International Journal of Interactive Mobile Technologies (iJIM) – eISSN: 1865-7923 – Vol. 15, No. 07, 2021


Short Paper—Evaluation of Students Performance using Fuzzy Set Theory in Online Learning of Islamic...  

 

Evaluation of Students Performance using Fuzzy Set 

Theory in Online Learning of Islamic Finance Course 

https://doi.org/10.3991/ijim.v15i07.20191 

Nashirah Abu Bakar () 
Universiti Utara Malaysia, Kedah, Malaysia  

nashirah@uum.edu.my 

Sofian Rosbi 
Universiti Malaysia Perlis, Perlis, Malaysia  

Azizi Abu Bakar 
Universiti Utara Malaysia, Kedah, Malaysia  

Abstract—The objective of this study is to evaluate student performance us-

ing fuzzy set theory in Islamic Finance online course. This study focuses on se-

lecting best individual among 30 students that registered for Islamic Bank Man-

agement course. The variables that involved in this study are online quiz marks, 

online assignment marks and online self-learning time. The outcome of the 

fuzzy set analysis was compared with final examination data. The methodology 

of this study involving converting real data to fuzzy set, intersection calculation, 

decision analysis using maximizing approach. Result of fuzzy set shows the 

best individual score is 0.9. This student selected as best candidate for student 

performance in online learning with considering three variables namely online 

quizzes, online assignment and online self-learning hour. The comparison with 

final examination marks shows a good agreement with fuzzy set theory that 

concluded best individual from fuzzy set theory exhibits highest performance 

during final examination. The main finding of this study can help educators to 

predict the best performer in online learning class. In the same time, finding of 

this study can act as guideline to advise students in achieving their desired 

grade for online learning course. 

Keywords—Fuzzy Set Theory; Student Performance; Online Learning; Islamic 

Finance 

1 Introduction 

Fuzzy logic was introduced in 1965 by Lotfi Zadeh. He has introduced the idea of 

fuzzy truth values and the associated idea of a fuzzy logic based upon these fuzzy 

truth values [1,2]. The function of fuzzy logic is to handle the concept of partial truth, 

where the truth value may range between completely true and completely false. Fuzzy 

logic can be applied to function representation and function implementation and the 

results may have useful applications to logic design, pattern recognition, fuzzy logic 

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mailto:nashirah@uum.edu.my


Short Paper—Evaluation of Students Performance using Fuzzy Set Theory in Online Learning of Islamic...  

 

and related areas [3]. Fuzzy logic deals with the problems that have fuzziness or 

vagueness. In fuzzy set theory based on fuzzy logic a particular object has a degree of 

membership in a given set that may be anywhere in the range of 0 (completely not in 

the set) to 1 (completely in the set) [4, 5]. Besides that, fuzzy logic is a new way to 

program computers and appliances to mimic the imprecise way humans make deci-

sions [6-8].  

Fuzzy set theory allows the elements of set to have varying degrees of member-

ship, from a non-membership grade of 0 to a full membership of 100 per cent or grade 

1. This smooth gradation of values is what makes fuzzy logic match well with the 

vagueness and uncertainty typical of many real-world problems [9-13]. However, 

study that focus fuzzy logic method implemented in the area of education is still lack 

of researches. Therefore, the objective of this study is to evaluate student performance 

using fuzzy set theory in Islamic Finance subject. Nowadays, the use of digital tech-

nologies in the most different areas and contexts become increasing intertwined with 

social life [14-19]. This study chose the subject Islamic Bank Management that are 

use Massive Open Online Learning (MOOC) method. MOOC is open online learning 

course platform that provided variety of courses. Students need to register via website 

and get more information regarding the courses that they register. MOOC online 

learning become a good platform in providing online teaching and learning lesson in 

higher education of Malaysia [20]. The objective of online learning is to provide a 

user-friendly environment of teaching and learning. Besides that, online learning 

platform provided a low cost, flexible schedule and can communicate with many 

students worldwide.  

