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 8

Adaptive Neuro-Fuzzy Inference

System Prediction of Calorific Value
Based on the Analysis of U.S. Coals
F. Rafezi, E. Jorjani and Sh. Karimi
Science and Research Branch, Islamic Azad
University, Tehran
Iran

1. Introduction
Coal is a chemically and physically heterogeneous and combustible substance that consists
of both organic and inorganic compounds. It currently is a major energy source worldwide,
especially among many developing countries, and will continue to be so for many years
(Miller, 2005).The chemical analysis of coal includes proximate and ultimate analyses. The
proximate analysis gives the relative amounts of moisture, volatile matter, and ash, as well
as the fixed carbon content of the coal. The ultimate or elemental analysis gives the amounts
of carbon, hydrogen, nitrogen, sulfur, and oxygen in the coal (Miller, 2005).
The measure of the amount of energy that a given quantity of coal will produce when
burned is kown as calorific value or heating value. Heating value is a rank parameter and a
complex function of the elemental composition of the coal, but it is also dependent on the
maceral and mineral composition (Hower and Eble, 1996). It can be determined
experimentally using a calorimeter.
Many equations have been developed for the estimation of gross calorific value (GCV)
based on proximate analysis and/or ultimate analysis (Mason and Gandhi, 1983; Mesroghli
et al., 2009; Given et al., 1986; Parikh et al., 2005; Custer, 1951; Spooner, 1951; Mazumdar,
1954; Channiwala and Parikh, 2002; Majumder et al., 2008).
Regression analyses and data for 775 U.S. coal samples (with less than 30% dry ash) were
used by Mason and Gandhi (1983) to develop an empirical equation that estimates the
calorific value (CV) of coal based on its C, H, S, and ash contents (all on dry basis). Their
empirical equation, expressed in SI units, is:

CV = 0.472C + 1.48H + 0.193S + 0.107A – 12.29 (MJ/kg) (1)

Given et al. (1986) developed an equation to calculate the calorific value of U.S. coals from
their elemental composition; expressed in SI units, their equation is:

CV = 0.3278C + 1.419H + 0.09257S – 0.1379O + 0.637 (MJ/Kg) (2)

Neural networks, as a new mathematical method, have been used extensively in research
areas related to industrial processes (Zhenyu and Yongmo, 1996; Jorjani et al., 2007; Specht,

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170 Artificial Neural Networks - Industrial and Control Engineering Applications

1991; Chen et al., 1991; Wasserman, 1993; Chehreh Chelgani et al., 2008; Hansen and
Meservy, 1996; Patel et al., 2007; Mesroghli et al., 2009; Bagherieh et al., 2008; Jorjani et al.,
2008; Chehreh Chelgani et al., 2010; Khandelwal and Singh, 2010 ; Sahu et al., 2010;
Yao et al., 2005; Patel et al., 2007; Salehfar and Benson, 1998; Wu et al., 2008; Karacan,
2007).
Patel et al. (2007) predicted the GCV of coal utilizing 79 sets of data using neural network
analyses based on proximate analysis, ultimate analysis, and the density of helium. They
found that the input set of moisture, ash, volatile matter, fixed carbon, carbon, hydrogen,
sulfur, and nitrogen yielded the best prediction and generalization accuracy.
Mesroghli et al. (2009) investigated the relationships of ultimate analysis and proximate
analysis with GCV of U.S. coal samples by regression analysis and artificial neural network
methods. The input set of C, Hexclusive of moisture (Hex) , N, Oexclusive of moisture (Oex), S, moisture,
and ash was found to be the best predictor.
The adaptive neuro-fuzzy inference system (ANFIS), which consists of both artificial neural
networks and fuzzy logic, has been used widely in research areas related to industrial
processes (Boyacioglu and Avci, 2010; Esen and Inalli, 2010; Soltani et al., 2010; Pena et al.,
2010; Chong-lin et al., 2009).
The aim of the present work is to assess the properties of 4540 samples of U.S. coal from 25
states with reference to the GCV and possible variations with respect to ultimate and
proximate analyses using multi-variable regression, the SPSS software package, and the
ANFIS, MATLAB software package.
This work is an attempt to answer the following important questions:
a. Is it possible to generate precise linear or non-linear equations between ultimate and
proximate analysis parameters and GCV for different U.S. coal samples that have a
wide range of calorific values from 4.82 to 34.85 MJ/kg?
b. Is ANFIS a better tool than regression analysis for improving accuracy and decreasing
errors in the estimation of the calorific value of coal?
c. Is it possible to improve the accuracy of predictions by changing “total hydrogen and
oxygen in coal (H and O)” to “Hex, Oex, and moisture?”
This work is different from previously published work because it involves the first use of
ANFIS to predict the GCV of coal.

