Tuition Reduction Determination Using Fuzzy Tsukamoto

International Journal of Engineering Science Invention
ISSN (Online): 2319 – 6734, ISSN (Print): 2319 – 6726
www.ijesi.org ||Volume 5 Issue 9|| September 2016 || PP. 68-72
www.ijesi.org 68 | Page
Tuition Reduction Determination Using Fuzzy Tsukamoto
Mochammad Iswan Perangin-angin1
, Wirda Fitriani2
, Nova Mayasari3
,
Andysah Putera Utama Siahaan4
Faculty of Computer Science, Universitas Pembangunan Panca Budi, Jl. Jend. Gatot Subroto Km. 4,5 Sei
Sikambing, 20122, Medan, Sumatera Utara, Indonesia
Abstract: The process of determining cuts tuition for students are usually given with the same nominal. And in
this paper is the determination of the pieces tuition for students who are less able to be different, depending on
how much income parents and the number of children covered. For income parents who get discounted tuition
fee of IDR Rp.1,500,000 and for the number of children in these families also determine the number of pieces
obtained. Tsukamoto Fuzzy system is the model used in this paper. Each input variable is divided into three
membership functions. In this paper, Nine Tsukamoto Fuzzy model rules have been applied. The system also
provides a consequent change of parameters if the current parameter values to be changed. The smaller the
parent's income, the greater the pieces obtained. The more children insured the greater the college acquired
pieces.
Keywords: Fuzzy Logic, Membership Function, Tsukamoto
I. Introduction
Education is a knowledge that is transferred from one generation to future generations, or from one individual to
the group by doing research and teaching. Education can be done by itself or any of the guidance of others.
Education is often performed in educational institutions as an example: the University of North Sumatra,
Bandung Institute of Technology, University of Indonesia, and others. Higher education affects the ability of the
human individual, and also influential for countries to achieve economic growth rates in the country. Countries
that are poor or developing highly required for the faster development of education so that they can adopt the
technology that has been tested or tried by the rich countries.
The scholarship is a reduction, given a piece of fees previously deducted expenses for the purpose of reward or
prize. Scholarships may be awarded by educational institutions, government agencies, companies, and
foundations. The amount of the scholarship depends on how many prizes or rewards given. To support the
ability of students in the learning process, the universities provide discounted tuition directly with applicable
regulations. A student gets a scholarship based on GPA and the high economic level of the parents is low. The
process of awarding scholarships that have been running in the universities still provided with the same nominal
amount. This process is still not effective because there is also a student whose parents can afford and her high
GPA, scholarship the same with parents whose ability is low but high GPA students. Therefore, this study will
produce a system that will provide a total number of scholarship varies depending on the economic level of the
parents and the students GPA. The purpose of this study, not to reduce the nominal tuition fee cuts or degrading
students low economic level of the parents, but the goal of this research is to improve and support the
development of the country of Indonesia's education. The method used for this research is to use the model
method Tsukamoto FIS (Fuzzy Inference System).
A previous study using the model Tsukamoto FIS is the determination of the purchase price of a mobile phone,
forecasting, study program and etc. [1][5][11].Electrical machines are also calculated by fuzzy system [9].
Determination of the risk of disease, and others. A researcher used Tsukamoto FIS models for each parameter
consequent to the rules if then shaped and represented by a fuzzy set that as a stand-alone membership function
(monotone) and the results of the inference to any rules which are defined as the crisp value.The research has
two variables such as the economic level of parents and GPA. Each of them consists of two membership
functions respectively. The taking of two variable and membership function will issue a nominal output cuts
tuition fees to be received by the students.
II. Theories
Fuzzy logic is a proper way to map an input space into a space of output [3][4][6]. Fuzzy is used to adjust the
solution or rank the problem into sequence [2]. The reasons for using fuzzy logic, among others; The concept of
fuzzy logic is more easily understood and fuzzy logic, if there are incorrect data, have a tolerance. In general,
fuzzy logic system has four elements:
1. The basic rule that contains the rules derived from the experts.
2. A decision-making mechanism in which the expert took the decision to apply the knowledge they have.