2 Literature Review 

Fuzzy logic method was applied in various research areas. Although fuzzy logic is 

being extensively used in electronics and mathematical sciences, it has found little 

application in the social sciences, especially on education areas. Therefore, fuzzy 

logic approach found as a new innovation method in education fields. Study that fo-

cuses on the applied science fields suggested that fuzzy logic method is very useful 

method for automated health monitoring strategies [21] and this method can improve 

the effectiveness of computation [22]. In the others study found that fuzzy logic is 

capable of handling uncertainties and improving decision-making processes even with 

insufficient information [23].  

Several studies have been found in education areas such the implementation of In-

telligent Tutoring Systems in teaching and learning process [24], used of fuzzy logic 

method in measuring the performance of students [25] and used fuzzy logic simula-

tion in examine either private higher education institution has the choice to adopt 

proactive or reactive strategy [26]. In recent decades there is a widespread interest 

used in the education system. With the continuous development of the internet, online 

learning was introduced in order to support the development of technology apply in 

education system. Malaysia was established Massive Open Online Courses (MOOCs) 

platform for online teaching and learning. MOOCs offered core modules and students 

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Short Paper—Evaluation of Students Performance using Fuzzy Set Theory in Online Learning of Islamic...  

 

from other public universities can participate in those courses through MOOCs online 

learning platform [27]. Online learning offers its learners access to education materi-

als at their own pace and time as well as lowering the average educational learning 

cost [28] and the achievement of online learning can be improved by providing in-

struction in a manner consistent with each student's learning style [29].  

3 Research Methodology 

The objective of this research is to evaluate the best student performance using 

fuzzy set theory. Fuzzy sets theory proposes to deal with unclear boundaries, repre-

senting vague concepts and working with linguistic variables. In this sense, fuzzy sets 

emerged as an alternative way to deal with uncertainties. Fuzzy set is a mathematical 

set with the property that an object can be a member of the set, not a member of the 

set, or any of a continuum of states of being a partial member of the set. Fuzzy set 

applied to education to test the variables that contributes to success condition in final 

examination for course in Islamic Finance course. Simple functions are used to build 

membership functions. Because this study is defining fuzzy concepts, using more 

complex functions does not add more precision. Fuzzy set is a mathematical model of 

vague qualitative or quantitative data, frequently generated by means of the natural 

language. The model is based on the generalization of the classical concepts of set and 

its characteristic function. With the implementation of fuzzy set in the education eval-

uation, it will help educators to assess students in more reliable and robust method.  

Fuzzy set theory is an extension of classical set theory where elements have degree 

of membership. Fuzzy logic uses the whole interval between zero (false) and one 

(true) to describe human reasoning. A fuzzy set is any set that allow its members to 

have different degree of membership, called membership function with interval [0,1]. 

A membership function for a fuzzy set A on the universe of discourse X is defined as 

: X
A


 → [0,1], where each element of X is mapped to a value between 0 and 1. This 

value, called membership value or degree of membership, quantifies the grade of 

membership of the element in X to the fuzzy set A. 

Membership functions allow us to graphically represent a fuzzy set. The x axis rep-

resents the universe of discourse, whereas the y axis represents the degrees of mem-

bership in the [0,1] interval. A fuzzy set is a pair 
( ),U m

 with U  and m is member-

ship function. The membership function is represented by 
 : 0,1m U →

 .The refer-

ence set represented by using U  for universe of discourse. The value of ( )
m x

 is 

considered as the grade of membership for variable x U  .The function A
m =

 is 

set as membership function for fuzzy set 
( ),A U m=

 . 

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Short Paper—Evaluation of Students Performance using Fuzzy Set Theory in Online Learning of Islamic...  

 

4 Result and Discussions 

The objective of this study is to evaluate the best candidate among learners of 

online course. This study selected 30 students that enrolled in Islamic Bank Manage-

ment course. The inputs variables are online quiz marks, online assignment marks and 

online self-learning hours. The benchmark variable is final examination marks. 

The sample of student data is taken from study period of 15 week in one semester. 