2. Experimental data
The data that were used to examine the proposed approaches were obtained from the U.S.
Geological Survey Coal Quality (COALQUAL) database, open file report 97-134 (Bragg et
al., 2009). Samples with more than 50% ash and samples that had a proximate analysis
and/or an ultimate analysis different from 100% were excluded from the database.
Analysis results for a total of 4540 coal samples were used.
The sampling procedures and chemical analytical methods are available at the following
website: http://energy.er.usgs.gov/products/databases/CoalQual/index.htm. The number
of samples and the range of GCV for different states are shown in Table 1.
Table 2 shows the ranges of input variables, i.e., C, H, Hex, N, O, Oex, total sulfur, ash,
moisture, and volatile matter, that were used in predicting GCV.

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Adaptive Neuro-Fuzzy Inference System Prediction
of Calorific Value Based on the Analysis of U.S. Coals 171

State Number of samples Range of GCV (MJ/kg)

Alabama 679 6.05-34.80

Alaska 51 8.65-27.42
Arizona 10 18.54-24.36
Arkansas 52 5.57-34.68
Colorado 172 7.24-33.81
Georgia 25 24.03-34.85
Indiana 101 19.23-28.96
Iowa 73 16.03-26.59
Kansas 19 20.87-28.86
Kentucky 720 18.68-34.03
Maryland 40 23.04-33.48
Missouri 68 23.83-28.63
Montana 140 5.55-20.63
New Mexico 114 8.81-32.15
North Dakota 124 4.85-13.61
Ohio 398 16.43-31.14
Oklahoma 25 23.89-33.31
Pennsylvania 498 13.58-33.10
Tennessee 42 24.61-33.48
Texas 33 9.54-27.74
Utah 103 4.82-30.14
Virginia 368 19.49-34.80
Washington 10 13.14-27.45
West Virginia 340 14.29-34.75
Wyoming 335 6.27-34.23
Table 1. Number of samples and range of GCV (as-received) for different U.S. states

Variable (%) Minimum Maximum Mean Std. Deviation

Moisture 0.4 49.60 8.90 9.90

Volatile matter 3.80 55.70 32.30 6.32
Ash 0.90 32.90 10.84 5.97
Hydrogen 1.70 8.10 5.27 0.69
Carbon 24.10 89.60 65.72 12.02
Nitrogen 0.20 2.41 1.29 0.33
Oxygen 0.90 54.70 14.86 11.27
Sulfur 0.07 17.30 1.90 1.73
Hex 0.19 5.86 4.36 0.79
Oex 0.09 22.14 7.50 3.27
Table 2. Ranges of proximate and ultimate analyses of coal samples (as-received)

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172 Artificial Neural Networks - Industrial and Control Engineering Applications

