FUZZY ALGORITHM FOR SELECTING STUDENTS FROM LOW INCOME

FAMILY

1Zamali, T.,

2Ling-Ling, U,

3Nasrah, N. &

4Tammie, S.

1,2,3,4Department of Mathematics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi

MARA, Sabah Branch, Locked Bag 71, 88997 Kota Kinabalu, Sabah, Malaysia 1zamalihj@sabah.uitm.edu.my, 2ungli720@sabah.uitm.edu.my ,

3nasra040@sabah.uitm.edu.my, &

4tammi023@sabah.uitm.edu.my

ABSTRACT

This research introduces a new algorithm to select

students from low income family using fuzzy

approach. It focuses on the refinement and

modification of certain variables in selection process.

The technique employs the intersection of fuzzy

goals and constraints concept in judgmental process.

The initial input was directly obtained based on the

multi-person opinion and experiences. A numerical

example was fully utilized to demonstrate the

applicability of the proposed method. It shows that

the proposed approach has successful dealt with the

uncertainty of the input datasets and beneficially for

student’s selection purposes. As a result, the decision

for selection process can be derived successfully in a

simple manner and the proposed algorithm offers a

new dimension technique as well from the tradition

point of views. Finally, our new refinement and

modification of the variables can derive more precise

in terms of representing the actual situation.

KEYWORDS

Fuzzy algorithm, fuzzy goals and constraints,

mengubah destini anak bangsa (MDAB).

1.0 INTRODUCTION

Admission to higher education system in

Malaysia mainly is based on the applicants’

academic performance or score. This has caused

disadvantages to students from low income

family, as they have limited access to better

education assistance such as tuition classes, extra

courseware and internet references, compared to

their peers from better wealth of family.

Therefore, this group of students is unable to

perform as good as their friends too. Poverty is

part of the explanation. Numerous studies have

been made; found that most rural community is

unable to provide well-education assistance to

their children [1]. If this continues on, the

country will face a group of people whose socio

economy will not be improved for many years.

According to the statistic, Sabah has the

highest poverty rate compared to the other states

in Malaysia [2-5]. In fact Sabah has lower score

in big examinations such as UPSR, PMR, SPM

or STPM. Due to this problem, a greater number

of the younger generations fail to pursue their

studies to higher level.

An initiative called Mengubah Destini

Anak Bangsa (MDAB) is designed to cater the so

called disadvantage group of student, by

considering their family background as one of

the criteria in the hunt for a seat into UiTM. A

group of researchers from UiTM Sabah Branch

has studied numerous algorithms to be

implemented in selecting students into the

programme, and decided to further investigate on

fuzzy algorithm in the selection process.

Fuzzy algorithm is chosen mainly due to

its robustness in dealing with ill-defined or

complex problems. Fuzzy logic is a sub

component of Artificial Intelligence field, has

tremendously evolved over the years.

Researchers from different fields, namely from

the manufacturing, health, automotive and

management see the importance of fuzzy

algorithm in many problem solving. Fuzzy

algorithm is used in pattern clustering [6-8],

optimization of solution [9, 10] and estimation

[11, 12].

Based on the literature, existing research

very seldom explores the intersection fuzzy goal,

the constraints approach and utilizes as an

evaluation tools. Moreover, since the nature of

the criteria or attributes evaluated is uncertainty

and the lack of information, this proposed

approach is believed to be more efficient in daily

evaluation procedures. Thus, the objectives of

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this research are; i) to propose the intersection

fuzzy goal and the constraints concept for

MDAB students selection process, and ii) to

design and developed the user friendly fuzzy

algorithm for MDAB students selection

purposes. To do so, the structure of this paper as

follows; Section 2 provides the problem

identification based on the real situation; Section

3 briefly describe the background of the

proposed method; Section 4 focuses on the

applicability of the proposed method using

numerical example, and finally the brief

discussion and conclusions were pointed out.

