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Automatic development of fuzzy membership functions on hepatitis patients

data using particle swarm optimization (PSO)

Article · December 2015

DOI: 10.11113/jt.v77.6670

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 Jurnal
Full Paper
Teknologi
AUTOMATIC DEVELOPMENT OF FUZZY MEMBERSHIP Article history
Received
FUNCTIONS ON HEPATITIS PATIENTS DATA USING 27 April 2015
Received in revised form
PARTICLE SWARM OPTIMIZATION (PSO) 15 June 2015
Accepted
Candra Dewi*, Ratna Putri P.S, Indriati 25 November 2015

Informatics Department, Brawijaya University, Malang, *Corresponding author:

Indonesia dewi_candra@ub.ac.id

Abstract
Information about the status of disease (prognosis) for patients with hepatitis is important to determine the type of action to
stabilize and cure this disease. Among some system, fuzzy system is one of the methods that can be used to obtain this prognosis.
In the fuzzification process, the determination of the exact range of membership function will influence the calculation of
membership degree and of course will affect the final value of fuzzy system. This range and function can usually be formed using
intuition or by using an algorithm. In this paper, Particle Swarm Optimization (PSO) algorithm is implemented to form the triangular
membership functions in the case of patients with hepatitis. For testing process, this paper conducts four scenarios to find the
best combination of PSO parameter values . Based on the testing it was found that the best parameters to form a membership
function range for the hepatitis data is about 0.9, 0.1, 2, 2, 100, 500 for inertia max, inertia min, local ballast constant, global
weight constant, the number of particles, and maximum iterations respectively.

Keywords: Hepatitis, fuzzy system, membership function, particle swarm optimization

© 2015 Penerbit UTM Press. All rights reserved

1.0 INTRODUCTION diagnosis. Recently, the usage of fuzzy to improve the

performance of inference system is broadly used.
Hepatitis is a medical condition in which the liver Accordingly, determining the prognosis of some
becomes inflamed. This can be caused by many things, disease uses Fuzzy Inference System (FIS) has been
including viruses, bacteria, toxins as a result of liver done [7-9].
injury, and by the body's own immune system [1]. Based Fuzzy inference process the mapping of input to
on data from the World Health Organization (WHO), an output with the fuzzy logic. This mapping will provide the
estimated 3% of the world population has been basis for a decision or determination of the pattern. FIS
infected with viral hepatitis. Beside, about could be used without hybrid it with another method
approximately 170 million people have been [7]. But, to improve the performance, FIS is usually hybrid
chronically infected, and the number of Hepatitis with some algorithm. This hybrid can be developed to
patients grow 3-4 million people each year [2]. The pre-process the input data or to develop fuzzy rule [8-
prognosis is needed to determine the next treatment to 9].
stabilize and cure this disease. Prognosis is done by Beside the data and rule base, the shape and
determining the status of the patient's condition based boundaries of membership function are also a
on the test results [3]. Thus, the status of the disease is significant factor in determining the membership
very important to identify with the process of healing degrees of input parameter. However, there is often no
the patients with hepatitis. reference or expert who can describe this limit.
The prognosis can be done using the computer Therefore, the determination of membership function
instead of referring to the doctor. Some research on boundary would be very helpful if it can be done
computer field has been done to diagnose this disease automatically. This process can be done using intuition
[4-6]. Among the methods used, the expert system is a or learning algorithm [9-14].
method that performs inference based on the doctor’s

77:22 (2015) 115-119 | www.jurnalteknologi.utm.my | eISSN 2180–3722 |

116 Candra Dewi, Ratna Putri, Indriati / Jurnal Teknologi (Sciences & Engineering) 77:22 (2015) 115-119

Particle Swarm Optimization algorithm (PSO) is a accuracy is 73,55%. The Naïve Bayes method produces
learning algorithm that is widely used. PSO is a the best accuracy of 86.35%, with an average
stochastic search algorithm that uses a modeling accuracy of 83.05 % and the lowest accuracy of 66.94
problem through n - dimensional space to minimize or %. While the FDT (Fuzzy Decision Tree) method has the
maximize the objective function of a problem [13, 15]. S highest value of 78.15 % accuracy, average accuracy
study that compared the performance of PSO with of 75.39 % and lowest accuracy of 61.49 % [6].
clustering methods in data mining mentioned that in Therefore, this study used the PSO to seek the optimal
500 running times, PSO has the best accuracy of 89.86 limits of fuzzy membership functions of the hepatitis
% with a mean accuracy of 82.66 % and the lowest disease patient parameters.

