Evaluation of student performance in laboratory applications using fuzzy logic

Abstract

Educational systems typically employ classical methods of performance evaluation. In this system, student performance depends on exam results and is evaluated only as success or failure. Alternative, non-classical performance evaluation methods may be used, such as fuzzy logic, a mathematical technique of set-theory that can be applied to many forms of decision-making including research on engineering and artificial intelligence.This study proposes a new performance evaluation method based on fuzzy logic systems. Student performance of Control Technique Laboratory in Marmara University Technical Education Faculty, Electricity Education Department, was carried out with fuzzy logic and it was compared with classical evaluating method. Study samples are notes which twenty students took the control technique laboratory course.Evaluation of the results showed variations between the classical and fuzzy logic methods. Although performance evaluation using fuzzy logic is complicated and requires additional software, it provides some evaluation advantages. Fuzzy logic evaluation is flexible and provides many evaluation options, while the classical method adheres to constant mathematical calculation. At the application stage, the teacher responsible for the laboratory application can edit the ranges of membership functions and rules, permitting non-homogenous but flexible and objective performance evaluation.

Full text

1877-0428 © 2010 Published by Elsevier Ltd.
doi:10.1016/j.sbspro.2010.03.124
Procedia Social and Behavioral Sciences 2 (2010) 902–909
A
vailable online at www.sciencedirect.com
WCES-2010
Evaluation of student performance in laboratory applications using
fuzzy logic
Gokhan Gokmen
a
*, Tahir Çetin Akinci
b
, Mehmet Tektaú
c
, Nevzat Onat
c
,
Gokhan Kocyigit
a
, Necla Tektaú
c
a
Marmara University, Faculty of Technical Education, Department of Electrical Education, Kadikoy, Istanbul34722, Turkey.
b
KÕrlareli University, Faculty of Technical Education, Department of Electrical Education, KavakiÕ, KÕrklareli Turkey.
c
Marmara University, Vocational School of Technical Studies, Kadikoy, Istanbul 34722, Turkey.
Received October 8, 2009; revised December 17, 2009; accepted January 5, 2010
Abstract
Educational systems typically employ classical methods of performance evaluation. In this system, student performance depends
on exam results and is evaluated only as success or failure. Alternative, non-classical performance evaluation methods may be
used, such as fuzzy logic, a mathematical technique of set-theory that can be applied to many forms of decision-making including
research on engineering and artificial intelligence.
This study proposes a new performance evaluation method based on fuzzy logic systems. Student performance of Control
Technique Laboratory in Marmara University Technical Education Faculty, Electricity Education Department, was carried out
with fuzzy logic and it was compared with classical evaluating method. Study samples are notes which twenty students took the
control technique laboratory course.
Evaluation of the results showed variations between the classical and fuzzy logic methods. Although performance evaluation
using fuzzy logic is complicated and requires additional software, it provides some evaluation advantages. Fuzzy logic evaluation
is flexible and provides many evaluation options, while the classical method adheres to constant mathematical calculation. At the
application stage, the teacher responsible for the laboratory application can edit the ranges of membership functions and rules,
permitting non-homogenous but flexible and objective performance evaluation.
© 2010 Elsevier Ltd. All rights reserved.
Keywords: Performance; evaluation; exam; fuzzy logic; laboratory application.
1. Introduction
Measurement of educational performance is usually expressed numerically, based on examination results.
Classical evaluation therefore consists of a judgment based on the comparison of student results against established
performance-criteria. Measurement and evaluating are inspirable and important parts of the educational process.
Evaluating student exam scores is performed using various methods.
* Gokhan Gokmen. Tel.: +90-216-3365770-265 ; fax: +90-216-337-9789.
E-mail address: gokhang@marmara.edu.tr.

