieras Zavadskas, and
Zenonas Turskis
Emergency alternative evaluation under group decision-makers: A method of Expert systems with applications
Ju, Yanbing, and Aihua Wang incorporating DS/AHP with extended TOPSIS
Vinodh, Shivraman, K. R. AHP‐based lean concept selection in a manufacturing organization Journal of Manufacturing Technology
Shivraman, and S. Viswesh Management
Zolfani, Sarfaraz Hashemkhani, A hybrid MCDM model encompassing AHP and COPRAS-G methods for selecting Technological and economic development of
I-Shuo Chen, Nahid company supplier in Iran economy
Rezaeiniya, and Jolanta
Tamošaitienė
Zolfani, Sarfaraz Hashemkhani, Quality control manager selection based on AHP-COPRAS-G methods: a case in Economic Research-Ekonomska Istraživanja
Nahid Rezaeiniya, Mohammad Iran
Hasan Aghdaie, and Edmundas
Kazimieras Zavadskas
Aminbakhsh, Saman, Murat Safety risk assessment using analytic hierarchy process (AHP) during planning and Journal of safety research
Gunduz, and Rifat Sonmez budgeting of construction projects
De Felice, Fabio, Birsen Publishing AHP/ANP Papers International Journal of the Analytic
Karpak, Enrique Mu, Leandro Hierarchy Process
Pecchia, Antonella Petrillo
Calabrese, Armando, Roberta Using Fuzzy AHP to manage Intellectual Capital assets: An application to the ICT Expert systems with applications
Costa, and Tamara Menichini service industry

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2000-2019

Samvedi, Avinash, Vipul Jain, Quantifying risks in a supply chain through integration of fuzzy AHP and fuzzy International Journal of production research
and Felix TS Chan TOPSIS
Multi-criteria supplier segmentation using a fuzzy preference relation based AHP European Journal of Operational Research
Rezaei, Jafar, and Roland Ortt
Ishizaka, Alessio, and Nam Calibrated fuzzy AHP for current bank account selection Expert systems with applications
Hoang Nguyen
Daim, Tugrul U., Andreas Use of analytic hierarchy process (AHP) for selection of 3PL providers Journal of Manufacturing Technology
Udbye, and Aparna Management
Balasubramanian
Aghdaie, Mohammad Hasan, Market segment evaluation and selection based on application of fuzzy AHP and Journal of Business Economics and
Sarfaraz Hashemkhani Zolfani, COPRAS-G methods Management
and Edmundas Kazimieras
Zavadskas
Tadic, Danijela, Alev Taskin An evaluation of quality goals by using fuzzy AHP and fuzzy TOPSIS methodology Journal of Intelligent & Fuzzy Systems
Gumus, Slavko Arsovski,
Aleksandar Aleksic, and
Miladin Stefanovic
Xu, Lei, D. Thresh Kumar, K. Analyzing criteria and sub-criteria for the corporate social responsibility-based The International Journal of Advanced
Madan Shankar, Devika supplier selection process using AHP Manufacturing Technology
Kannan, and Gang Chen
Junior, Francisco Rodrigues A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection Applied Soft Computing
Lima, Lauro Osiro, and Luiz
Cesar Ribeiro Carpinetti
Bhandari, Ashish, and Amrit Performance evaluation of commercial banks in Nepal using AHP International Journal of the Analytic
Man Nakarmi Hierarchy Process
Pegetti, Ana Lucia, and Jessé Cognitive maps and AHP for supplier selection in a private higher education International Journal of the Analytic
D. Souza Júnior institution Hierarchy Process
A fuzzy AHP-TOPSIS framework for ranking the solutions of Knowledge Expert systems with applications
Patil, Sachin K., and Ravi Kant Management adoption in Supply Chain to overcome its barriers
Somsuk, Nisakorn, and Tritos A fuzzy AHP to prioritize enabling factors for strategic management of university Technological forecasting and social change
Laosirihongthong business incubators: Resource-based view
Rezaei, Jafar, Patrick BM Supplier selection in the airline retail industry using a funnel methodology: Expert systems with applications
Fahim, and Lori Tavasszy Conjunctive screening method and fuzzy AHP
Mandic, Ksenija, Boris Analysis of the financial parameters of Serbian banks through the application of the Economic Modelling
Delibasic, Snezana Knezevic, fuzzy AHP and TOPSIS methods
and Sladjana Benkovic
Lolli, Francesco, Alessio New AHP-based approaches for multi-criteria inventory classification International journal of production economics
Ishizaka, and Rita Gamberini
Cevik Onar, Sezi, Başar Strategic decision selection using hesitant fuzzy TOPSIS and interval type-2 fuzzy International Journal of Computational
Oztaysi, and Cengiz Kahraman AHP: a case study intelligence systems
Gudienė, Neringa, Audrius Identification and evaluation of the critical success factors for construction projects Journal of Civil Engineering and Management
Banaitis, Valentinas Podvezko, in Lithuania: AHP approach
and Nerija Banaitienė

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Kamvysi, Konstantina, Capturing and prioritizing students’ requirements for course design by embedding European Journal of Operational Research
Katerina Gotzamani, Andreas Fuzzy-AHP and linear programming in QFD
Andronikidis, and Andreas C.
Georgiou
Rezaie, Kamran, Sara Saeidi Evaluating performance of Iranian cement firms using an integrated fuzzy AHP– Applied Mathematical Modelling
Ramiyani, Salman Nazari- VIKOR method
Shirkouhi, and Ali Badizadeh
Radivojević, Gordana, and Supply chain risk modeling by AHP and Fuzzy AHP methods Journal of Risk Research
Vladimir Gajović
Jakhar, Suresh Kumar, and An integrated model of supply chain performance evaluation and decision-making Production Planning & Control
Mukesh Kumar Barua using structural equation modelling and fuzzy AHP
Arroyo, P., I. D. Tommelein, Comparing AHP and CBA as decision methods to resolve the choosing problem in Journal of Construction Engineering and
and G. Ballard detailed design Management
Mangla, Sachin Kumar, Risk analysis in green supply chain using fuzzy AHP approach: A case study Resources, Conservation and Recycling
Pradeep Kumar, and Mukesh
Kumar Barua
Saracoglu, Burak Omer, A comparative study of AHP, ELCTRE iii & ELECTRE iv by equal objective & International Journal of the Analytic
Orhantepe Mahallesi, Tekel shannon's entropy objective & saaty's subjective criteria weighting in a private small Hierarchy Process
Caddesi, and Geziyolu Sokak hydropower plants investments selection problem
Singh, Rana Pratap, and Hans Prioritizing hydropower development using analytical hierarchy process (AHP). a International Journal of the Analytic
Peter Nachtnebel case study of Nepal Hierarchy Process
Kozak, Meryem Akoğlan, An analytic hierarchy process (AHP) model for understanding convention planners International Journal of the Analytic
Emre Ozan Aksoz, and Çağıl ‘prior factors of convention hotel selection Hierarchy Process
Hale Özel.
Jantscher, Martin, Christopher Decision support in it service management: Applying AHP methodology to the itil International Journal of the Analytic
Schwarz, and Erwin Zinser incident management process Hierarchy Process
GIS-Based Geo Hazard Assessment of Pakistan For Future Urban Development International Journal of the Analytic
Minhas, Amer Imran Using AHP Hierarchy Process
Comparability, Decision Theory and The AHP International Journal of the Analytic
von Solms, Sibs Hierarchy Process
Mosadeghi, Razieh, Jan Comparison of Fuzzy-AHP and AHP in a spatial multi-criteria decision-making Computers, Environment and Urban Systems
Warnken, Rodger Tomlinson, model for urban land-use planning
and Hamid Mirfenderesk
Chen, Jeng-Fung, Ho-Nien Evaluating teaching performance based on fuzzy AHP and comprehensive Applied Soft Computing
Hsieh, and Quang Hung Do evaluation approach
Prakash, Chandra, and M. K. Integration of AHP-TOPSIS method for prioritizing the solutions of reverse logistics Journal of Manufacturing Systems
Barua adoption to overcome its barriers under fuzzy environment
Su, Xiaoyan, Sankaran Dependence assessment in human reliability analysis using evidence theory and Risk Analysis
Mahadevan, Peida Xu, and AHP
Yong Deng
Abdullah, Lazim, and Integration of fuzzy AHP and interval type-2 fuzzy DEMATEL: An application to Expert systems with applications
Norsyahida Zulkifli human resource management
Beikkhakhian, Yokabed, The application of ISM model in evaluating agile supplier’s selection criteria and Expert systems with applications
Mohammad Javanmardi, Mahdi ranking suppliers using fuzzy TOPSIS-AHP methods