where,
vik : speed of agent i at iteration k
2.0 EXPERIMENTAL
ω : weight function (inertia)
ci : weighting factor
2.1 Membership Function rand : random value between 0 and 1
sik : last position of agent i at iteration k
Fuzzy logic is used to overcome fuzziness phenomenon pbesti: the best position of agent i
and is modeled through the truth value that is taken gbest : the best value of pbest
from the succession scale [16]. The fuzzy set can be
characterized by using certain membership functions. The value of inertia is updated at every iteration using
This paper models a triangular membership function the following equation [19]:
formed by three values, i.e. a, b and c [17, 18]. The term
a and c in the triangular membership function describe
 
the end point, while b describes the peak point. This max min
   x iter (3)
function is represented using the following formula: max iter
mx
 0, x  a
 xa
 , a  x  b where,
Triangular ( x : a , b , c )  
ba (1)
cx
ωmax : initial value of inertia
 b  x  c ωmin : the last value inertia
cb
 itermax : maximum number of iterations
 0 x  c
iter : number of the last iteration

2.2 Particle Swarm Optimization The position of the agent will change at every iteration
according to the velocity changing and can be
Particle Swarm Optimization (PSO) algorithm is a calculated using the following equation [15]:
population based optimization technique to find the
optimal solutions using a population of particles
sik 1  sik  vik (4)
themselves. PSO is based on the idea that every particle where,
crowd is a solution of the solution space [13]. The sik 1 : the position of the current agent
pseudo code of PSO algorithm is described in
sik : prior agent position
Figure 1.
vik : the current speed
Start
for each particle i
initialize the position and velocity
end for 2.3 Encoding Scheme of Particle
while (not max iteration)
for each particle i
describe fitness value ωi
if ωi is better than current pbest
The process of encoding of particle is based on the
then pbest_fitness = ωi , pbest = sik parameter of input which is the hepatitis factors. The
if ωi is better than current gbest
then gbest_fitness = ωi , gbest = sik membership function of each linguistics variable uses
end for
for each particle i triangular membership function. The system process six
calculate vik
update vik parameters, i.e. bilirubin, ALK Phosphate, AST, Albumin
end for
update ω
and ProTime of which each has three linguistics
end while variable, and age parameter which has four linguistic
End
variable. Therefore, the total linguistic function being
Figure 1 Pseudo code of general PSO processed is 19.
The triangular membership function is formed by
three parameters, namely a, b, and c. Thus the total
The changing of velocity has been described in the dimension of each particle is 57 dimensions obtained
pseudo code can be represented by the following from 19 linguistic functions with each linguistic function
equation [15]: have 3 parameters. The encoding scheme of particle
k 1 for this paper is shown in Figure 2
(2)
k k k
vi  v i  c1 rand 1 x ( pbest i  s i )  c 2 rand 2 x ( gbest  s i )
117 Candra Dewi, Ratna Putri, Indriati / Jurnal Teknologi (Sciences & Engineering) 77:22 (2015) 115-119