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Using current, classical evaluation systems, educational success or failure is therefore based on separation via
certain scoring thresholds. For instance, in laboratory applications, a student scoring above 50 is evaluated as
successful, but is otherwise unsuccessful. However, in laboratory applications, evaluation of student performance
based on rigid scoring criteria may not be appropriate.
Fuzzy logic theory emerged during the twentieth century and, by the beginning of the twenty-first century, was
predicted to be applied extensively in many fields (Altrock, 1995). One of the applications of the fuzzy logic theory
is the measurement and evaluation in education. In this context, the aim of this paper is to define the “impact of the
fuzzy logic theory on the measurement of student’s performance” (Semerci, 2004). The use of fuzzy logic models
permits more flexible forms of evaluation. Electrical control laboratory is one of the courses given in departments of
Electrical, Electronics and Computer Education. Electrical control laboratory is one of the most important courses
because it has a practical focus and is closely-related to industry.
2. Methods
2.1. Study Group
The study group comprised sixth term students of Electrical Education at the Technical Education Faculty of Marmara
University, Turkey. The study used exam scores which twenty students took the control technique laboratory course.
2.2. The Aim of the Study
The aim of the study is to determine students’ performance using a fuzzy logic model in place of classical
assessment methods. The study aimed to address the following research questions:
1. Is there any difference between classical and fuzzy logic evaluation methods?
2. Is there any difference in assessment results between classical and fuzzy logic evaluation methods?
3. What are the comments of academics about these two methods?
2.2.1.Fuzzy Logic
The fuzzy logic set was introduced in 1965 as a mathematical way to represent linguistic vagueness (Zadeh,
1965). According to the fuzzy logic concept, factors and criteria can be classified without certain limits. Fuzzy logic
is very useful for addressing real-world problems, which usually involve a degree of uncertainty. The modeling of
many systems involves the consideration of some uncertain variables. The statistical uncertainties associated with
these variables are handled through probability theory. There also exists non-statistical uncertainty (in the form of
‘vagueness’ or ‘imprecision’) associated with many variables. These variables and their influences on the system are
defined in linguistic terms. This form of uncertainty can be handled in a rational framework of ‘fuzzy set theory’. It
can be said that probability deals with statistical uncertainty, whereas fuzziness has been introduced as a means of
representing and manipulating non-statistical uncertainty (Bezdek, 1994). It is not always meaningful to relate
uncertainty to frequency (Dubois & Prade, 1993). Fuzzy logic uses variables like “low”, “normal”, ”high” in place
of ”yes/no” or ”true/false” variables. Fuzzy sets are determined by membership functions. The membership
function of a fuzzy set is expressed as ȝA(x) and membership degree of its fuzzy set is determined as a number
between 0 and 1. If factor x definitely belongs to set A, ȝA(x) is 1 and if it definitely does not belong to set A,
ȝA(x) is 0. A higher membership function value (up to a value of 1) shows that factor x has a stronger degree of
membership to set A (Mathworks, 2009; Timothy, 2004; Zimmermann, 2001). Boundary conditions of the
membership function can be expressed with flexible structure in fuzzy sets. The most significant difference between
traditional sets and fuzzy sets is the membership function. While traditional sets can be characterized by only one
membership function, fuzzy sets can be characterized by numerous membership functions (ùen & Cenkçi, 2009)
3. Performance Evaluation with Fuzzy Logic
The application of a fuzzy model comprised three stages:
1. Fuzzification of input exams results and output performance value

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2. Determination of application rules and inference method
3. Defuzzification of performance value
Students sit two exams, so there are two input variables. The output variable is the performance value, which is
determined by fuzzy logic (Figure 1).
Figure 1. Determination of students’ performance using fuzzy logic
3.1. Fuzzification of Exam Results and Performance Value
Fuzzification of exam results was carried out using input variables and their membership functions of fuzzy sets.
Each student has two exam results, both of which form input variables of the fuzzy logic system. Each input variable
has five triangle membership functions.
Initially, membership functions have the same interval, so both exams have same weighted average. The fuzzy
set of input variables is shown Table 1.
Table 1. Fuzzy set of input variables
Linguistic Expression Symbol Interval
Very Low VL (0, 0, 25)
Low L (0, 25, 50)
Average A (25, 50, 75)
High H (50, 75, 100)
Very High VH (75, 100, 100)
It is seen that exam notes can belong to one or two membership functions but their membership weighting of
each membership function can be different (Figure 2).
Figure 2. Membership functions of Exam 1 and Exam 2
For instance, while a score of 25 only belongs to the “Low” membership function, a score of 30 belongs to both
“Low” and “Average” membership functions, but is weighted more heavily within the “Low” membership functions
than the “Average” membership function.
The output variable, which is the performance value, is entitled “Result” and has five membership functions. For
reasons of convenience within the application, a value range between 0 and 1 was chosen (Table 2 and Figure 3).
Table 2. Fuzzy set of output variable
Linguistic Expression Symbol Interval
Very Unsuccessful VU (0, 0, 0.25)
Unsuccessful
U
(0 0
25 0 5)