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Karbasian, and Bijan

Khayambashi
Kumar, Ajay, Ravi Shankar, Analyzing customer preference and measuring relative efficiency in telecom sector: Telematics and Informatics
and Roma Mitra Debnath A hybrid fuzzy AHP/DEA study
Zhou, Yanhong, Kudzayi Resource-based destination competitiveness evaluation using a hybrid analytic Tourism Management Perspectives
Maumbe, Jinyang Deng, and hierarchy process (AHP): The case study of West Virginia
Steven W. Selin
Büyüközkan, Gülçin, and Ali Evaluation of product development partners using an integrated AHP-VIKOR model Kybernetes
Görener
Thanki, Shashank, Kannan An investigation on lean-green implementation practices in Indian SMEs using Journal of Cleaner Production
Govindan, and Jitesh Thakkar analytical hierarchy process (AHP) approach
Boltürk, Eda, S. Çevik Onar, Multi-attribute warehouse location selection in humanitarian logistics using hesitant International Journal of the Analytic
Başar Öztayşi, Cengiz fuzzy AHP Hierarchy Process
Kahraman, and K. Goztepe
Bhandari, Ashish, and Amrit A financial performance evaluation of commercial banks in Nepal using AHP model International Journal of the Analytic
Man Nakarmi Hierarchy Process
Wang, Xia, Xiang Robert Li, How smart is your tourist attraction? Measuring tourist preferences of smart tourism Tourism Management
Feng Zhen, and JinHe Zhang attractions via a FCEM-AHP and IPA approach
Bouzon, Marina, Kannan Identification and analysis of reverse logistics barriers using fuzzy Delphi method Resources, Conservation and Recycling
Govindan, Carlos M. Taboada and AHP
Rodriguez, and Lucila MS
Campos
Tavana, Madjid, Mohsen An integrated intuitionistic fuzzy AHP and SWOT method for outsourcing reverse Applied Soft Computing
Zareinejad, Debora Di Caprio, logistics
and Mohamad Amin Kaviani
Luthra, Sunil, Sachin Kumar Using AHP to evaluate barriers in adopting sustainable consumption and production International journal of production economics
Mangla, Lei Xu, and Ali Diabat initiatives in a supply chain
Dong, Qingxing, and Orrin A peer-to-peer dynamic adaptive consensus reaching model for the group AHP European Journal of Operational Research
Cooper decision making
Dong, Qingxing, and Orrin An orders-of-magnitude AHP supply chain risk assessment framework International journal of production economics
Cooper
Delbari, Seyyed Ali, Siew Imm An investigation of key competitiveness indicators and drivers of full-service Journal of Air Transport Management
Ng, Yuhanis Abdul Aziz, and airlines using Delphi and AHP techniques
Jo Ann Ho
Aguarón, Juan, María Teresa The precise consistency consensus matrix in a local AHP-group decision making Annals of Operations Research
Escobar, and José María context
Moreno-Jiménez
Adebanjo, Dotun, Tritos Prioritizing lean supply chain management initiatives in healthcare service Production Planning & Control
Laosirihongthong, and operations: a fuzzy AHP approach
Premaratne Samaranayake
Zyoud, Shaher H., and Daniela A bibliometric-based survey on AHP and TOPSIS techniques Expert systems with applications
Fuchs-Hanusch
The magic of the analytic hierarchy process (AHP) International Journal of the Analytic
Cooper, Orrin Hierarchy Process

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AHP conflict resolution in action: the Peruvian hostage crisis of 1996-1997 re- International Journal of the Analytic
Mu, Enrique visited Hierarchy Process
Kokangül, Ali, Ulviye Polat, A new approximation for risk assessment using the AHP and Fine Kinney Safety science
and Cansu Dağsuyu methodologies
Zhou, Xinyi, Xinyang Deng, Dependence assessment in human reliability analysis based on D numbers and AHP Nuclear Engineering and Design
Yong Deng, and Sankaran
Mahadevan
Emrouznejad, Ali, and The state-of-the-art development of AHP (1979–2017): a literature review with a International Journal of production research
Marianna Marra social network analysis
Kumar, Divesh, Zillur Rahman, A fuzzy AHP and fuzzy multi-objective linear programming model for order International Journal of Computer Integrated
and Felix TS Chan allocation in a sustainable supply chain: A case study Manufacturing
Wang, Ting-Kwei, Qian Zhang, Integrated supplier selection framework in a resilient construction supply chain: An Sustainability
Heap-Yih Chong, and Xiangyu approach via analytic hierarchy process (AHP) and grey relational analysis (GRA)
Wang
Pramanik, Dipika, Anupam Resilient supplier selection using AHP-TOPSIS-QFD under a fuzzy environment International Journal of Management Science
Haldar, Samar Chandra and Engineering Management
Mondal, Sukanta Kumar
Naskar, and Amitava Ray
Abdel-Basset, Mohamed, Mai An extension of neutrosophic AHP–SWOT analysis for strategic planning and Symmetry
Mohamed, and Florentin decision-making
Smarandache
A Brief Literature Review for Fuzzy AHP International Journal of the Analytic
Kahraman, Cengiz Hierarchy Process
Mimovic, Predrag Miroslav, MEASURING PERFORMANCE OF MIDDLE EAST AIRLINES–AHP International Journal of the Analytic
Kristina Budimčević, and APPROACH. Hierarchy Process
Aleksandra Marcikić-Horvat
Warehouse risk assessment using interval-valued intuitionistic fuzzy AHP International Journal of the Analytic
Cebi, Selcuk, and Esra Ilbahar Hierarchy Process
Awasthi, Anjali, Kannan Multi-tier sustainable global supplier selection using a fuzzy AHP-VIKOR based International journal of production economics
Govindan, and Stefan Gold approach
Sirisawat, Pornwasin, and Fuzzy AHP-TOPSIS approaches to prioritizing solutions for reverse logistics Computers & Industrial Engineering
Tossapol Kiatcharoenpol barriers
Third-party logistics (3PLs) provider selection via Fuzzy AHP and EDAS integrated Technological and Economic Development of
Ecer, Fatih model Economy
Supplier selection study under the respective of low-carbon supply chain: A hybrid Sustainability
He, Xiangshuo, and Jian Zhang evaluation model based on FA-DEA-AHP
Karaman, Abdullah S., and Taking-off corporate social responsibility programs: An AHP application in airline Journal of Air Transport Management
Engin Akman industry
Ghorbanzadeh, Omid, Bakhtiar An interval matrix method used to optimize the decision matrix in AHP technique Environmental earth sciences
Feizizadeh, and Thomas for land subsidence susceptibility mapping
Blaschke
Deng, Xinyang, and Yong D-AHP method with different credibility of information Soft Computing
Deng