a1 b1 c1 a... b... c... an bn cn 50 training data and 30 testing data. Attributes used in
this papers arenamely Age, bilirubin, ALK Phosphate,
Linguistic 1 Linguistic ... Linguistic n
AST, Albumin, and Protime.
The test is done to obtain the best combination of
Figure 2 Encoding scheme of particle
PSO parameter values that is measured based on
smallest MSE value. Testing is done with 4 scenarios. The
2.4 Developing Membership Function first scenario is done by changing the parameter value
of the maximum inertia (ωmax) and minimum inertia
The process of developing the membership functions (ωmin). The second scenario is done by changing the
using PSO is shown in Fig. 3. The input of the process is values of constant local weights (c1) and constant
maximum inertia (ωmax) and minimum inertia (ωmin), global weight (c2). The third scenario is done by
maximum iteration (itermax), weight factor (c1 , c2), and changing the value of particle number. The fourth
the number of particles (particle_num). The fitness scenario is done by changing the value of the
measurement is calculated based on the value of the maximum iteration. Each test was repeated 10 times
membership degree of the particle positions (s). Initial and was recorded the value of the parameter that
gbest value (the best value of the particle of the whole produces the smallest average error.
dimension) use the membership functions are
Table 1 Testing result of the combination of inertia
predefined and initial position value of the particle is
randomly taken from the training data value. Each Average MSE at ωmin
particle is designed in 3 dimensions, where each ωmax 0,1 0,2 0,3
dimension (v) represents a boundary point of each 0,7 0,003619 0,004398 0,006481
membership function. 0,8 0,002628 0,003738 0,004497
The results of modeling fuzzy membership function 0,9 0,002119 0,002512 0,002905
can be measured by the Mean Square Error (MSE). The
calculation of MSE shown in Equation (5) is used as a
fitness function for the implementation of the PSO The first scenario uses ωmaxvalue of 0.7, 0.8, 0.9 and
algorithm [16]. The smaller of MSE value generated, the ωmin value of 0.1, 0.2, 0.3. This test is done at value of c1
better of the results of experiments resulted. = 2, c2 = 2, the maximum iterations = 100, and the
 ( y k  yˆ k ) 2 number of particle = 10. The test result for the first
q
(5)
MSE  k 1 q scenario is shown in Table 1 where the greater the value
k 1 k
y 2
of ωmax and the smaller the value of ωmin used produce
where, increasingly smaller MSE value. The best results obtained
yk : target data value at ωmax = 0.9 and ωmin = 0.1 with an average MSE is
0.002119.
ŷk : estimated data value The second scenario conducted with c1 of 0.5, 1, 2
and c2 of 0.5, 1, 2. Each experiment use ωmax = 0.9, and
ωmin = 0.2, maximum iterations = 100, and the number
Start
of particles = 10. The testing results of this scenario are
Input : ωmax, ωmin,c1,c2, iter_max and particle_num shown in
initialize s, v, spbest, msepbest, cost, r1, r2,
gbest, msegbest Table 2.
create random value of s0
By comparing the average MSE values at each testing
v0=0, Gbest = initial_limit
while (msegbest > 0.01) or (i<= iter_max) value, it was found that the average value of MSE
For j=1 to particle_num obtained at the value of c1 = 2, and c2 = 2. This table
calculate MSE indicates that the best results obtained at balanced
check pbest search of the local and global particles.
create random value of r1, r2
calculate ω, vi+1, si+1
calculate gbest
Table 2 Testing result for the combination of weight factors
End for
End while Average MSE at c2
Ouput: new linguistic range c1 0,5 1 2
End. 0,5 0,005842 0,005455 0,004045
1 0,005581 0,005077 0,003647
Figure 3 The process of developing membership function using 2 0,003615 0,003132 0,002486
PSO

In the third scenario is used the number of particles

3.0 RESULTS AND DISCUSSION
between 10 to 200, ωmax = 0.9, ωmin = 0.1 , c1 = 2 , c2 =
2, and the maximum iteration = 100. The result of this
The data used in this paper is a hepatitis patient data
scenario is shown in Table 3. This table shows that the
from the UCI machine learning repository. Total records
experiment with the number of particles 200 produces
are 80 without missing values. The data are divided into
the smallest MSE that is 0.002645. The table also shows
118 Candra Dewi, Ratna Putri, Indriati / Jurnal Teknologi (Sciences & Engineering) 77:22 (2015) 115-119