3. Methods
3.1 Regression analysis
Regression nalysis is a statistical tool that is used to investigate the relationships between
variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon
another. To explore such issues, the investigator assembles data on the underlying variables
of interest and employs regression analysis to estimate the quantitative effect of the causal
variables upon the variable that they influence. The investigator also typically assesses the
statistical significance of the estimated relationships, that is, the degree of confidence that
the true relationship is close to the estimated relationship (An introduction to regression
analysis, Alan O. Sykes).
Linear regression estimates the coefficients of the linear equation, involving one or more
independent variables, which are required to have a reliable prediction of the value of the
dependent variable. All variables must pass the tolerance criterion to be entered in the
equation, regardless of the entry method specified. The default tolerance level is 0.0001.
Also, a variable is not entered if it would cause the tolerance of another variable already in
the model to drop below the tolerance criterion. All independent variables selected are
added to a single regression model. However, different entry methods can be specified for
different subsets of variables. Method selection allows specifying how independent
variables will be entered into the analysis. Using different methods, a variety of regression
models can be selected from the same set of variables (SPSS Inc., 2004).
Non-linear regression is a method of finding a non-linear model of the relationship between
the dependent variable and a set of independent variables. Unlike traditional linear
regression, which is restricted to estimating linear models, non-linear regression can
estimate models with arbitrary relationships between independent and dependent variables.
This is accomplished using iterative estimation algorithms (SPSS Inc., 2004).
In this study, both single-variable and multi-variable regressions were used to develop
correlations between ultimate and proximate analyses of coal samples with their gross
calorific value (GCV). A stepwise procedure for selecting variables was used, and the
variables were entered sequentially into the model. The first variable considered for use in
the equation was the one with the largest positive or negative correlation with the
dependent variable. This variable was entered into the equation only if it satisfied the
criterion for entry. The next variable, with the largest partial correlation, was considered as
the second input to the equation. The procedure stops when there are no variables that meet
the entry criterion (SPSS Inc., 2004).

3.2 Adaptive neuro fuzzy inference system

In the artificial intelligence field, the term “neuro-fuzzy” refers to combinations of artificial
neural networks and fuzzy logic. Fuzzy modeling and neural networks have been recognized
as powerful tools that can facilitate the effective development of models and integrate
information from different sources, such as empirical models, physical laws, or measurements
and heuristics (Babuska, 1998); these two tools were combined in order to achieve readability
and learning ability at the same time (Jantzen, 1998). The neuro-fuzzy approach in the fuzzy
modeling research field is divided into two areas: 1) linguistic fuzzy modeling that is focused
on interpretability, mainly the Mamdani model and 2) precise fuzzy modeling that is focused
on accuracy, mainly the Takagi-Sugeno-Kang (TSK) model (Wikimedia Foundation Inc., 2009).
ANFIS is an architecture that is functionally equivalent to a Takagi-Sugeno-Kang-type fuzzy

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Adaptive Neuro-Fuzzy Inference System Prediction
of Calorific Value Based on the Analysis of U.S. Coals 173

rule base (Jang & Sun, 1995); it is a class of adaptive, multi-layer, feed-forward networks that is
functionally equivalent to a fuzzy inference system.
A fuzzy rule in a Sugeno fuzzy model has the form of:

If x is A and y is B then z = f(x, y) , (3)

where A and B are input fuzzy sets in the antecedent, and, usually, z = f(x, y) is a zero- or
first-order polynomial function in the consequent. The fuzzy reasoning procedure for the
first-order Sugeno fuzzy model and equivalent ANFIS structure is shown in Fig. 1.
Here, the defuzzification procedure in the Mamdani fuzzy model is replaced by the
operation of the weighted average in order to avoid the time-consuming procedure of
defuzzification. Defuzzification refers to the way a crisp value is extracted from a fuzzy set
as a representative value (Jang and Sun, 1995).
Jang and Sun (1995) and Jantzen (1998) have provided more details about the ANFIS
architecture, learning algorithms, and training methods.

Fig. 1. (a) The Sugeno fuzzy model reasoning; (b) equivalent ANFIS structure (Jang and Sun,
1995)

4. Results and discussion

4.1 Relationships between GCV and individual input variables
By a least squares mathematical method, the correlation coefficients (R2) of C, H, Hex, N, O,
Oex, total sulfur, ash, moisture, and volatile matter with GCV were determined to be +0.99, -
0.25, +0.72, +0.52, -0.86, -0.51, +0.01, -0.05, -0.85, and +0.03, respectively. From the above-
mentioned results, it can be concluded that the worthy relationships are for carbon with
positive effect and oxygen with negative effect, because they are rank parameters; and
moisture with negative effect, because it is also a rank parameter at low rank coals and
because it is a diluent with respect to heating value. Non-linear relationships between
individual input variables and GCV were examined as well, but the results were not better
than the results obtained when the linear procedure was used.