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Hosseini, Seyedmohsen, and A hybrid ensemble and AHP approach for resilient supplier selection Journal of Intelligent Manufacturing
Abdullah Al Khaled
Stević, Željko, Marko Evaluation of suppliers under uncertainty: a multiphase approach based on fuzzy Transport
Vasiljević, Adis Puška, Ilija AHP and fuzzy EDAS
Tanackov, Raimundas
Junevičius, and Slavko
Vesković
Calabrese, Armando, Roberta Integrating sustainability into strategic decision-making: A fuzzy AHP method for Technological Forecasting and Social Change
Costa, Nathan Levialdi, and the selection of relevant sustainability issues
Tamara Menichini
Exploring the utility of Analytic Hierarchy Process (AHP) in ranking livelihood Evaluation and program planning
activities for effective and sustainable rural development interventions in developing
Baffoe, Gideon countries
Ghorbanzadeh, Omid, Sarbast Sustainable urban transport planning considering different stakeholder groups by an Sustainability
Moslem, Thomas Blaschke, interval-AHP decision support model
and Szabolcs Duleba
An integrated approach to catering supplier selection using AHP-ARAS-MCGP Journal of Air Transport Management
Fu, Yan-Kai methodology
Chou, Ying-Chyi, Hsin-Yi Assessing the Human Resource in Science and Technology for Asian Countries: Symmetry
Yen, Van Thac Dang, and Application of Fuzzy AHP and Fuzzy TOPSIS
Chia-Chi Sun
Vladeanu, Greta J., and John C. Consequence-of-failure model for risk-based asset management of wastewater pipes Journal of Pipeline Systems Engineering and
Matthews using AHP Practice
Rafiee, Marzieh, and Salman Prioritization of critical individual factors influencing willingness to communicate: Journal of Multilingual and Multicultural
Abbasian-Naghneh AHP method Development
A study on foreign direct investment mode based on AHP and entropy learning International Journal of Machine Learning
Fu, Jing and Cybernetics
Moslem, Sarbast, Omid Analysing Stakeholder Consensus for a Sustainable Transport Development Sustainability
Ghorbanzadeh, Thomas Decision by the Fuzzy AHP and Interval AHP
Blaschke, and Szabolcs Duleba.
Benítez, Julio, Silvia Carpitella, Management of uncertain pairwise comparisons in AHP through probabilistic Applied Soft Computing
Antonella Certa, and Joaquín concepts
Izquierdo
Danaeefard, Hassan, Hanieh Expert consensus on factors reducing policy coherence in the context of Iran: International Journal of Public Administration
Ahmadi, and Ali Asghar Delphi-AHP
Pourezzat
A framework based on fuzzy AHP-TOPSIS for prioritizing solutions to overcome International Journal of Sustainable
Singh, P. K., and P. Sarkar the barriers in the implementation of eco-design practices in SMEs Development & World Ecology
A novel hesitant intuitionistic fuzzy linguistic AHP method and its application to International Journal of the Analytic
Karasan, Ali prioritization of investment alternatives Hierarchy Process
Go, Daryn Joy, Michael An AHP-based composite index for sector prioritization International Journal of the Analytic
Angelo Promentilla, Kathleen Hierarchy Process
Aviso, and Krista Danielle Yu

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Measuring corporate social responsibility performance: a comprehensive AHP based International Journal of the Analytic
Bahurmoz, Asma Mohammed index Hierarchy Process
Enhancing the work-life balance through AHP modelling of early career decision- International Journal of the Analytic
Gawlik, Remigiusz making Hierarchy Process

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Appendix C
HEALTH SCIENCES
Table 7
Research publications in health sciences category for ANP-2000 to 2019

ANP
Authors Research Titles Journal Name

(Herat, Noorossana, & Serkani, Using DEMATEL Analytic network process (ANP) hybrid algorithm approach for African Journal of Business Management
2012) selecting improvement projects of Iranian excellence model in healthcare sector.
(Ortiz, Felizzola, & Isaza, A contrast between DEMATEL-ANP and ANP methods for six sigma project BMC medical informatics and decision making
2015) selection: a case study in healthcare industry
(Nilashi, Ahmadi, Ahani, Determining the importance of hospital information system adoption factors using Technological Forecasting and Social Change
Ravangard, & Ibrahim, 2016) fuzzy analytic network process (ANP)
(Marcarelli, 2017) Evaluating healthcare organizations by a network model which integrates ANP with International Journal of the Analytic
a revised-BSC Hierarchy Process

Table 8
Research publications in health sciences category for AHP-2000 to 2019

AHP
Authors Research Title Journal Name

(Omasa, Kishimoto, Kawase, & An attempt at decision making in tissue engineering: reactor evaluation using the Biochemical Engineering Journal
Yagi, 2004) analytic hierarchy process (AHP)
(Huang, Chang, Hung, Wang, An AHP model for bringing experts to consensus on medical payment standards Journal of Systems Science and Systems
& Chang, 2006) Engineering
(Ohta, et al., 2007) Analysis of the geographical accessibility of neurosurgical emergency hospitals in International journal of geographical
Sapporo city using GIS and AHP information science
(Dolan, 2008) Shared decision-making–transferring research into practice: The Analytic Hierarchy Patient education and counseling
Process (AHP)
(Vahidnia, Alesheikh, & Hospital site selection using fuzzy AHP and its derivatives JOURNAL OF ENVIRONMENTAL
Alimohammadi, 2009) MANAGEMENT
(Hsu & Pan, 2009) Application of Monte Carlo AHP in ranking dental quality attributes Expert Systems with Applications

(Wang, Fan, & Wang, 2010) Integration of fuzzy AHP and FPP with TOPSIS methodology for aeroengine health Expert Systems with Applications
assessment
(Buyukozkan, Cifci, & Strategic analysis of healthcare service quality using fuzzy AHP methodology Expert Systems with Applications
Guleryuz, 2011)

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(Danner, Hummel, Volz, van Integrating patients' views into health technology assessment: Analytic hierarchy International journal of technology assessment
Manen, & Wiegard, 2011) process (AHP) as a method to elicit patient preferences in health care
(Pecchia, Martin, Ragozzino, & User needs elicitation via analytic hierarchy process (AHP). A case study on a BMC medical informatics and decision making
Vanzanella, 2013) Computed Tomography (CT) scanner
(Jain & Rao, 2013) Application of AHP tool for decision making of choice of technology for extraction International Journal of the Analytic
of anti-cancer bioactive compounds of plant origin Hierarchy Process
(Nguyen & Nahavandi, 2015) Modified AHP for gene selection and cancer classification using type-2 fuzzy logic IEEE Transactions on Fuzzy Systems