The students are tested using two informative assessment which are online quizzes 

and online assignments. There are three quizzes were performed and two assignments 

that carried out by students. The assignment is divided to individual assignment and 

group assignments. In completing the study, the researchers develop qualitative meas-

urement of self-dependence using self-online learning hours as indicator. Next, the 

final examination is performed by each student in assessing the understanding the 

course content by the end of semester of study period.  

In developing a reliable and robust assessment method for student in Islamic Fi-

nance course, the independent variable needs to be converted to fuzzy membership 

value using fuzzy set. This study implemented fuzzy set to categorized the perfor-

mance of student in final examination. The characteristics of students are difficult to 

analysis because the categorization of student performance is difficult to have clear 

boundaries between level of achievement among students. Therefore, this study im-

plemented fuzzy set analysis to convert the input variables to fuzzy value. 

Next, this study converted three input variables into fuzzy set. The first fuzzy set 

conversion is for online quiz marks using Equation (1). 

 

( )
0 ; 0 4

; 5 10
10

A

x

x x
x



 


= 
 



 (1) 

Next, the second input namely online assignment marks using Equation (2). In this 

membership function, the value of online quiz from 0 to 5 is set as zero. Then, value 

that larger than 5 is using trapezium function.  

 

( )
0 ; 0 5

; 6 10
10

B

x

x x
x



 


= 
 



 (2) 

Then, the third input namely online self-learning hours using Equation (3). In this 

membership function, the value of online self-learning hours from 0 to 6 is set as zero. 

Then, value that larger than 6 is using trapezium function.  

 

( )
0 ; 0 6

; 7 10
10

C

x

x x
x



 


= 
 



 (3) 

Next, this study performed intersection operation of three types of fuzzy sets from 

three variables namely online quiz marks, online assignment marks and online student 

learning hours. The intersection operation was performed using Equation (4). 

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Short Paper—Evaluation of Students Performance using Fuzzy Set Theory in Online Learning of Islamic...  

 

( ) ( ) ( ) ( ) ( )( )min , , ,M A B C A B Cx x x x x x U     = = 
 

(4) 

Next, this study performed maximization operation to evaluate best candidate 

among students using Equation (5). 

 

( )( ) ( )( )

( ) ( ) ( )( )( )

max
max max

max min , , ,

M A B C

A B C

X x x

x x x x U

 

  

 
= =

= 
 

(5) 

In Equation (5), this study performed union operation for fuzzy set for universe 

matrix. The function of union after the intersection is to search for best candidate that 

involved with online assessments namely online quiz, online assignment and online 

self-learning hours. The Equation (5) performed involving intersection and union 

operation to calculate the best potential candidate in online course of Islamic Finance. 

Next, this study performed union operation of fuzzy set to calculate best candidate 

for overall performance in online course of Islamic finance. From Table 1, the maxi-

mum value of intersection value is 0.9 for student with identification number 8. 

Then, this study comparing with examination marks to prove the finding in fuzzy 

set theory. The best performance of online learning is student number 8 with fuzzy 

value 0.9. The final examination marks for student number 8 is 97 percentages. There-

fore, the evaluation using fuzzy set is valid and reliable because the finding of fuzzy 

set is similar to outcome of final examination marks. The operation of fuzzy set in-

cluding the setting of input variables is valid in determining student performance in 

online course of Islamic finance. 

Table 1.  Intersection operation using Fuzzy set theory 

Student 

Number 

Online Quiz 

Marks 

Online  

Assignment 

Marks 

Online  

Self-Learning 

Hours 

Intersection 

Value 

Final  

Examination 

Marks 

1 0 0 0 0 50 

2 0 0 0 0 40 

3 0.6 0.7 0 0 63 

4 0.8 1.0 0.8 0.8 83 

5 0 0 0 0 43 

6 0 0 0 0 40 

7 0 0 0 0 40 

8 0.9 1.0 1.0 0.9 97 

9 0.7 0.8 0.7 0.7 73 

10 0 0 0 0 40 

11 0 0 0 0 47 

12 0.7 0.8 0.7 0.7 73 

13 0 0 0 0 47 

14 0 0 0 0 37 

15 0 0 0 0 33 

16 0.5 0.6 0 0 57 

17 0.8 0.7 0.7 0.7 73 

18 0 0 0 0 40 

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Short Paper—Evaluation of Students Performance using Fuzzy Set Theory in Online Learning of Islamic...  

