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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 8, November 2010
Fuzzy expert system for evaluation of
students and online exams
1 2
Mohammed E. Abd-Alazeem Sherief I. Barakat,
Computer science department, Information system department,
Faculty of computers and information, Faculty of computers and information,
Mansoura Egypt, Mansoura ,Egypt,
mmandouh_work@yahoo.com sherifiib@yahoo.com
Abstract- In this paper we will introduce an expert describes the results of the assessment students and
system for evaluation of online exam. We use fuzzy online exams. Section 5 shows the feedback of
system for classifying students based on their usage
evaluating students and online exams. Section 6
concludes the work and indicates future research
data and the final marks obtained in their respective directions.
courses. We have used real data from nine Moodle
II. Knowledgebase expert system
courses with Mansoura University Pharmacy students
All needed data is acquired from a teacher and
and apply techniques on two hundred students. This stored in a “Knowledge Based” which should be
expert system will be able to facilitate education and able to face student training and their up growing
problem. [2] We use knowledge base expert system
play the role to play the role of virtual intelligent
as follow to model knowledge domain “fig.1”
teacher referring to student capabilities by following
the feedback mechanisms and will evaluate the online
exams and questions to measure the difficulty level of
exams.
The main components of this expert system are
Inference Engine, Knowledge Acquisition Facility and
Knowledge-base that construct back-end of the
system. We realize the model by a fuzzy rule-based
expert system with its inference engine that uses
various inference methods for education.
Figure1. Knowledge base expert system
Keywords: Fuzzy rule base, Knowledge base, Inference
engine
I. INTRODUCTION Global Data Base consists of student state variables,
teaching state variables and exam state variables
Modern information management systems
enable the recording and the management of data • Student state variable (xi):
using sophisticated data models and a rich set of x1-Exercise grade for every student
management tools. In the context of educational x2-Exam grade for every student
systems, the information typically includes details x3- Interesting course
about learning material, the tasks and the objectives, x4- Student level
the course information, the contact information, the
teacher and the student profiles, and the information • Teaching state variable (yi):
related to student assignments, the tests, the grades, y1- Difficulty level exam
and other records[1].
In this paper, we seek means to model the y2-Teaching content
imprecision of information and simplify the access y3-Teaching method
to information systems, in terms of fuzzy modeling.
The paper is organized as follows. Section 2 y4-Teaching schedule
presents the knowledge base of expert system for y5- Degree of course usages
student grades assessment Section 3 discuss the
components of fuzzy rule based controller. Section 4 y6- Degree of creating motivation.
125 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 8, November 2010
• Exam state variable (zi) A. Fuzzy Inference Process
z1- Exam average grade A fuzzy system works similar to a
conventional system: it accepts an input value,
z2- Exam level
performs some calculations, and generates an output
Fuzzy logic was primarily designed to represent and value. This process is called the Fuzzy Inference
reason with some particular form of knowledge. Process and works in three steps illustrated in
Fuzzy logic is powerful problem solving “Fig.3” [5]:
methodology with a myriad of applications in • Fuzzification where a crisp input is translated
embedded control and information processing. into a fuzzy value.
Fuzzy systems are mathematically based systems • Rule Evaluation, where the fuzzy output truth
that enable computers to deal with values are computed, and
imprecise, ambiguous, or uncertain information and • Defuzzification where the fuzzy output is
situations. translated to a crisp value.
Fuzzy set theory was proposed in 1965 by
Zadeh to help computers reason with uncertain Crisp Input
and ambiguous information. Zadeh proposed
fuzzy technology as a means to model the
uncertainty of natural language [3]. He Fuzzification
reasoned that many difficult problems can be
expressed much more easily in terms of
linguistic variables. Linguistic variables are
words and attributes which are used to describe
certain aspects of the real world. One Fuzzy Input
important feature of linguistic variables is the
notion of their utility as an expression of data
compression. Zadeh describes this as Rule Evaluation
compression granulation. He argues that this is
important because it is more general than use
of discrete values. This point means that an
agent using linguistic variables may be able to Fuzzy Output
deal with more continuous and robust
descriptions of reality and problem spaces. Our
approach is to design a fuzzy rule base system
to control training process. Defuzzification
III. FUZZY RULE BASED
This system is designed for evaluating and
teaching the students so that the resulting control Crisp Output
system will reliably and safely achieve high
Figure3. Fuzzy System Process
performance operation.
A block diagram of fuzzy system is shown in
“Fig.2” Basically in fuzzy control system, there are B. Fuzzification
four major stages to accomplish the control process:
Fuzzification where a crisp input is translated
[4]
into a fuzzy value.