(Hillerman, Souza, Reis, & Applying clustering and AHP methods for evaluating suspect healthcare claims Journal of computational science
Carvalho, 2017)
(IIbahar, Karasan, Cebik, & A novel approach to risk assessment for occupational health and safety using Safety science
Kahraman, 2018) Pythagorean fuzzy AHP & fuzzy inference system
(Gul, Application of Application of Pythagorean fuzzy AHP and VIKOR methods in occupational health International journal of occupational safety
Pythagorean fuzzy AHP and and safety risk assessment: the case of a gun and rifle barrel external surface and ergonomics
VIKOR methods in oxidation and colouring unit
occupational health and safety
risk assessment: the case of a
gun and rifle barrel external
surface oxidation and colouring
unit, 2018)
(Singh & Prasher, 2019) Measuring healthcare service quality from patients’ perspective: using Fuzzy AHP Total Quality Management & Business
application Excellence
(Ganguly & Kumar, 2019) Evaluating supply chain resiliency strategies in the Indian pharmaceutical sector: a International Journal of the Analytic
fuzzy analytic hierarchy process (F-AHP) approach Hierarchy Process

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Appendix D
ENVIRONMENTAL STUDIES
Table 9
Research publications in environmental studies category for ANP-2000 to 2019

ANP
Authors Research Titles Journal Name

(Wolfslehner, Vacik, & Lexer, Application of the analytic network process in multi-criteria analysis of sustainable Forest ecology and management
2005) forest management
(Chen, Li, & Wong, 2005) EnvironalPlanning: analytic network process model for environmentally conscious Journal of construction engineering and
construction planning management
(Erdogmus, Aras, & Koc, Evaluation of alternative fuels for residential heating in Turkey using analytic Renewable and Sustainable Energy Reviews
Evaluation of alternative fuels network process (ANP) with group decision-making
for residential heating in
Turkey using analytic network
process (ANP) with group
decision-making, 2006)
(Bahurmoz, 2006) A strategic model for safety during the Hajj pilgrimage: An ANP application Journal of Systems Science and Systems
Engineering
(Neaupane & Piantanakulchai, Analytic network process model for landslide hazard zonation Engineering Geology
2006)
(Promentilla, Furuichi, & Evaluation of remedial countermeasures using the analytic network process Waste Management
Tanikawa, 2006)
(Kone & Buke, 2007) An Analytical Network Process (ANP) evaluation of alternative fuels for electricity Energy policy
generation in Turkey
(Zheng & Ruan, 2007) General Conception of Livable City Basing on ANP [J] Urban Studies

(Simunich, 2007) In the Fall of 2002, the ANP had shown a better way to deal with Iraq Mathematical and Computer Modelling

(Dagdeviren, Yuksel, & Kurt, A fuzzy analytic network process (ANP) model to identify faulty behavior risk Safety science
2008) (FBR) in work system
Priority determination in strategic energy policies in Turkey using analytic network International Journal of Energy Research
Dağdeviren, M. and Eraslan, E process (ANP) with group decision making
Chen, Zhen, Heng Li, Andrew Knowledge-driven ANP approach to vendors evaluation for sustainable construction Journal of Construction Engineering and
Ross, Malik M. Khalfan, and Management
Stephen C. Kong
Application of ANP and DEMATEL to evaluate the decision-making of municipal Environmental Monitoring and Assessment
Tseng, Ming-Lang solid waste management in Metro Manila
Chang, Yu-Hern, Wann-Ming Using ANP priorities with goal programming for revitalization strategies in historic Expert Systems with Applications
Wey, and Hsiao-Yu Tseng transport: A case study of the Alishan Forest Railway

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Demirel, Tufan, Hande Muşdal, Multi-criteria evaluation of land cover policies using fuzzy AHP and fuzzy ANP: Human and Ecological Risk Assessment
Nihan Cetin Demirel, and G. The case of Turkey
Nilay Yücenur
Use of an ANP to prioritize managerial responsibilities of maritime stakeholders in Transportation Research Part D: Transport
Celik, M. and Topcu, Y.I. environmental incidents: An oil spill case and Environment
Lin, YuanHsu, Hui-Ping Using QFD and ANP to analyze the environmental production requirements in Expert Systems with Applications
Cheng, Ming-Lang Tseng, and linguistic preferences
Jim CC Tsai
Integrating the analytic network process (ANP) and the driving force-pressure-state- Management of Environmental Quality: An
Bottero, Marta, and Valentina impact-responses (DPSIR) model for the sustainability assessment of territorial International Journal
Ferretti transformations
García‐Melón, Mónica, Tomás An ANP approach to assess the sustainability of tourist strategies for the coastal Technological and Economic Development of
Gómez‐Navarro, and Silvia national parks of Venezuela Economy
Acuña‐Dutra
Wang, Wei-Ming, Amy HI An integrated FDM–ANP evaluation model for sustainable development of housing Optimization Letters
Lee, and Ding-Tsair Chang community
Lin, Chin-Tsai, Chie-Bein A green purchasing model by using ANP and LP methods Journal of Testing and Evaluation
Chen, and Ying-Chan Ting
Büyüközkan, Gülçin, and A novel hybrid MCDM approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy Expert Systems with Applications
Gizem Çifçi TOPSIS to evaluate green suppliers
García-Melón, Mónica, Tomás A combined ANP-delphi approach to evaluate sustainable tourism Environmental Impact Assessment Review
Gómez-Navarro, and Silvia
Acuña-Dutra
Zammori, Francesco, and ANP/RPN: A multi criteria evaluation of the risk priority number Quality and Reliability Engineering
Roberto Gabbrielli International
Vujanović, Davor, Vladimir Evaluation of vehicle fleet maintenance management indicators by application of Expert Systems with Applications
Momčilović, Nebojša Bojović, DEMATEL and ANP
and Vladimir Papić
Rezaeiniya, Nahid, Sarfaraz Greenhouse locating based on ANP-COPRAS-G methods–an empirical study based International Journal of Strategic Property
Hashemkhani Zolfani, and on Iran Management
Edmundas Kazimieras
Zavadskas
Toosi, SL Razavi, and JM V. Evaluating water transfer projects using analytic network process (ANP) Water resources management
Samani
Ghajar, Ismael, and Akbar Evaluation of harvesting methods for sustainable forest management (SFM) using Forest policy and economics
Najafi the analytical network process (ANP)
Demirel, Nihan Çetin, G. Nilay Risk-based evaluation of Turkish agricultural strategies using fuzzy AHP and fuzzy Human and Ecological Risk Assessment: An
Yücenur, Tufan Demirel, and ANP International Journal
Hande Muşdal
A revised Inno-Qual performance system for higher education: the integrated Journal of the Operational Research Society
Chen, I-Shuo applications of DEMATEL and ANP
Catron, Jonathan, G. Andrew Bioenergy development in Kentucky: A SWOT-ANP analysis Forest Policy and Economics
Stainback, Puneet Dwivedi, and
John M. Lhotka