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174 Artificial Neural Networks - Industrial and Control Engineering Applications

4.2 Multi-variable relationships of GCV with ultimate and proximate analysis

parameters
The best-correlated linear equations, using a stepwise procedure between the various
mentioned parameters and GCV, can be presented as follows:
a. Ash, moisture, and volatile matter inputs:

GCV (MJ/kg) = 37.777 – 0.647M – 0.387A – 0.089VM R2 = 0.97 (4)

b. Carbon, hydrogen, nitrogen, oxygen, sulfur, and ash inputs:

GCV (MJ/kg) = 5.833 + 0.284C – 0.321O + 1.031H + 0.519N – 0.046Ash

R2 = 0.994 (5)
c. Carbon, hydrogen exclusive of moisture, nitrogen, oxygen exclusive of moisture, sulfur,
moisture, and ash inputs:

GCV (MJ/kg) = 26.452 + 0.074C – 0.405M + 0.89Hex - 0.446 Oex – 0.256Ash - 0.195S

R2 = 0.995 (6)
Estimated deviations of GCV from target values for equations (4) through (6) are shown in
Table 3.
GCV deviation from target (MJ/kg) Eq. (4) Eq. (5) Eq. (6)
Less than 0.5 39.4% 71.7% 78.2%
Less than 1 72.5% 95.2% 96.5%
More than 1 27.2% 4.8% 3.5%
Table 3. Estimated deviations of GVC from target values for various linear regression
equations
The non-linear equations were examined as well, and the exponential equation was the best
predictor of GCV. The results for the input sets of (a), (b), and (c) are shown in the following
equations:
a. Ash, moisture, and volatile matter inputs:

GCV = 182.667 + 37.564e-0.027M – 0.381e0.042VM – 182.79e0.002A R2 = 0.988 (7)

b. Carbon, hydrogen, nitrogen, oxygen, sulfur, and ash inputs:

GCV = -156.641 – 0.091e-0.073A + 60.15e0.004C – 13.95e-0.322H + 0.33e0.648N + 109.885-0.003O – 0.318 e-0.363S

R2 = 0.995 (8)
c. Carbon, hydrogen exclusive of moisture, nitrogen, oxygen exclusive of moisture, sulfur,
moisture, and ash inputs:

GCV = -278.474 + 4.487e0.016C + 24.485e-0.019M + 7.173e0.013N + 76.532e0.012Hex +

189.349e-0.001Oex – 0.033e0.221S – 4.727e0.021A R2 = 0.999 (9)

The estimation of GCV deviations from target values for equations (7) through (9) are
shown in Table 4. By comparing Tables 3 and 4, it can be concluded that exponential
equations are more precise than linear equations for predicting the GCV of coal.

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Adaptive Neuro-Fuzzy Inference System Prediction
of Calorific Value Based on the Analysis of U.S. Coals 175

GCV deviation from target (MJ/kg) Eq. (7) Eq. (8) Eq. (9)
Less than 0.5 60% 28.98% 74.8%
Less than 1 86.65% 71.34% 99.1%
More than 1 13.35% 28.66% 0.9%
Table 4. Estimation of the deviations of GCV from target values for various non-linear
regression equations

4.3 ANFIS prediction

Three input sets, (a), (b) and (c), were used to determine whether ANFIS is able to predict
GCV better than regression. This was done using the ANFIS menu in the MATLAB software
package to identify the relationships between GCV and input variables.
In a neuro-fuzzy inference system, the first step is to determine the system inputs and
outputs that will be used to predict GCV. In this study, input set (a) was comprised of three
variables, i.e., ash, volatile matter, and moisture; input set (b) was comprised of six
variables, i.e., C, H, N, O, S, and ash; input set (c) was comprised of seven variables, i.e., C,
Hex, N, Oex, S, ash, and moisture.
The Sugeno fuzzy inference system was used in this research. The output functions in the
Sugeno system are linear or constant. A rule in the fuzzy Sugeno model is:

If input 1 = x and input 2 = y, then the output is z = ax + by + c (10)

In the Sugeno system, for a zero-order model, the z plane is constant (a = b = 0). The plane of
zi, the output of any rule, is weighted by wi. The final output of the system is the weighted
average of all outputs, which is calculated as follows:

N
∑ wi zi
final output = =N
i 1
(11)
∑ w
i =1 i
The subtractive clustering scheme was used to cluster data; the best-designed, neuro-fuzzy
system for input sets (a), (b), and (c) were systems with three, five, and twelve clusters,
respectively. For input set (a), the range of influence, squash factor, accept ratio, and reject
ratio were selected as 0.5, 1.25, 0.5, and 0.15, respectively; for input set (b), they were 0.35,
1.25, 0.5, and 0.15, respectively; and, for input set (c), they were 0.25, 1.2, 0.5, and 0.125,
respectively. The Gaussian membership function was used. For training of the ANFIS, the
hybrid method was used with 3200 sets of data; the remaining 1340 sets of data were used
Number of
Training set Testing set
Model Basis Model inputs membership R2
size size
functions
Ash, volatile matter,
a As received 3200 1340 3 0.997
moisture
b As received C, H, N, O, S, ash 3200 1340 5 0.999
C,Hex, N, Oex, S, ash,
c As received 3200 1340 12 0.999
moisture
Table 5. Details of the best-correlated neuro-fuzzy models

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176 Artificial Neural Networks - Industrial and Control Engineering Applications

for testing. For the training stage, we selected 100 epochs. Details of the best-correlated
neuro-fuzzy models are shown in Table 5. As Table 5 shows, the designed neuro-fuzzy
systems can predict the GCV with acceptable correlation coefficients (R2) of 0.997 , 0.999,
and 0.999 for the ( a), (b), and (c) input sets, respectively.
As an example, the neuro-fuzzy design structure for model (c) to predict GCV is shown in
Fig. 2.
The estimates of the deviations of the GCV from target values produced by the neuro-fuzzy
models are shown in Table 6. It can be seen that the prediction precision of GCV from
ANFIS and using all three input sets (a), (b), and (c) (Table 6) are better than those from
linear and non- linear regression (Tables 3 and 4).

Fig. 2. ANFIS model structure for the prediction of GCV using input set (c)

Model a Model b Model c

GCV deviation from target (MJ/kg) (3-member (5-member (12-member
function) function) function)
Less than 0.5 83% 97.6% 99.4%
Less than 1 99.4% 100% 100%
More than 1 0.5% 0% 0%
Table 6. Estimation of deviations of GCV from target values for neuro-fuzzy models
The GCV predicted (GCVP) by ANFIS in the testing stage for input sets (a), (b), and (c)
compared to the actual values determined in the laboratory (GCVa) are shown in Figs. 3, 4,
and 5, respectively. The distributions of the differences between actual and estimated GCVs
are shown in Figs. 6, 7, and 8 for input sets (a), (b), and (c), respectively.

5. Technical considerations
According to Eqs. (4) through (9) and the results presented in Tables 3 and 4, it can be seen
that the exponential equations are better than linear equations for predicting GCV; among
the exponential equations, Eq (9) is the most suitable equation. A correlation coefficient of
0.999 and a deviation from experimentally calculated GCVs that was only 0.9 % more than

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Adaptive Neuro-Fuzzy Inference System Prediction
of Calorific Value Based on the Analysis of U.S. Coals 177

Fig. 3. ANFIS-estimated GCV in testing stage versus actual determined value (model a)

Fig. 4. ANFIS-estimated GCV in testing stage versus actual determined value (model b)

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178 Artificial Neural Networks - Industrial and Control Engineering Applications

Fig. 5. ANFIS-estimated GCV in testing stage versus actual determined value (model c)

GCV difference
 (MJ/kg)

Fig. 6. Distribution of difference between actual and estimated GCV in testing stage (model a)

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Adaptive Neuro-Fuzzy Inference System Prediction
of Calorific Value Based on the Analysis of U.S. Coals 179

GCV difference
 (MJ/kg)

Fig. 7. Distribution of difference between actual and estimated GCV in testing stage (model b)

GCV difference
 (MJ/kg)

Fig. 8. Distribution of difference between actual and estimated GCV in testing stage (model c)
0.5 (MJ/kg) were achieved by Eq (9). With reference to the above results, it can be concluded
that the input set of carbon, hydrogen exclusive of moisture, nitrogen, oxygen exclusive of
moisture, sulfur, moisture, and ash can be used as the best and most-reliable input for the