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Average A (0.25, 0.5, 0.75)
Successful S (0.5, 0.75, 1)
Very Successful VS (0.75, 1, 1)
Figure 3. Membership functions of performance value
3.2. Rules and Inference
The rules determine input and output membership functions that will be used in inference process. These rules
are linguistic and also are entitled “If-Then” rules (Altrock, 1995; Semerci, 2004).
1. If Exam1 is VL and Exam2 is VL then Result is VU
2. If Exam1 is VL and Exam2 is L then Result is VU
3. If Exam1 is VL and Exam2 is A then Result is U
4. If Exam1 is VL and Exam2 is H then Result is U
5. If Exam1 is VL and Exam2 is VH then Result is A
6. If Exam1 is L and Exam2 is VL then Result is VU
7. If Exam1 is L and Exam2 is L then Result is U
8. If Exam1 is L and Exam2 is A then Result is U
9. If Exam1 is L and Exam2 is H then Result is A
10. If Exam1 is L and Exam2 is VH then Result is A
11. If Exam1 is A and Exam2 is VL then Result is U
12. If Exam1 is A and Exam2 is L then Result is U
13. If Exam1 is A and Exam2 is A then Result is A
14. If Exam1 is A and Exam2 is H then Result is S
15. If Exam1 is A and Exam2 is VH then Result is S
16. If Exam1 is H and Exam2 is VL then Result is U
17. If Exam1 is H and Exam2 is L then Result is A
18. If Exam1 is H and Exam2 is A then Result is S
19. If Exam1 is H and Exam2 is H then Result is S
20. If Exam1 is H and Exam2 is VH then Result is VS
21. If Exam1 is VH and Exam2 is VL then Result is A
22. If Exam1 is VH and Exam2 is L then Result is S
23. If Exam1 is VH and Exam2 is A then Result is S
24. If Exam1 is VH and Exam2 is H then Result is VS
25. If Exam1 is VH and Exam2 is VH then Result is VS
In case of several rules are active for the same output membership function, it is necessary that only one
membership value is chosen. This process is entitled “fuzzy decision” or “fuzzy inference”. Several authors,
including Mamdami, Takagi-Surgeno and Zadeh have developed a range of techniques for fuzzy decision-making
and fuzzy inference. The present study uses the method proposed by Mamdami, shown in Equation (1) (Semerci,
2004; Zadeh, 1965; Rutkowski, 2004).
11
( ) max min ( ( )). ( ( ))
CAB
k
y input i input j
PPP
ªº
ªº
¬¼
¬¼
k=1,2........r (1)

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This expression determines an output membership function value for each active rule. When one rule is active, an
AND operation is applied between inputs. The smaller input value is chosen and its membership value is determined
as membership value of the output for that rule. This method is repeated, so that output membership functions are
determined for each rule. To sum up, graphically AND (min) operations are applied between inputs and OR (max)
operations are between outputs.
3.3. Determination of Performance Value
After completing the fuzzy decision process, the fuzzy number obtained must be converted to a crisp value. This
process is entitled defuzzification. Many methods have been developed for defuzzification. In this study, a
“Centroid” (Center of Area) technique was applied, which is one of the most common methods. After
defuzzification process, obtained fuzzy number is geometrical figure. The crisp value is calculated as below (Figure
4, Equation 2) (Semerci, 2004).
Figure 4. Defuzzification with Centroid method
()
()
C
C
z
zdz
z
z
dz
P
P

uu
u
³
³
(2)
3.4. Application Of Fuzzy Logic
Table 3 shows the scores achieved by 20 students in Exam 1 and Exam 2. For each student, both exam scores
were fuzzified by means of the membership functions previously described in section 3.2 (Rules and Inference).
Active membership functions were determined according to rule table, using the Mamdami fuzzy decision
technique. The output (performance value) was then defuzzified by calculating the center (centroid) of the resulting
geometrical shape. This sequence was repeated using the exam scores for each student.
Table 3. Exam scores and calculated performance values
No Exam 1 Exam 2 Performance Value No Exam 1 Exam 2 Performance Value
1 40 65 0.53 11 65 45 0.576
2 20 35 0.243 12 89 100 0.908
3 50 65 0.645 13 100 100 0.92
4 10 20 0.203 14 65 35 0.5
5 45 65 0.576 15 48 50 0.473
6 34 60 0.462 16 45 55 0.5
7 48 55 0.533 17 55 25 0.31
8 56 90 0.759 18 84 80 0.765
9 74 70 0.735 19 63 65 0.639
10 45 50 0.44 20 28 30 0.31
Both inputs had same triangle membership functions. Therefore, replacing Exam 1 with Exam 2 would not
change the calculated performance value (e.g. (45 & 65) and (65 & 45)). If the symmetry or the value range of the
membership functions is not equal, one of the exams has a greater influence on the output performance value than
the other. For example, let’s change the membership functions and value range of Exam 2 (Figure 5), while