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Xu, Pengpeng, and Edwin HW ANP model for sustainable Building Energy Efficiency Retrofit (BEER) using Habitat International
Chan Energy Performance Contracting (EPC) for hotel buildings in China
Agarwal, Etishree, Rajat Delineation of groundwater potential zone: An AHP/ANP approach Journal of earth system science
Agarwal, R. D. Garg, and P. K.
Garg
Isalou, A. A., V. Zamani, B. Landfill site selection using integrated fuzzy logic and analytic network process (F- Environmental Earth Sciences
Shahmoradi, and H. Alizadeh ANP)
Constructing a social vulnerability index to earthquake hazards using a hybrid factor Natural hazards
Zebardast, Esfandiar analysis and analytic network process (F’ANP) model
Lee, Paul Tae-Woo, Jei-Zheng Applying analytic network process (ANP) to rank critical success factors of International Journal of Shipping and
Wu, Kai-Chieh Hu, and waterfront redevelopment Transport Logistics
Matthew Flynn
Azizi, Ali, Bahram Land suitability assessment for wind power plant site selection using ANP- Environmental monitoring and assessment
Malekmohammadi, Hamid DEMATEL in a GIS environment: case study of Ardabil province, Iran
Reza Jafari, Hossein Nasiri,
and Vahid Amini Parsa
Toosi, SL Razavi, and J. M. V. A new integrated MADM technique combined with ANP, FTOPSIS and fuzzy max- Water resources management
Samani min set method for evaluating water transfer projects
Lam, Jasmine Siu Lee, and Developing environmental sustainability by ANP-QFD approach: the case of Journal of Cleaner Production
Kee-hung Lai shipping operations
Xu, Pengpeng, Edwin HW Sustainable building energy efficiency retrofit for hotel buildings using EPC Journal of Cleaner Production
Chan, Henk J. Visscher, mechanism in China: analytic Network Process (ANP) approach
Xiaoling Zhang, and Zezhou
Wu
Fazli, Safar, Reza Kiani Mavi, Crude oil supply chain risk management with DEMATEL–ANP Operational Research
and Mohammadali
Vosooghidizaji
Kuo, R. J., C. W. Hsu, and Y. Integration of fuzzy ANP and fuzzy TOPSIS for evaluating carbon performance of International journal of environmental science
L. Chen suppliers and technology
Asadzadeh, Asad, Theo Kötter, An augmented approach for measurement of disaster resilience using connective International Journal of Disaster Risk
and Esfandiar Zebardast factor analysis and analytic network process (F’ANP) model Reduction
Grošelj, Petra, and Lidija The environmental management problem of Pohorje, Slovenia: A new group Journal of environmental management
Zadnik Stirn approach within ANP–SWOT framework
Dobrea, Răzvan, Gabriela Food Sustainable Model Development: An ANP Approach to Prioritize Sustainable Sustainability
Molănescu, and Cristian Buṣu Factors in the Romanian Natural Soft Drinks Industry Context
Büyüközkan, Gülçin, and Sezin An integrated DEMATEL-ANP approach for renewable energy resources selection International Journal of Production
Güleryüz in Turkey Economics
Ignatius, Joshua, Amirah An integrated fuzzy ANP–QFD approach for green building assessment Journal of Civil Engineering and Management
Rahman, Morteza Yazdani,
Jonas Šaparauskas, and
Syarmila Hany Haron
Morteza, Zarei, Fatemi Selection of the optimal tourism site using the ANP and fuzzy TOPSIS in the Ocean & coastal management
Mohamad Reza, Mortazavi framework of Integrated Coastal Zone Management: A case of Qeshm Island
Mohammad Seddiq,

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Pourebrahim Sharareh, and

Ghoddousi Jamal
Chung, Chih-Chao, Li-Chung The establishment of a green supplier selection and guidance mechanism with the Sustainability
Chao, and Shi-Jer Lou ANP and IPA
Zhao, Shuang-Yao, Shanlin Where is the way for rare earth industry of China: An analysis via ANP-SWOT Resources Policy
Yang, Changyong Liang, and approach
Dongxiao Gu
LCA integrated ANP framework for selection of sustainable manufacturing Environmental Modeling & Assessment
Vimal, K. E. K., and S. Vinodh processes
Di Lallo, Giulio, Mauro Analyzing strategies to enhance small and low intensity managed forests Small-scale Forestry
Maesano, Mauro Masiero, certification in Europe using SWOT-ANP
Giuseppe Scarascia Mugnozza,
and Marco Marchetti
Malmir, Maryam, Mir Masoud Analysis of land suitability for urban development in Ahwaz County in southwestern Environmental Modeling & Assessment
Kheirkhah Zarkesh, Seyed Iran using fuzzy logic and analytic network process (ANP)
Masoud Monavari, Seyed Ali
Jozi, and Esmail Sharifi
Arsić, Sanela, Djordje Nikolić, Hybrid SWOT-ANP-FANP model for prioritization strategies of sustainable Forest policy and economics
and Živan Živković development of ecotourism in National Park Djerdap, Serbia
Zhao, Xiaojing, Long Chen, AHP-ANP–fuzzy integral integrated network for evaluating performance of Journal of construction engineering and
Wei Pan, and Qiuchen Lu innovative business models for sustainable building management
Chou, Ying-Chyi, Chia-Han Building criteria for evaluating green project management: An integrated approach sustainability
Yang, Ching-Hua Lu, Van of DEMATEL and ANP
Dang, and Pei-An Yang
Chen, Tingqiang, Lei Wang, Transparent assessment of the supervision information in China’s food safety: A Journal of Food Quality
and Jining Wang fuzzy-ANP comprehensive evaluation method
Aliani, H., S. BabaieKafaky, A. Land evaluation for ecotourism development—an integrated approach based on International Journal of Environmental
Saffari, and S. M. Monavari FUZZY, WLC, and ANP methods Science and Technology
Pakand, Mehran, and Vahab A multi-criteria study on rammed earth for low carbon buildings using a novel ANP- Energy and Buildings
Toufigh GA approach
Aminu, Mansir, Abdul Nasir Analytic network process (ANP)-based spatial decision support system (SDSS) for Arabian Journal of Geosciences
Matori, Khamaruzaman Wan sustainable tourism planning in Cameron Highlands, Malaysia
Yusof, Amirhossein
Malakahmad, and Rosilawati
Binti Zainol
Zheng, Xiong, Fangchao Xu, Analysis of Driving Factors for Extended Producer Responsibility by Using Sustainability
and Lipan Feng Interpretative Structure Modelling (ISM) and Analytic Network Process (ANP)
Garewal, Sahajpreet Kaur, A GIS-based Modified DRASTIC (ANP) method for assessment of groundwater Water Quality Research Journal
Avinash D. Vasudeo, Vishrut vulnerability: a case study of Nagpur city, India
S. Landge, and Aniruddha D.
Ghare
Gharedaghi, Gholamreza, and A pattern of contractor selection for oil and gas industries in a safety approach using International Journal of Occupational Safety
Manouchehr Omidvari ANP-DEMATEL in a Grey environment and Ergonomics