3. The process of fuzzification that changes the amount crisp into the magnitude fuzzy.
4. The process of defuzzification, is the reverse of the process that is changing the magnitude result of the
fuzzy inference engine, be assertive magnitude (crisp).
In the implementation of the system, fuzzy has three parts, such as fuzzification, fuzzy inference, and
defuzzification [7][8][10]. However, the process here is optimal defuzzification i.e., when the conclusion is
already meeting or as expected, then no defuzzification process. However, if a conclusion has not met the
defuzzification process is still being done.Fuzzy logic membership functions consisting of boundary value data
input and data output values. The definition of the membership function is a graph that there are points of
boundary value data input into a valuable membership value between 0 and 1.
In the graph membership functions, there are three sections, such as core, support, and boundary. The part cores
or core part graph represent the complete area of the entire set of fuzzy, so if expressed in a function where x is a
member of the set μ (x) = 1. Furthermore, the second part is the support, the support or the support of a part
graph representing the region with a membership value of the fuzzy set is not 0, then if expressed in a function
where x is a member of the set μ (x)> 0. And lastly, part of boundary or limit. Boundary in the graph
membership functions declared the value of the minimum and maximum limits of the fuzzy set, then it if
expressed in a function where x is a member of the set is 0 <μ (x)> 1.
Tsukamoto Fuzzy method is one method of Fuzzy Inference System, system decision makers. In the method of
using the Tsukamoto fuzzy rules or rules shaped "causation" or "if-then". The calculation method of fuzzy
Tsukamoto, the first rule is formed representing the fuzzy set, then calculate the degree of membership by the
rules that have been created. After getting a degree of membership value, look for the value of the predicate
alpha (α) by finding the minimum value of the value of the degree of membership. The final step, look for the
value output is crisp values (z) called defuzzification process, which is expressed in the equation 1.
Z = (1)
Where α = alpha predicate (the minimum value of the degree of membership is), Zi = crisp values obtained from
the formula degree of membership of fuzzy sets which is the value of output, and Z = defuzzification average
centralized (Center Average Defuzzyfier).
III. Design And Implementation
The method used is a model FIS Tsukamoto, membership functions used are linear, i.e., the triangle and
trapezium. Every each of the variable input is divided into two membership functions. First to economic levels
is divided into two functions both for GPA membership and is divided into two membership functions. Of each
variable give each of the two membership functions are demonstrated in figure 1.
Rendah Tinggi
1500 2500
Tingkat Ekonomi( Dalam
Ribuan)
0
Fig. 1 Economics Level Membership Function
Frendah (EL) =
Ftinggi (EL) =

Buruk Baik
2.75 3.25
IPK (Index Prestasi
Kumulatif)
0
Fig.2GPA Membership Function
Fburuk (GPA) =
Fbaik (GPA) =
Sedikit Banyak
150 500 Potongan Biaya (Ribuan)0
Fig. 3 Tuition Reduction Membership Function
Fsedikit (TR) =
Fbanyak (TR) =
where:
EL : Economy Level
GPA : Grade Point Average
TR : Tuition Reduction
Table I Fuzzy Rules
Aturan ke- Aturan
Tingkat Ekonomi IPK Potongan Biaya
1 Rendah Tinggi Banyak
2 Tinggi Tinggi Banyak
3 Tinggi Rendah Sedikit
4 Rendah Rendah Sedikit