 

19 0.6 0.8 0.7 0.6 70 

20 0.6 0.7 0.7 0.6 67 

21 0 0 0 0 40 

22 0.8 0.9 0.8 0.8 80 

23 0.7 0.8 0 0 70 

24 0.6 0.7 0 0 63 

25 0.5 0.7 0.7 0.5 63 

26 0.5 0.6 0 0 53 

27 0 0 0 0 40 

28 0 0 0 0 50 

29 0.7 0.8 0.7 0.7 73 

30 0.9 0.8 0.9 0.8 87 

5 Conclusion 

The main objective of this study is to examine student performance in online learn-

ing course using fuzzy logic approach. The online course that selected in this study is 

Islamic Bank Management. The sample number of this study is 30 students that par-

ticipate in online course. This study implemented fuzzy set theory using three input 

variables namely online quiz marks, online assignment marks and online self-learning 

hours. This study implemented union and intersection method for fuzzy set theory. 

Then, maximum value of intersection was calculated. Result shows student with fuzzy 

value 0.9 considered the best performance candidate for online learning class. Then 

evaluation with final examination marks indicates the agreement with fuzzy set theory 

analysis. This is proved that the fuzzy set theory is reliable and accurate in examine 

student performance for online learning courses. 

The novelty of this study is it will help educators in predicting student performance 

for online class. The problem with online class is less face-to-face interaction, there-

fore the prediction and advising student performance is quite difficult to manage by 

educators. With the implementation of fuzzy set analysis, it will help educators to 

predict and advise students about amount of marks that need to attaint to increase their 

performance during final examination of online learning.  

Further research can be extended to analysis another qualitative factor that contrib-

utes to success of student in their study. The suggestion of qualitative variables is 

motivation level, financial status and family support. This study can be carry out us-

ing survey instrument a research tool. The finding will help to compliment the fuzzy 

analysis. In the same time, this study can be carry out to more number of sample and 

involving more courses in online learning especially in Islamic finance education. 

6 Acknowledgement 

This research was supported by University Teaching and Learning Centre (UTLC) 

of Universiti Utara Malaysia (UUM) under Scholarship of Teaching and Learning 

Research Grant (SoTL). SO Code: 14148. 

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7 References 

[1] Zadeh, L.A. (1975). Fuzzy Logic and Approximate Reasoning. Synthese, 30, 407-428. 

https://doi.org/10.1007/bf00485052 

[2] Yager, R. (1983). Presupposition in Binary and Fuzzy Logics. Kybernetes, 12(2), 135-139. 

https://doi.org/10.1108/eb005649 

[3] Lee, E. and Chou, T. (1995). Fuzzy Threshold Functions and Applications. Kybernetes, 

24(7), 99-122. https://doi.org/10.1108/03684929510095711 

[4] Tsoukalas, L.H. and Uhrig, R.E. (1997). Fuzzy and Neural Approches in Engineering. 

John Wiley, NY.  

[5] Kumar, V. and Joshi, R.R. (2005). Hybrid Controller Based Intelligent Speed Control of 

Induction Motor. Journal of Theoretical and Applied Information Technology, 71-75. 

[6] Ray, K. and Chakraborty, A. (2011). A Fuzzy Version of Default Logic. International 

Journal of Intelligent Computing and Cybernetics, 4(1), 5-24. 

[7] Metaxiotis, K., Psarras, J. and Samouilidis, E. (2003). Integrating Fuzzy Logic into Deci-

sion Suppport Systems: Current Research and Future Prospects. Information Management 

& Computer Security, 11(2), 53-59. https://doi.org/10.1108/09685220310468592 

[8] Lee, E. (1996). Intelligent Factories Using Fuzzy Expert Systems. Kybernetes, 25(3), 51-

55. https://doi.org/10.1108/03684929610116428 

[9] Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338-53. 