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Mavi, Reza Kiani, and Craig Critical success factors of sustainable project management in construction: A fuzzy Journal of cleaner production
Standing DEMATEL-ANP approach
Rad, Tahere Ghaemi, A methodological framework for assessment of ubiquitous cities using ANP and Sustainable cities and society
Abolghasem Sadeghi-Niaraki, DEMATEL methods
Alireza Abbasi, and Soo-Mi
Choi
Feng, Yixiong, Zhaoxi Hong, Environmentally friendly MCDM of reliability-based product optimisation Information Sciences
Guangdong Tian, Zhiwu Li, combining DEMATEL-based ANP, interval uncertainty and Vlse Kriterijumska
Jianrong Tan, and Hesuan Hu Optimizacija Kompromisno Resenje (VIKOR)
Chen, Lihong, and Jingzheng Multi-attribute sustainability evaluation of alternative aviation fuels based on fuzzy Journal of Air Transport Management
Ren ANP and fuzzy grey relational analysis
Alizadeh, Mohsen, Ibrahim A hybrid analytic network process and artificial neural network (ANP-ANN) model Remote Sensing
Ngah, Mazlan Hashim, for urban earthquake vulnerability assessment
Biswajeet Pradhan, and Amin
Pour
Arsić, Sanela, Djordje Nikolić, A new approach within ANP-SWOT framework for prioritization of ecosystem Ecological Economics
Ivan Mihajlović, Aleksandra management and case study of National Park Djerdap, Serbia
Fedajev, and Živan Živković
Reisi, Marzieh, Afsaneh Afzali, Applications of analytical hierarchy process (AHP) and analytical network process Environmental earth sciences
and Lu Aye (ANP) for industrial site selections in Isfahan, Iran
He, Gang, Baohua Yu, Comprehensive evaluation of ecological security in mining area based on PSR– Environmental technology
Shuzhou Li, and Yanna Zhu ANP–GRAY
Zou, Tong, Yikun Su, and Research on the Hybrid ANP-FCE Approach of Urban Community Sustainable Mathematical Problems in Engineering
Yaowu Wang Construction Problem
Chuang, Yen Hsun, Ruey Fang Sustainable planning for a coastal wetland system with an integrated ANP and Wetlands ecology and management
Yu, Wei Yea Chen, Ho Wen DPSIR model for conflict resolution
Chen, and Yu-Ting Su
Alilou, Hossein, Omid Evaluation of watershed health using Fuzzy-ANP approach considering geo- Journal of environmental management
Rahmati, Vijay P. Singh, environmental and topo-hydrological criteria
Bahram Choubin, Biswajeet
Pradhan, Saskia Keesstra, Seid
Saeid Ghiasi, and Seyed
Hamidreza Sadeghi
Starr, Morgan, Omkar Joshi, Perceptions regarding active management of the Cross-timbers forest resources of Land use policy
Rodney E. Will, and Chris B. Oklahoma, Texas, and Kansas: A SWOT-ANP analysis
Zou
Landscape Assessment for Stream Regulation Works in a Watershed Using the Sustainability
Peng, Szu-Hsien Analytic Network Process (ANP)
Chen, Zhihua, Xinguo Ming, A rough-fuzzy DEMATEL-ANP method for evaluating sustainable value Journal of Cleaner Production
Xianyu Zhang, Dao Yin, and requirement of product-service system
Zhaohui Sun

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Table 10
Research publications in environmental studies category for AHP-2000 to 2019

Authors Research Title Journal Name

(Kurttila, Pesonen, Kangas, & Utilizing the analytic hierarchy process (AHP) in SWOT analysis—a hybrid method Forest policy and economics
Kajanus, 2000) and its application to a forest-certification case
(Modarres & Zarei, 2002) Application of network theory and AHP in urban transportation to minimize Journal of the Operational Research Society
earthquake damages
(Solnes, 2003) Environmental quality indexing of large industrial development alternatives using Environmental Impact Assessment Review
AHP
(Mardle, Pascoe, & Herrero, Management objective importance in fisheries: an evaluation using the analytic Environmental Management
2004) hierarchy process (AHP)
(Kovacs, Malczewski, & Examining local ecological knowledge of hurricane impacts in a mangrove forest Journal of coastal research
Flores-Verdugo, 2004) using an analytical hierarchy process (AHP) approach
(Tesfamariam & Sadiq, 2006) Risk-based environmental decision-making using fuzzy analytic hierarchy process Stochastic Environmental Research and Risk
(F-AHP) Assessment
(Yoshimatsu & Abe, 2006) A review of landslide hazards in Japan and assessment of their susceptibility using Landslides
an analytical hierarchic process (AHP) method
(Karami, 2006) Appropriateness of farmers’ adoption of irrigation methods: The application of the Agricultural systems
AHP model
(Ying, et al., 2007) Combining AHP with GIS in synthetic evaluation of eco-environment quality—A Ecological modelling
case study of Hunan Province, China
(Lee, Yoon, & Kim, 2007) A study on making a long-term improvement in the national energy efficiency and Energy policy
GHG control plans by the AHP approach
A decision support system using analytical hierarchy process (AHP) for the optimal Environmental Geology
Bascetin, A environmental reclamation of an open-pit mine
Sambasivan, Murali, and Ng Evaluation of critical success factors of implementation of ISO 14001 using analytic Journal of cleaner production
Yun Fei hierarchy process (AHP): a case study from Malaysia
Srdjevic, Bojan, and Yvonilde Fuzzy AHP assessment of water management plans Water Resources Management
Dantas Pinto Medeiros
Parra-López, Carlos, Javier A systemic comparative assessment of the multifunctional performance of Ecological Economics
Calatrava-Requena, and Tomás alternative olive systems in Spain within an AHP-extended framework
de-Haro-Giménez
Sinha, R., G. V. Bapalu, L. K. Flood risk analysis in the Kosi river basin, north Bihar using multi-parametric Journal of the Indian Society of Remote
Singh, and B. Rath approach of analytical hierarchy process (AHP) Sensing
Rezaei-Moghaddam, K., and E. A multiple criteria evaluation of sustainable agricultural development models using Environment, Development and Sustainability
Karami AHP
Al-Barqawi, Hassan, and Tarek Infrastructure management: Integrated AHP/ANN model to evaluate municipal Journal of Infrastructure Systems
Zayed water mains’ performance

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2000-2019

Evaluation of hazardous waste transportation firms by using a two-step fuzzy-AHP Expert systems with applications
Gumus, Alev Taskin and TOPSIS methodology
Wang, Guiqin, Li Qin, Guoxue Landfill site selection using spatial information technologies and AHP: a case study Journal of environmental management
Li, and Lijun Chen in Beijing, China
Sadiq, Rehan, and Solomon Environmental decision-making under uncertainty using intuitionistic fuzzy analytic Stochastic Environmental Research and Risk
Tesfamariam hierarchy process (IF-AHP) Assessment
Shapira, Aviad, and Meir AHP-based weighting of factors affecting safety on construction sites with tower Journal of construction engineering and
Simcha cranes management
Kaya, Tolga, and Cengiz Multicriteria renewable energy planning using an integrated fuzzy VIKOR & AHP Energy
Kahraman methodology: The case of Istanbul
Şener, Şehnaz, Erhan Şener, Combining AHP with GIS for landfill site selection: a case study in the Lake Waste management
Bilgehan Nas, and Remzi Beyşehir catchment area (Konya, Turkey)
Karagüzel
Heo, Eunnyeong, Jinsoo Kim, Analysis of the assessment factors for renewable energy dissemination program Renewable and Sustainable Energy Reviews
and Kyung-Jin Boo evaluation using fuzzy AHP
Moeinaddini, Mazaher, Siting MSW landfill using weighted linear combination and analytical hierarchy Waste management
Nematollah Khorasani, Afshin process (AHP) methodology in GIS environment (case study: Karaj)
Danehkar, and Ali Asghar
Darvishsefat
Risk-based maintenance policy selection using AHP and goal programming Safety science
Arunraj, N. S., and J. Maiti
Awasthi, Anjali, and Satyaveer Using AHP and Dempster–Shafer theory for evaluating sustainable transport Environmental Modelling & Software
S. Chauhan solutions
Şener, Şehnaz, Erhan Sener, Solid waste disposal site selection with GIS and AHP methodology: a case study in Environmental monitoring and assessment
and Remzi Karagüzel Senirkent–Uluborlu (Isparta) Basin, Turkey
Kaya, Tolga, and Cengiz An integrated fuzzy AHP–ELECTRE methodology for environmental impact Expert systems with applications
Kahraman assessment
Kaya, Tolga, and Cengiz Fuzzy multiple criteria forestry decision making based on an integrated VIKOR and Expert systems with applications
Kahraman AHP approach
Reza, Bahareh, Rehan Sadiq, Sustainability assessment of flooring systems in the city of Tehran: An AHP-based Construction and Building Materials
and Kasun Hewage life cycle analysis
Pires, Ana, Ni-Bin Chang, and An AHP-based fuzzy interval TOPSIS assessment for sustainable expansion of the Resources, Conservation and Recycling
Graça Martinho solid waste management system in Setúbal Peninsula, Portugal
Pourghasemi, Hamid Reza, Application of fuzzy logic and analytical hierarchy process (AHP) to landslide Natural Hazards
Biswajeet Pradhan, and Candan susceptibility mapping at Haraz watershed, Iran
Gokceoglu
Zheng, Guozhong, Neng Zhu, Application of a trapezoidal fuzzy AHP method for work safety evaluation and early Safety science
Zhe Tian, Ying Chen, and warning rating of hot and humid environments
Binhui Sun
Awasthi, Anjali, and Satyaveer A hybrid approach integrating Affinity Diagram, AHP and fuzzy TOPSIS for Applied Mathematical Modelling
S. Chauhan sustainable city logistics planning
Hasekioğulları, Gökçe Deniz, A new approach to use AHP in landslide susceptibility mapping: a case study at Natural Hazards
and Murat Ercanoglu Yenice (Karabuk, NW Turkey)