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retaining the original criteria for Exam 1. With this arrangement, the value range of Average membership function
shrinks; the top value of L membership function is moved to 20; the top value of H membership function is moved
to 80; and value ranges of VL and VH membership functions are moved to 40 and 60, respectively.
Figure 5. Arrangement membership functions for Exam 2
Aim of this arrangement in Exam 2 is to penalize scores below 50 and to reward scores above 50. This situation
can be seen in Table 4. For exam scores below 50, performance values decreased and for exam scores above 50,
performance values increased. There is no change for scores of 50, because this is the boundary of the limit value.
Figure 6 shows the active rules and performance value obtained for exam scores of 45 and 65.
Figure 6. Active rules and performance value for exam scores of 45and 65
In this scenario, rules 9,10,14 and 15 are active and at the end of defuzzification, a performance value of 0.656 is
obtained.
Table 4. Variations in performance value according to Exam 2 criteria
No Exam 1 Exam 2 Performance Value No Exam 1 Exam 2 Performance Value
1 40 65 0.637 11 65 45 0.551
2 20 35 0.242 12 89 100 0.908
3 50 65 0.75 13 100 100 0.92
4 10 20 0.202 14 65 35 0.384
5 45 65 0.676 15 48 50 0.473
6 34 60 0.625 16 45 55 0.505
7 48 55 0.54 17 55 25 0.3
8 56 90 0.76 18 84 80 0.778
9 74 70 0.761 19 63 65 0.753

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10 45 50 0.44 20 28 30 0.238
4. Conclusion
When the results are evaluated, a difference in outcomes is seen between the classical method and the proposed
fuzzy logic method. While the classical method adheres to a constant mathematical rule, evaluation with fuzzy logic
has great flexibility. At the application stage, course-conveners can edit rules and membership functions to obtain
various performance values but it is important that the same rules and membership functions are used for all students
taking the same lesson. It is also important for the students to understand the assessment criteria before taking
exams.
For this reason, members of the educational board should communicate with each other and come to an
agreement on rules, membership functions and any other criteria.
Performance values using the classical method and fuzzy logic method are given in Table 5. For comparison,
average scores with classical method is divided to 100 and the success limit is accepted as 0.5.
In the Fuzzy 1 scenario, all membership functions are the same for both exams, whereas in the Fuzzy 2 scenario,
membership functions of Exam 2 are modified. From Table 5, a linear relationship can be seen between the classical
method and Fuzzy 1. If a student is successful in the classical assessment method, they will also be successful in the
Fuzzy 1 scenario. Comparison of the classical method with the Fuzzy 2 scenario reveals differences in the
performance values. For scores blow 50, the performance value of Fuzzy 2 is smaller than the classical method;
however, for scores above 50, the performance value is larger than the classical method. For example, a student
scoring 34 in exam 1 and 60 in exam 2 is unsuccessful in the classical method, but is successful in the Fuzzy 2
scenario.
We interviewed Electrical Education board in Marmara University and asked 20 academics about evaluation of
student performance fuzzy logic. The views of academics varied on the use of the two assessment methods. Some
valued the potential flexibility of the fuzzy logic method, but others pointed out drawbacks in that the calculation of
performance values may be difficult to explain to students. The use of an automated computer system to perform
calculations should address these issues. In conclusion, performance evaluation using fuzzy logic is suitable not only
for laboratory application, but can also be used for performance evaluation of theoretical lessons.
Table 5. Comparison of Performance Evaluation Methods
No Exam 1 Exam 2 Classical Method Fuzz
y
1 Fuzz
y
2
1 40 65 0.525 0.53 0.637
2 20 35 0.275 0.243 0.242
3 50 65 0.575 0.645 0.75
4 10 20 0.15 0.203 0.202
5 45 65 0.55 0.576 0.676
6 34 60 0.47 0.462 0.625
7 48 55 0.515 0.533 0.54
8 56 90 0.73 0.759 0.76
9 74 70 0.72 0.735 0.761
10 45 50 0.475 0.44 0.44
11 65 45 0.55 0.576 0.551
12 89 100 0.945 0.908 0.908
13 100 100 1 0.92 0.92
14 65 35 0.5 0.5 0.384
15 48 50 0.49 0.473 0.473
16 45 55 0.5 0.5 0.505
17 55 25 0.4 0.31 0.3
18 84 80 0.82 0.765 0.778
19 63 65 0.64 0.639 0.753
20 28 30 29 0.31 0.238

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Acknowledgment
This study is supported by T.R Marmara University Scientific Research Project Presidency; under project no
FEN-E-050608-138.
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