[10] Beheshti, H. and Lollar, J. (2008). Fuzzy Logic and Performance Evaluation: Discussion 

and Application. International Journal of Productivity and Performance Management, 

57(3), 237-246. https://doi.org/10.1108/17410400810857248 

[11] Bannatyne, R. (1994). Development of Fuzzy Logic in Embedded Control. Sensor Review, 

14(3), 11-14. https://doi.org/10.1108/eum0000000004241 

[12] Stotts, L. and Kleiner, B. (1995). New Developments in Fuzzy Logic Computers. Industri-

al Management & Data Systems, 95(4), 22-27. https://doi.org/10.1108/02635579510086 

706a 

[13] Sobrino, A. (2013). Fuzzy Logic and Education: Teaching the Basics of Fuzzy Logic 

through an Example (by Way of Cycling). Education Sciences, 3(2), 75-97. https://doi. 

org/10.3390/educsci3020075 

[14] Albina Hashimova, Valeriy Prasolov, Vyacheslav Burlakov and Larisa Semenova (2020). 

Flexible and Contextual Cloud Applications in Mobile Learning. International Journal of 

Interactive Mobile Technologies, 14(21), 51-63. https://doi.org/10.3991/ijim.v14i21.18469 

[15] Douglas Rossi Ramos (2020). An Analysis of Subjectivation Processes Mediated 

by New Digital Technologies, International Journal of Emerging Technologies in 

Learning, 15(24), 15- 25. https://doi.org/10.3991/ijet.v15i24.19315 
[16] Eko Aprianto, Oikurema Purwati, Syafi’ul Anam (2020). Multimedia-Assisted Learning in 

a Flipped Classroom: A Case Study of Autonomous Learning on EFL University Students, 

International Journal of Emerging Technologies in Learning, 15(24), 114-127. https://doi. 

org/10.3991/ijet.v15i24.14017 

[17] Galina Volkovitckaia, Yuliya Tikhonova, Olga Kolosova (2020). Educational Experience 

in the Mobile Learning Environment: Consumer Behaviour Perspective, International 

Journal of Interactive Mobile Technologies, 14(21), 92-106. https://doi.org/10.3991/ijim. 

v14i21.18441 

[18] Korlan Zhampeissova, Irina Kosareva, Uliana Borisova, (2020). Collaborative Mobile 

Learning with Smartphones in Higher Education, International Journal of Interactive Mo-

bile Technologies, 14(21), 4-18. https://doi.org/10.3991/ijim.v14i21.18461 

208 http://www.i-jim.org

https://doi.org/10.1007/bf00485052
https://doi.org/10.1108/eb005649
https://doi.org/10.1108/03684929510095711
https://doi.org/10.1108/09685220310468592
https://doi.org/10.1108/03684929610116428
https://doi.org/10.1108/17410400810857248
https://doi.org/10.1108/eum0000000004241
https://doi.org/10.1108/02635579510086706a
https://doi.org/10.1108/02635579510086706a
https://doi.org/10.3390/educsci3020075
https://doi.org/10.3390/educsci3020075
https://doi.org/10.3991/ijim.v14i21.18469
https://doi.org/10.3991/ijet.v15i24.19315
https://doi.org/10.3991/ijet.v15i24.14017
https://doi.org/10.3991/ijet.v15i24.14017
https://doi.org/10.3991/ijim.v14i21.18441
https://doi.org/10.3991/ijim.v14i21.18441
https://doi.org/10.3991/ijim.v14i21.18461


Short Paper—Evaluation of Students Performance using Fuzzy Set Theory in Online Learning of Islamic...  