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2000-2019

Anane, Makram, Lamia Ranking suitable sites for irrigation with reclaimed water in the Nabeul-Hammamet Resources, Conservation and Recycling
Bouziri, Atef Limam, and region (Tunisia) using GIS and AHP-multicriteria decision analysis
Salah Jellali
Ranking management strategies with complex outcomes: An AHP-fuzzy evaluation Environmental Modelling & Software
of recreational fishing using an integrated agent-based model of a coral reef
Gao, Lei, and Atakelty Hailu ecosystem
Donevska, Katerina R., Pece V. Regional non-hazardous landfill site selection by integrating fuzzy logic, AHP and Environmental Earth Sciences
Gorsevski, Milorad Jovanovski, geographic information systems
and Igor Peševski
Akıncı, Halil, Ayşe Yavuz Agricultural land-use suitability analysis using GIS and AHP technique Computers and electronics in agriculture
Özalp, and Bülent Turgut
Kayastha, Prabin, Megh Raj Application of the analytical hierarchy process (AHP) for landslide susceptibility Computers & Geosciences
Dhital, and Florimond De mapping: a case study from the Tinau watershed, west Nepal
Smedt
Zou, Qiang, Jianzhong Zhou, Comprehensive flood risk assessment based on set pair analysis-variable fuzzy sets Stochastic Environmental Research and Risk
Chao Zhou, Lixiang Song, and model and fuzzy AHP Assessment
Jun Guo
Stefanidis, Stefanos, and Assessment of flood hazard based on natural and anthropogenic factors using Natural Hazards
Dimitrios Stathis analytic hierarchy process (AHP)
Orencio, Pedcris M., and A localized disaster-resilience index to assess coastal communities based on an International Journal of Disaster Risk
Masahiko Fujii analytic hierarchy process (AHP) Reduction
Assessment of groundwater vulnerability based on a modified DRASTIC model, Hydrogeology Journal
Sener, Erhan, and Aysen GIS and an analytic hierarchy process (AHP) method: the case of Egirdir Lake basin
Davraz (Isparta, Turkey)
Evaluation of reallocation criteria in land consolidation studies using the Analytic Land use policy
Cay, Tayfun, and Mevlut Uyan Hierarchy Process (AHP)
Kim, Mincheol, Yong-Chul Application of Delphi-AHP methods to select the priorities of WEEE for recycling Journal of environmental management
Jang, and Seunguk Lee in a waste management decision-making tool
Nefeslioglu, Hakan A., Ebru A modified analytical hierarchy process (M-AHP) approach for decision support Computers & Geosciences
Akcapinar Sezer, Candan systems in natural hazard assessments
Gokceoglu, and Z. Ayas
Ertay, Tijen, Cengiz Kahraman, Evaluation of renewable energy alternatives using MACBETH and fuzzy AHP Technological and Economic Development of
and İhsan Kaya multicriteria methods: the case of Turkey Economy
Janackovic, Goran Lj, Suzana Selection and ranking of occupational safety indicators based on fuzzy AHP: A case South African Journal of Industrial
M. Savic, and Miomir S. study in road construction companies Engineering
Stankovic
Ouma, Yashon, and Ryutaro Urban flood vulnerability and risk mapping using integrated multi-parametric AHP Water
Tateishi and GIS: methodological overview and case study assessment
Kaliraj, S., N. Chandrasekar, Identification of potential groundwater recharge zones in Vaigai upper basin, Tamil Arabian Journal of Geosciences
and N. S. Magesh Nadu, using GIS-based analytical hierarchical process (AHP) technique
MSW landfill site selection by combining AHP with GIS for Konya, Turkey Environmental Earth Sciences
Uyan, Mevlut
Shi, Lei, Jian Shuai, and Kui Fuzzy fault tree assessment based on improved AHP for fire and explosion accidents Journal of hazardous materials
Xu for steel oil storage tanks

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2000-2019

Shi, Shenggang, Jingcan Cao, Construction of a technique plan repository and evaluation system based on AHP Journal of hazardous materials
Li Feng, Wenyan Liang, and group decision-making for emergency treatment and disposal in chemical pollution
Liqiu Zhang accidents
Feng, Lan, Xiaodong Zhu, and Assessing coastal reclamation suitability based on a fuzzy-AHP comprehensive Marine pollution bulletin
Xiang Sun evaluation framework: a case study of Lianyungang, China
Roodposhti, Majid Shadman, PROMETHEE II and fuzzy AHP: an enhanced GIS-based landslide susceptibility Natural Hazards
Saeed Rahimi, and Mansour mapping
Jafar Beglou
Graham, Gary, James Freeman, Green supplier selection using an AHP-Entropy-TOPSIS framework Supply Chain Management: An International
and Tao Chen Journal
Zhang, Jiuquan, Yirong Su, GIS-based land suitability assessment for tobacco production using AHP and fuzzy Computers and Electronics in Agriculture
Jinshui Wu, and Hongbo Liang set in Shandong province of China
Beskese, Ahmet, H. Handan Landfill site selection using fuzzy AHP and fuzzy TOPSIS: a case study for Istanbul Environmental Earth Sciences
Demir, H. Kurtulus Ozcan, and
H. Eser Okten
Shen, Lixin, Kamalakanta Developing a sustainable development framework in the context of mining Resources Policy
Muduli, and Akhilesh Barve industries: AHP approach
Delineation of groundwater potential zone in hard rock terrain of India using remote Geocarto International
Shekhar, Shashank, and Arvind sensing, geographical information system (GIS) and analytic hierarchy process
Chandra Pandey (AHP) techniques
Taheri, Kamal, Francisco Sinkhole susceptibility mapping using the analytical hierarchy process (AHP) and Geomorphology
Gutiérrez, Hassan Mohseni, magnitude–frequency relationships: A case study in Hamadan province, Iran
Ezzat Raeisi, and Milad Taheri
Hossen, Muhammed Mufazzal, Construction schedule delay risk assessment by using combined AHP-RII Nuclear engineering and technology
Sunkoo Kang, and Jonghyun methodology for an international NPP project
Kim
Zyoud, Shaher H., Lorenz G. A framework for water loss management in developing countries under fuzzy Expert systems with applications
Kaufmann, Hafez Shaheen, environment: Integration of Fuzzy AHP with Fuzzy TOPSIS
Subhi Samhan, and Daniela
Fuchs-Hanusch
Kohara, Kazuhiro, and Takuya Simulating tsunami evacuation with multi-agents and determining a countermeasure International Journal of the Analytic
Sugiyama with AHP Hierarchy Process
Veisi, Hadi, Houman Liaghati, Developing an ethics-based approach to indicators of sustainable agriculture using Ecological Indicators
and Ali Alipour analytic hierarchy process (AHP)
Chen, Wei, Wenping Li, GIS-based landslide susceptibility mapping using analytical hierarchy process Environmental Earth Sciences
Huichan Chai, Enke Hou, (AHP) and certainty factor (CF) models for the Baozhong region of Baoji City,
Xiaoqin Li, and Xiao Ding China
Kumar, Rohan, and R. Landslide susceptibility mapping using analytical hierarchy process (AHP) in Tehri Journal of the Geological Society of India
Anbalagan reservoir rim region, Uttarakhand
Althuwaynee, Omar F., A novel integrated model for assessing landslide susceptibility mapping using International Journal of Remote Sensing
Biswajeet Pradhan, and Saro CHAID and AHP pair-wise comparison
Lee
Khalil, Natasha, Syahrul Nizam Ranking the indicators of building performance and the users’ risk via Analytical Ecological Indicators
Kamaruzzaman, and Mohamad Hierarchy Process (AHP): Case of Malaysia