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180 Artificial Neural Networks - Industrial and Control Engineering Applications

prediction of the GCV of coal using exponential equations. Restating “hydrogen and
oxygen” in the form of “hydrogen exclusive of moisture, oxygen exclusive of moisture, and
moisture” can decrease the errors and deviations from experimentally calculated GCV by
regression. According to Table 5, which presents the correlation coefficients of the ANFIS
models for the (a), (b), and (c) input sets, the correlation coefficients in the test stage were
determined ot be 0.997 (model a) to 0.999 (models b and c). In addition, Table 6, which
presents the deviations of the ANFIS model predictions from targets values, shows that the
errors and deviations from experimentally calculated GCVs in ANFIS models are less than
those produced by regression models. Although Mesroghli et al. (2009) reported that
artificial neural network is not better or very different from regression results when the
proximate and ultimate analyses are the GCV predictors. However, in the current work, a
suitable, structured ANFIS model predicted GCV with a high precision that has not been
reported in previous published works.

6. Conclusions
• In this work, proximate and ultimate analyses of 4540 coal samples from 25 U.S. states
and two mathematical modelling methods, i.e., multi-variable regression and adaptive
neuro-fuzzy interface systems were used to estimate GCV.
• The best-correlated linear equation was achieved using input set (c) (C, Hex, N, Oex,
S, M, ash) with a correlation coefficient of 0.995. The results also showed that, for
input set (c), the difference between actual and predicted values of GCV in about
78% of the data was less than 0.5 MJ/kg, and, in 96% of the data, the difference was
less than 1 MJ/kg.
• Exponential equations provided improved correlation coefficients in comparison to
linear equations. The best result was achieved using input set (c) with a correlation
coefficient of 0.999. The difference between actual and predicted values of GCV in
about 75% of the data was less than 0.5 MJ/kg, and, in 99% of the data, the
difference was less than 1 MJ/kg.
• The neuro-fuzzy modeling system improved prediction accuracy for input sets (a),
(b), and (c).
• The neuro-fuzzy rules that were designed using 3, 5, and 12 membership functions
can predict the GCV with R2 = 0.997, 0.999, and 0.999, respectively. They also
produced a deviation from target values of less than 0.5 MJ/kg for about 83, 97,
and 99% of data, respectively, and less than 1 MJ/kg for about 99, 100, and 100% of
data for input sets (a), (b), and (c), respectively.
• The GCV prediction precision achieved in the current work using neuro-fuzzy
systems has not been reported previously in the literature.

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 Artificial Neural Networks - Industrial and Control Engineering
Applications
Edited by Prof. Kenji Suzuki

ISBN 978-953-307-220-3
Hard cover, 478 pages
Publisher InTech
Published online 04, April, 2011
Published in print edition April, 2011

Artificial neural networks may probably be the single most successful technology in the last two decades which
has been widely used in a large variety of applications. The purpose of this book is to provide recent advances
of artificial neural networks in industrial and control engineering applications. The book begins with a review of
applications of artificial neural networks in textile industries. Particular applications in textile industries follow.
Parts continue with applications in materials science and industry such as material identification, and
estimation of material property and state, food industry such as meat, electric and power industry such as
batteries and power systems, mechanical engineering such as engines and machines, and control and robotic
engineering such as system control and identification, fault diagnosis systems, and robot manipulation. Thus,
this book will be a fundamental source of recent advances and applications of artificial neural networks in
industrial and control engineering areas. The target audience includes professors and students in engineering
schools, and researchers and engineers in industries.

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F. Rafezi, E. Jorjani and Sh. Karimi (2011). Adaptive Neuro-Fuzzy Inference System Prediction of Calorific
Value Based on the Analysis of U.S. Coals, Artificial Neural Networks - Industrial and Control Engineering
Applications, Prof. Kenji Suzuki (Ed.), ISBN: 978-953-307-220-3, InTech, Available from:
http://www.intechopen.com/books/artificial-neural-networks-industrial-and-control-engineering-
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