2.0 PROBLEM IDENTIFICATION

Mengubah Destini Anak Bangsa (MDAB) is a

programme that introduced by UiTM to give the

opportunity to Malay and Bumiputera youths

from low income family to further their studies

in pre-Diploma level (i.e., Pre-

Diploma(Commerce) and Pre-Diploma(Science))

offered by UiTM. After more than 3 years

introduced, this programme gets a lot of positive

responses but then due to the drastic phenomena

have causes the admission procedure become

more complicated and took a longer time in

order to process their application. Recent

selection process practiced is inadequate

considering the deeper elements of each criteria

selection concern. For instance, if two applicants

with the similar academic qualification apply for

MDAB programme from difference background

family income, say RM500 and RM1800,

respectively. The existing system failing to

discriminate efficiently which applicant should

be given priority. This problem occurs in other

criteria as well such as the number of credit

obtained, number of sibling, etc. Actually, this

discriminate element becoming more significant

in most cases due to UiTM Sabah has faced

financial constraints as well as limited space

available to be offered. Therefore, based on this

phenomenon and the inadequate comprehensive

procedures existing, we proposed the new

algorithm that believed can dealing with more

efficient to discriminate of above lacking.

Moreover, the proposed method is ease and more

precise to measures all criteria situation in

selection process. In addition, we not solely

proposed a new approach but in the same time

develop user friendly algorithm for UiTM

management users. As a result, the both

proposed method can improve the existing

selection process and beneficial to UiTM,

particularly for MDAB student’s selection

decision.

3.0 METHODOLOGY AND THE

PROPOSED ALGORITHM

3.1 The Background Theory and

Methodology

In this section we discuss briefly the similar

method which has been proposed by [13].

Consider a simple decision-making model

consisting of a goal described by a fuzzy set G

with membership function µG(x). A constraint

described by a fuzzy set K with membership

function µK(x) where x is an element of the crisp

set of alternatives Lalt.. Hence, the decision is a

fuzzy set D with membership function µD(x),

expressed as intersection of G and K.

D = G K = {(x, µD(x)/x [d1,d2], µD(x) [0,

h ≤ 1]}

(1)

Where [d1,d2] is the crisp set of selection from

the set of alternatives (Lalt) µD(x) is the degree to

which any x [d1,d2] belongs to the decision D

Here, the operation intersection of A and B

denoted as A B is defined by

µA B(x) = min(µA(x), µB(x)), x U;

(2)

if µA(x)= a1 < a2 = µB(x), min(a1,a2) = a1

Using the membership functions and operation

intersection –(2), formula –(1) gives

µD(x) = min(µG(x), µK(x)), x Lalt

(3)

Hence, the goal and constraint in –(1) can be

formally interchanged as follows:

D = G K = K D

(4)

To obtain [d1,d2] with the highest degree of

membership in the set D, the maximization

decision is expressed by

Xmax = {x/max µD(x)= max min(µG(x), µK(x))}

(5)

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Thus, formula –(1), -(3) & -(4) have been

generalized with many goals and constraints.

For goals Gi, i = 1,2,3, …,n, and constraints Kj, j

= 1,2,3, …,m, the decision is given by

D = G1 G2 G3 … Gn K1 K2 K3 ….

Km

(6)

The membership function of D is

µD(x)= min(µG1(x), …, µGm(x), µk1(x), …,

µkm(x))

and the maximization decision is given by

Xmax = {x/µD(x) is max}

(7)

Based on Eq (7), we can identify the best n-

options by descending order. For instance, if we

have n-alternatives,

XD = {x/µD1(x) > x/µD2(x), > x/µD3(x), >, …, >

x/µDn1(x) > x/µDn(x)}

(8)

Where the symbol ‘>’ means ‘is preferred or

superior to’.

Generally, the summarizing of above selection

decision process shown on Figure 1

Goal G

Constraint K

Alternative Aalt

Intersection

G K

Fuzzy decision

D

Maximizing

decision

Xmax

Figure 1: Process of decision-making by intersection

operator

Since the nature of selection process for MDAB

students involved the multiple objectives, here

we construct the membership functions for three

objectives; i) G1, parents gross monthly income

(PI) must less than RM3000, ii) G2c; obtain at

least three credit (CR) in Sijil Pelajaran Malaysia

(SPM) results including Bahasa Malaysia

subject, or G2s; obtain at least three credit (CR)

in SPM results including Bahasa Malaysia and

Mathematics subjects, plus at least passed one of

the pure science subject, and iii) G3, number of

sibling (NS), respectively, given as follows:

x

x

x

xPI 3000;

30001

3000;0

)(~

-(9)

10;1

105;10

53;5

2

)(~

x

xx

xx

xCR

(10)

6;1

63;75.0

31;5.0

)(~

x

x

x

xNS

(11)

Also the committee has a main constraint, the

candidates offered should be Bumiputera and

he/she must provide the complete necessary

documents during their application. Here, we

categorize the completeness of the applicants’

document as shown in Table 1.