 

[19] Paola Cabrera-Solano (2020). The Use of Digital Portfolios to Enhance English as a For-

eign Language Speaking Skills in Higher Education, International Journal of Emerging 

Technologies in Learning, 15(24), 159-175. https://doi.org/10.3991/ijet.v15i24.15103 

[20] Abu Bakar, N., Rosbi, S. (2019). Framework of Outcome-Based-Education (OBE) for 

Massive Open Online Courses (MOOCs) in Islamic Finance Education. International 

Journal of Advanced Engineering Research and Science, 6(10), 247-253. https://doi.org/ 

10.22161/ijaers.610.38 

[21] Demirci, S., Hajiyev, C. and Schwenke, A. (2008). Fuzzy Logic‐based Automated Engine 

Health Monitoring for Commercial Aircraft. Aircraft Engineering and Aerospace Technol-

ogy, 80(5), 516-525. https://doi.org/10.1108/00022660810899883 

[22] Vimal, K. and Vinodh, S. (2013). Application of Artificial Neural Network for Fuzzy Log-

ic Based Leanness Assessment. Journal of Manufacturing Technology Management, 24(2), 

274-292. https://doi.org/10.1108/17410381311292340 

[23] Singh, M. and Soni, S. (2017). A Comprehensive Review of Fuzzy-based Clustering 

Techniques in Wireless Sensor Networks. Sensor Review, 37(3), 289-304. https://doi.org/ 

10.1108/sr-11-2016-0254 

[24] Machadoa, M.A.S., Moreira, T.D.R.G., Gomes, L.F.A.M., Caldeirad, A.M. and Santose, 

D.J. (2016). A Fuzzy Logic Application in Virtual Education. Procedia Computer Science, 

91, 9–26.  

[25] Semerci, C. (2004). The Influence of Fuzzy Logic Theory on Students’ Achievement. The 

Turkish Online Journal of Educational Technology, 3(2), 56-61. 

[26] Bourini, I.F. and Al-Bourini, F.A. (2017). Fuzzy Logic Approach to Simulate the Role of 

Academic Performance and Competition on Strategic Intention within Jordanian Higher 

Education Institutions”, International Journal of Business and Society, 18(3), 567-584. 

[27] Abu Bakar, N., Rosbi, S. and Abu Bakar, A. (2020). Robust Estimation of Student Perfor-

mance in Massive Open Online Course using Fuzzy Logic Approach. International Jour-

nal of Engineering Trends and Technology (IJETT) – Editor’s Issues, 143-152. https://doi. 

org/10.14445/22315381/cati2p223 

[28] Ahmad Fesol, S.F., Salam, S. and Shaarani, A.S. (2017). An Evaluation of Students’ Per-

ception on MOOC Instructional Design Elements. Journal of Applied Environmental and 

Biological Sciences, 7(10), 173-179. 

[29] Zapalska A. and Brozik, D. (2006). Learning Styles and Online Education. Campus-Wide 

Information Systems, 23(5), 325-335.  https://doi.org/10.1108/10650740610714080 

8 Authors 

Nashirah Abu Bakar is a senior lecturer in Islamic Business School, Universiti 

Utara Malaysia. Her main research interest is Islamic Corporate Finance and man-

agement. Dr. Nashirah already published 58 articles in reputable international jour-

nals. Dr. Nashirah serves as reviewers for eight international journals.  

Sofian Rosbi is a senior lecturer in Faculty of Applied and Human Sciences, Uni-

versiti Malaysia Perlis. His main research interest are structural equation modelling 

and optimization. He published 50 journal articles in reputable international journals.  

Azizi Abu Bakar is an Associate Professor in Islamic Business School, Universiti 

Utara Malaysia. He is an active researcher in Islamic Business Study.  

Article submitted 2020-12-01. Resubmitted 2021-02-08. Final acceptance 2021-02-08. Final version 
published as submitted by the authors. 

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https://doi.org/10.3991/ijet.v15i24.15103
https://doi.org/10.22161/ijaers.610.38
https://doi.org/10.22161/ijaers.610.38
https://doi.org/10.1108/00022660810899883
https://doi.org/10.1108/17410381311292340
https://doi.org/10.1108/sr-11-2016-0254
https://doi.org/10.1108/sr-11-2016-0254
https://doi.org/10.14445/22315381/cati2p223
https://doi.org/10.14445/22315381/cati2p223
https://doi.org/10.1108/10650740610714080