that the decrease of MSE values on the number of Table 5 The limits value of each membership function
particles 100, 150, and 200 is not too significant.
Parameter Linguistic a b c
Table 3 Testing result for some particle number
Bilirubin Low 0,332 0,694 1,291
Particle Particle Bilirubin Normal 0,385 0,929 1,660
MSE MSE
Number Number
10 0,004565 100 0,002830 Bilirubin High 1,141 2,686 6,994
20 0,004145 150 0,002697 ALP Low 34,313 61,734 64,288
50 0,003756 200 0,002645
ALP Normal 45,569 95,807 157,626
ALP High 103,788 137,850 256,502
In the fourth scenario uses the maximum iterations of
Albumin Low 1,249 2,566 3,768
100, 200, and 500, ωmax = 0.9, ωmin= 0.1, c1 = 2, c2 = 2
and the number of particles = 100. The result of this Albumin Normal 3,133 3,599 5,015
scenario is shown in Table 4. This table shows that the Albumin High 4,706 5,323 6,970
smallest value of average MSE obtained at the number
SGOT Low 10,542 12,521 21,222
of iteration 700. However, a decrease in the value of
MSE at iteration of 500, 600, and 700 is not too SGOT Normal 12,465 28,638 51,101
significant. This does not mean that the less iteration will SGOT High 36,211 55,588 358,174
give the worse result. The testing shows that the number
of iteration has a great impact on the shifting value of ProTime Low 13,453 18,286 24,169
the inertia. The greater the value of the maximum ProTime Normal 16,615 22,051 38,368
iteration, the shift value of inertia is also getting smaller. ProTime High 22,613 52,588 131,779

Table 4 Testing result for some iteration number Age Child 6,473 14,935 22,943
Age Adolescent 14,134 20,794 29,590
Iteration
MSE Age Adult 17,317 35,090 54,372
Number
100 0,004771 Age Old 44,917 61,610 72,766
200 0,003590
500 0,003016
600 0,002916
700 0,002851 4.0 CONCLUSION

This paper implements PSO algorithm to obtain the

optimal end point and peak point of triangular
As shown at (3), the maximum number of iterations
associated with the particle velocity, in which the membership function automatically for hepatitis patient
greater the maximum iteration will result the smaller data. The data is used for testing consist of 80 data
inertia. Thus, these results suggest that the greater without missing values. These data is obtained from the
UCI machine learning repository. Based on the
decline of inertia will result in a better MSE values and
accuracy testing results that is measured using MSE, it
the resulting inertia value will go down faster. The
can be concluded that the combination of PSO
amount of inertia will affect the speed of the particle.
parameter that provide the best results are 0.9 and 0.1
The magnitude of velocity at the beginning of the
for the maximum and minimum inertia, 2 for local and
search will also affect the final result, because at high
global weights, 200 for the number of particles, and 700
speeds these particles can reach the global optimum
for maximum iterations. This optimal value of the PSO
value freely. This is due to the condition that the search
parameter can then be used to obtain the limits of the
process will be more focused on the local search area
triangular membership function of the hepatitis disease
at the smaller speed. The magnitude of the particle
data. The example of this limit value of each hepatitis
velocity that is move will be better if the particles move
parameter can be seen in Table 5. However, it needs
closer to the optimal value. However, when the particle
further testing to observe the most optimal number of
moves away from the optimal value, then the value of
testing data due to the limitation of data in this paper.
the resulting MSE will also be greater.
Furthermore, the use of the membership function of
Furthermore, the most optimal PSO parameter value
fuzzy inference system is needed to ensure whether it
is considered used in testing the limits of the
will offer the better accuracy or not.
membership functions. The values of the parameters
used is 0.9, 0.1, 2, 2, 100, 500 respectively for maximum
inertia, minimum inertia, weighting factor c1 and c2, the
number of particles, and the maximum iteration. The Acknowledgement
results of these tests are shown in Table 5. The values of
a, b and c indicate the end point and peak point of the I would like to thank to Program of Information
membership function. Technology and Computer Science, Brawijaya
University for the support to our research.
 119 Candra Dewi, Ratna Putri, Indriati / Jurnal Teknologi (Sciences & Engineering) 77:22 (2015) 115-119

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