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2000-2019

Rizal Baharum

Torabi-Kaveh, M., R. Landfill site selection using combination of GIS and fuzzy AHP, a case study: Waste Management & Research
Babazadeh, S. D. Mohammadi, Iranshahr, Iran
and M. Zaresefat
Pourghasemi, Hamid Reza, and Landslide susceptibility modeling in a landslide-prone area in Mazandaran Province, Theoretical and Applied Climatology
Mauro Rossi north of Iran: a comparison between GLM, GAM, MARS, and M-AHP methods
Rahmat, Zeinab Ghaed, Mehdi Landfill site selection using GIS and AHP: a case study: Behbahan, Iran KSCE Journal of Civil Engineering
Vosoughi Niri, Nadali Alavi,
Gholamreza Goudarzi, Ali
Akbar Babaei, Zeinab Baboli,
and Mohsen Hosseinzadeh
Gigović, Ljubomir, Dragan Application of GIS-interval rough AHP methodology for flood hazard mapping in Water
Pamučar, Zoran Bajić, and urban areas
Siniša Drobnjak
Modak, Mousumi, Khanindra Performance evaluation of outsourcing decision using a BSC and Fuzzy AHP Resources Policy
Pathak, and Kunal Kanti Ghosh approach: A case of the Indian coal mining organization
Yousefi, Hossein, Mohammad GA/AHP-based optimal design of a hybrid CCHP system considering economy, Energy and Buildings
Hasan Ghodusinejad, and energy and emission
Younes Noorollahi
Chen, Luyuan, and Xinyang A modified method for evaluating sustainable transport solutions based on AHP and Applied Sciences
Deng Dempster–Shafer evidence theory
Lyu, Hai-Min, Jack Shen, and Assessment of geohazards and preventative countermeasures using AHP Sustainability
Arul Arulrajah incorporated with GIS in Lanzhou, China
Assessment of groundwater potential zones in coal mining impacted hard-rock Geocarto International
Kumar, Akshay, and Akhouri terrain of India by integrating geospatial and analytic hierarchy process (AHP)
Pramod Krishna approach
Ghimire, Laxman Prasad, and An analysis on barriers to renewable energy development in the context of Nepal Renewable energy
Yeonbae Kim using AHP
Yazdi, Mohammad, Orhan Application of fuzzy fault tree analysis based on modified fuzzy AHP and fuzzy International journal of occupational safety
Korhan, and Sahand Daneshvar TOPSIS for fire and explosion in the process industry and ergonomics
Gottfried, Oliver, Djavan De SWOT-AHP-TOWS analysis of private investment behavior in the Chinese biogas Journal of cleaner production
Clercq, Elena Blair, Xin Weng, sector
and Can Wang
Arabameri, Alireza, Khalil GIS-based gully erosion susceptibility mapping: a comparison among three data- Environmental Earth Sciences
Rezaei, Hamid Reza driven models and AHP knowledge-based technique
Pourghasemi, Saro Lee, and
Mojtaba Yamani
Hatefi, Seyed Morteza, and Construction projects assessment based on the sustainable development criteria by Sustainability
Jolanta Tamošaitienė an integrated fuzzy AHP and improved GRA model.
Kamaruzzaman, Syahrul Developing weighting system for refurbishment building assessment scheme in Energy policy
Nizam, Eric Choen Weng Lou, Malaysia through analytic hierarchy process (AHP) approach
Phui Fung Wong, Ruth Wood,
and Adi Irfan Che-Ani

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2000-2019

Ren, Chongfeng, Zhehao Li, Integrated multi-objective stochastic fuzzy programming and AHP method for Journal of cleaner production
and Hongbo Zhang agricultural water and land optimization allocation under multiple uncertainties
Wang, Bo, Junnian Song, Selecting sustainable energy conversion technologies for agricultural residues: A Resources, Conservation and Recycling
Jingzheng Ren, Kexin Li, fuzzy AHP-VIKOR based prioritization from life cycle perspective
Haiyan Duan, and Xian’en
Wang
Kadam, Ajaykumar, Animesh Hydrological response-based watershed prioritization in semiarid, basaltic region of Environment, Development and Sustainability
S. Karnewar, Bhavana western India using frequency ratio, fuzzy logic and AHP method
Umrikar, and R. N. Sankhua
Arulbalaji, P., D. Padmalal, and GIS and AHP techniques-based delineation of groundwater potential zones: a case Scientific reports
K. Sreelash study from southern Western Ghats, India
Solangi, Yasir Ahmed, An Integrated Delphi-AHP and Fuzzy TOPSIS Approach toward Ranking and Processes
Qingmei Tan, Nayyar Hussain Selection of Renewable Energy Resources in Pakistan
Mirjat, Gordhan Das Valasai,
Muhammad Waris Ali Khan,
and Muhammad Ikram
Laroche, Geneviève, Gérald Integrating agroforestry intercropping systems in contrasted agricultural landscapes: Agroforestry Systems
Domon, Nancy Gélinas, a SWOT-AHP analysis of stakeholders’ perceptions
Maurice Doyon, and Alain
Olivier
Souissi, Dhekra, Lahcen GIS-based MCDM-AHP modeling for flood susceptibility mapping of arid areas, Geocarto International
Zouhri, Salma Hammami, southeastern Tunisia
Mohamed Haythem Msaddek,
Adel Zghibi, and Mahmoud
Dlala
Büyüközkan, Gülçin, Fethullah A new group decision-making approach with IF AHP and IF VIKOR for selecting Measurement
Göçer, and Yağmur Karabulut hazardous waste carriers
Ruan, Zhuen, Cuiping Li, A New Risk Assessment Model for Underground Mine Water Inrush Based on AHP Mine Water and the Environment
Aixiang Wu, and Yong Wang and D–S Evidence Theory
Xu, Shuobo, Dishi Xu, and Construction of regional informatization ecological environment based on the Sustainable Computing: Informatics and
Lele Liu entropy weight modified AHP hierarchy model Systems
Ma, Ye, Tianyu Shi, Wei Comprehensive policy evaluation of NEV development in China, Japan, the United Journal of cleaner production
Zhang, Yu Hao, Junbing States, and Germany based on the AHP-EW model
Huang, and Yinan Lin

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