Identify the best n-options by

descending order

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Table 1: The four difference definitions of

document status

Membership

values

Description

0

0.3

0.7

If the candidate is Bumiputera but not

provide all necessary documents

(DS1)(i.e., identification card, birth of

certificate, and pay slip/certified monthly

income statement for applicant and their

parent)

If the candidate is Bumiputera but not

provide both relevant documents (DS2)

(i.e., identification card or birth of

certificate and pay slip/certified monthly

income statement for applicant and their

parent)

If the candidate is Bumiputera but not

provide parent’s pay slip/certified

monthly income statement (DS3).

1 If the candidates is Bumiputera with

complete all necessary documents (DS4)

3.2 Our Proposed Algorithm

In this research we design the convenient

algorithm based on five steps given as follows:

i. Design the algorithm based on the

method that we have proposed in sub-

section 3.1.

ii. Illustrate and synthesis the appropriate

flow-chart thoroughly as respect to above

algorithm

iii. Design the step-by-step procedures base

on the objectives and constraints that we

have proposed earlier.

iv. Testing the proposed algorithm that we

have designed the complete procedures

using dummy variables and hypothetical

example

Thus, the next section (Section 4) we will show

the comprehensive numerical example for

application purposes.

4.0 A NUMERICAL EXAMPLE

To show our propose algorithm has applicable

and suitable for the issues concern, here we

provide an numerical example with some

modification and definition refinement from

[13].

Every semester MDAB committee of

UiTM Sabah received more than 1000

applications from low income family candidates

especially from the rural area a cross state of

Sabah. Since UiTM Sabah has faced financial

constraint and limited space available to be

offered, the committee make an initial screening

and short listed for qualified candidates (i.e., A1,

A2, A3, …,An) for Pre-Diploma (Commerce)

programmes. UiTM Sabah has three specific

objectives (goals) which the candidates have to

satisfy: i) G1, parents gross monthly income (PI)

must less than RM3000, ii) G2c; obtain at least

three credit (CR) in SPM results including

Bahasa Malaysia subject, and iii) G3, number of

sibling (NS). Also the committee has a main

constraint, the candidates offered should be

Bumiputera and he/she must provide the

complete necessary documents during their

application. Thus, the committee was

constructing the membership function as given in

Eq-(8) – (10), respectively. For the constraint,

the committee also decided to categorize the

status of documents of Bumiputera using three

difference scores (i.e., membership values)

depend on the completeness of documents

provided during the application submission,

given in Table 1. For calculation example

purposes, say five candidates applied as shown

in Table 2. Here, we substitute three objectives

(i.e., G1, G2, G3) from raw datasets in Table 2

using the three memberships function

respectively. Meanwhile, for constraint (K1), we

derive the membership values based on Table 1

definition. Then, we obtain all membership

values as shown in last row (Table 3):

Table 2: The raw information for three objective attributes

and one constraint

Applicants A1 A2 A3 A4 A5

G1: Income (in

RM)

1800 1000 700 2780 550

G2: Number of

credit obtained

3 5 4 3 5

G3: Number of

sibling

3 5 4 7 7

K1: Document

status

DS4 DS1 DS2 DS3 DS4

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Table 3: The membership values (i.e., the scores) derived

from Table 2

Applicants A1 A2 A3 A4 A5

G1: Income (RM) 0.4 0.67 0.77 0.07 0.82

G2: Number of

credit obtained

0.2 0.5 0.4 0.2 0.5

G3: Number of

sibling

0.5 0.75 0.75 1 1

K1: Document

status

1 0 0.3 0.7 1

Based on membership values in Table 3 above,

we can write as follows:

G1 = {(A1, 0.4), (A2, 0.67), (A3, 0.77), (A4, 0.07),

(A5, 0.82)}

G2 = {(A1, 0.2), (A2, 0.5), (A3, 0.4), (A4, 0.2),

(A5, 0.5)}

G3 = {(A1, 0.5), (A2, 0.75), (A3, 0.75), (A4, 1),

(A5, 1)}

And

K1 = {(A1,1), (A2, 0), (A3, 0.3), (A4, 0.7), (A5,1)}

From Eq.-(6), we have

µD(x) = min (µG1(x), …, µGm(x), µk1(x), …,

µkm(x))

= {(A1, 0.2), (A2, 0), (A3, 0.4), (A4, 0.07),

(A5, 0.5)}

And from Eq.-(7) we can obtain as

XD = Maks{(A1, 0.2), (A2, 0), (A3, 0.4), (A4,

0.07), (A5, 0.5)} or

XD = {x/µD1(x) > x/µD2(x), > x/µD3(x), >, …, >

x/µDn1(x) > x/µDn(x)}

From above result it shows that the applicant A5

is the best or the most preferred applicants as

compared to the rest due to highest score of the

membership values. Finally, we can identify the

most five superior options using Eq-(8) as

follows:

XD = {(A5, 0.5) > (A3,04) > (A1, 0.2) > (A4, 0.07)

> (A2, 0)}

Thus we have,

A5 = 0.5 > A3 = 0.4 > A1= 0.2 > A4 = 0.07 > A2

= 0

where the symbol ‘>’ means ‘is preferred or

superior to’.

It is apparent that A5 is the best candidates,

followed by A3, A1, A4 and lastly is A2

candidates.

5.0 DISCUSSION AND CONCLUSIONS

In this research the refinement and modification

from [13] have been made for the following

variables; i) the number of credit (NC)

membership functions obtained by candidates

(see Eq. (9 – 11)) and, ii) the definition of

documents status in Table 1 from three to four

categories. It clearly seen that the new definition

that we have modified are meaningful and more

represented the actual situation. In addition,

previous research did not consider at all the

qualification criteria from Pre-Diploma (Science)

applicants which require a minimum credit in

Mathematics and at least passed one of the pure

science subject (i.e., Physic, Chemistry, Biology

or Sains Tambahan) in SPM level. Also, in this

research we rectify or improvise the second

objective into G2s; obtain at least three credits

(CR) in SPM results including Bahasa Malaysia

and Mathematics subjects plus at least passed

one pure science subjects.

Thus, in this research we have proposed

the intersection of fuzzy goals and constraints

concept in judgmental process. Since the

evaluation generally involve uncertainty, it is

important to incorporate the fuzzy approach to

derive precise results in any proposed method.

From numerical example, it can be clearly seen

that the intersection between fuzzy goal and

constraints is beneficial in terms of evaluation

perspective. Also, we provide some

straightforward procedures by constructing the

relevant membership functions to derive the

membership values in the range of [0, 1], which

is extremely significant in fuzzy environment. In

addition, we also develop the user friendly

algorithm for UiTM management users that can

utilize directly from our proposed method,

particularly for MDAB students’ selection

purposes.

Therefore, based on the algorithm and the

new refinement that we have proposed, it fulfil

the following significant advantages; i) the

algorithm is successfully dealing with the

uncertainty of the initial information/datasets

which was rarely explored previously,

particularly in students selection process, ii) the

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modification of the memberships function of

both parent gross monthly income and number of

credits obtained will representing the actual

situation. As a result, it gives an alternative

judgment and allowed the committee to judge

beyond the traditional method using the existing

system available, and iii) it offers more

convenient and confident decision process by

equipping the convenient step-by-step

procedures so that the users can utilize and

applies directly the concept from our proposed

algorithm.

6.0 ACKNOWLEDGEMENTS

The authors acknowledge University Teknologi

MARA (Sabah Branch) and Research

Management Institute (RMI), UiTM for

supporting this research by Research Excellent

Grant (Grant No. 500-

UiTMKSH(PJI/UPP.5/1)(1/2013).

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