From Table 1, it is already obtained the degree of membership of the output of each rule and to see the detail of
the rules of fuzzy logic are described in Table 1.0. Having obtained the number of rules by using models
Tsukamoto FIS acquired two (2) rule using the AND operator. After searching the degree of membership of the
output of each rule created or generated from the combined level of parents and the GPA, then the next step is to
look for the cost cuts output value of each rule listed in Table 1.0. In the search for cost cuts output value, using
the following equation:
TR = (2)
where :
w : output of inference
z : degree of the output membership
The input limit of the economic level variable is Rp. 1,500,000 to Rp. 2,000,000 and variable GPA is 2.75 up to
3.25. If there are students, who are below the economic level of Rp. 1,500,000 then they are put into the lower
limit value of the economic level, while if his economy rate of more than Rp. 2,500,000, the level of economic
is added to upper limit economic level. Restrictions on variable input GPA, cannot be below the 2.75 because if
below 2.75 there is no requirement to obtain a reduced fee. But if the GPA is more than 3.25, the value of its
variable GPA entered the upper limit value of the GPA.
IV. Evaluation
The students get a discount on tuition fees this study assumed that get a piece of the fee is a student at a rating of
the first five in class in every subject or area of expertise. So, to the value of the variable GPA below 2.75 will
not appear because the GPA is ranked into the first five who is GPA> 3.00. From the system that researchers do,
obtained GPA vary and economic level also vary from every student who was ranked top five in class expertise,
and computer engineering is expected. The institution can provide discounted tuition fairly and spur directly to
students to get a high GPA and rank in the class in their respective fields.
Table II Earlier Tuition Reduction
No. Name Economy Level GPA Tuition Reduction
1 Putri 1.700.000 3.23 500.000
2 Ayu 1.850.000 3.20 500.000
3 Sindi 1.850.000 3.17 500.000
4 Bobby 1.700.000 3.12 500.000
5 Marisa 2.250.00 3.08 500.000
Table III Fuzzy tuition reduction
No. Name Economy Level GPA Tuition Reduction Fuzzy Tuition Reduction
1 Putri 1.700.000 3.23 500.000 397.750
2 Ayu 1.850.000 3.20 500.000 361.458
3 Sindi 1.850.000 3.17 500.000 365.780
4 Bobby 1.700.000 3.12 500.000 387.414
5 Marisa 2.250.000 3.08 500.000 386.955
Table 2 shows the cost cuts that have been made by instituion. The calculations are still the same for the
distribution of flat and there is no difference in cost cuts obtained. With pieces such as tables, a bit difficult to
encourage students economic level parents a little to study hard for their pieces acquired equal value and to the
economic level of the parents a lot can be pushed higher again on the intention of learning for many students
whose parents have high economic level lazy to learn.
In Table 3, showing different cuts costs because it is calculated using the FIS models Tsukamoto based on two
variables, the level of economic and GPA that each variable has a lower limit and upper limit respectively. For
the discounted cost also has an upper limit and a lower limit value in the process of formulating a reduced fee
for students who get it.
V. Conclusion
By comparing the reduction between Table 2 and Table 3, it can be concluded that the method of determining
the pieces of tuition fees already running before they are less fair and less clear on what students get discounted
cost because the previous system already runs still use one variable to determine the cost cuts.Function FIS
models Tsukamoto aims to provide value discounted cost varies according to the specified variable. If a student

has a high GPA and low economic level, he gains more reduction but for students who [1]have a high GPA and
economic level high gets a reduction too but not as much as that obtained by the previous students.
Variable determination for cost cuts proposed by the researchers, there are two, namely: the level of economic
and GPA (Grade Point Index), but can also be added for further variables to get the value discounted cost more
focused. Previously, the determination of cost cuts, there is no comparison of variables and still determined by
GPA (Grade Point Index) alone. For that study is done to determine the pieces that were not already have
become variables, have variables and get a piece of good cost and fair. In this study may resolve the problem on
cost cuts in sevel instituions by using two variables, but this research also has drawbacks.
In this study, there are also some disadvantages and advantages in the process of cutting costs. The disadvantage
is not too noticeable difference cuts costs because of the difference of each student is still about IDR Rp.1,000 -
15,000. As for the advantages of this research is the value of the discounted cost of not using Tsukamoto is
greater than the value that is generated by using Tsukamoto. Therefore, it is suggested to institution to add up
the number of students who get a discounted cost of the previous five students to 10 students. So that students in
instution have a good education because it encouraged the discounted cost of the course.
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