• Fuzzy input and output variables & their
The membership functions defined on the input
fuzzy value
variables are applied to their actual values to
• Fuzzy rule base determining the degree of truth.
• Fuzzy inference engine For example for the fuzzification crisp inputs, x1
• Fuzzification and defuzzification modules and y1 and determine the degree to which these
inputs belong to each of the appropriate fuzzy sets
(Figure 3).
At first it gets inputs and then fuzzifies them. After
fuzzification, make decision through fuzzy inference
engine according to fuzzy rule based system.
C. The Fuzzy Inference engine fuzzy rule based:
This is an interface for fuzzifying the user-
requested parameters of the test items. The fuzzified
parameters, along with a set of fuzzy rules, are then
sent to an expert system to perform the inference
Figure2. Fuzzy System process.
.
126 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
ournal of Compu Science and Information Sec
(IJCSIS) International Jo uter d curity,
No. er
Vol. 8, N 8, Novembe 2010
D. Defuz
zzification nd hen ult
R9: If z1 is low an y1 is low Th z2 is difficu
Defu onverting outpu
uzzification is a process of co ut
ariable into a un
fuzzy va nique number. BLE1. Fuzzy R
TAB m
Rules for exam evaluation
Defuzzi ss
ification proces has the capa ce
ability to reduc L
Low dium
Med High
s to
a fuzzy set into a crisp single-valued quantity or int
set; t rix
a crisp s to convert a fuzzy matr into a cris sp Low
L Diff
fficult Diff
ficult Mod
derate
ber
matrix; or to convert a fuzzy numb into a cris sp
number. [6]
edium
Me Diff
fficult derate
Mod asy
Ea
IV. RIMENTS AN RESULTS
EXPR ND
A. Evaluating an online exam high
h Mod
derate Mod
derate Ea
asy
f
We consider two fuzzy input va m
ariables as exam
average grade z1 (Figg4.a) and diff of
ficulty level o
exam y1 (Fig4.b). And the output will be the exam
1 d w m logy" course:
For Exam "Cyptol
2). ip f
level (z2 Membershi function of z1, y1 and z z2
1- Exam averag grade for all students (
ge (exam
be 0
should b as follows (0 ≤ µ≤ 1).[7]
ted
grade) is calculat as:
Fig 4-a
(Sum of student grades)/no of students
ts o
xam rade = 66%
Ex average gr
ulty
2- Exam difficu level
ollowing form
Fo culating the Exam
mula for calc
Diifficulty: [8]
Wheere ed fficulty,
denote the item dif enoted
de
xaminees that answered the item
the number of ex e
corr
rectly, and denoted th total numb of
he ber
Fig 4-b minees. Exam difficulty level = 62%
exam l
y n p
Firs we can apply fuzzification where a crisp input
st
is translated into a fuzzy value,
angle Membe
By applying Tria on
ership Functio for
“Fig 4.a”
g
(z1) = 60%
µA( 0%
µA(y1) = 20
µB(z1) = 20% 0%
µB(y1) = 80
a ence mechanism
By applying infere m
e4. ip
Figure Membershi function of e exam average
A(x1) = 60% a µA(y1) = 2
if µA and 20% then
d vel
grade (z1) and difficulty lev (y1)
(z2) = 20%
µA(
ule valuating exam is designed a
Fuzzy ru base for ev m as A(z1) = 60% a µB(y1) = 8
if µA and 80% then
follows: (z2) = 60%
µA(
1
R1: If z1 is high and y1 is high Then z2 is easy B(x1) = 40% a µA(y1) = 2
if µB and 20% then
z1 d um
R2: If z is high and y1 is mediu Then z2 i is
(z2) = 20%
µA(
moderate e
1 z2
R3: If z1 is high and y1 is low Then z is moderate B(z1) = 40% a µB(y1) = 80% then
if µB and
1 nd hen
R4: If z1 is medium an y1 is high Th z2 is easy
(z2) = 40%
µA(
and
R5: If z1 is medium a y1 is med dium Then z2 iis
moderate e valuation, wher the fuzzy o
ond: Rule Ev
Seco re output
z m ow
R6: If z1 is medium and y1 is lo Then z2 i is
h omputed.
truth values are co
difficult
R7: If z1 is low and y1 is high Then z is moderate
1 z2 cording to fuzzy based rule, we find
Acc y w
z d um
R8: If z1 is low and y1 is mediu Then z2 i is
0%
∆z2 = µA(z2) = 20 "Easy" Rule 1
difficult
127 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 8, November 2010
∆z2 = µB(z2) = 60% "Moderate" Rule 2 Fuzzy rule base for evaluating student is designed as
follows:
Third: We will apply defuzzification where the
R1: If x1 is low and y1 is low Then x4 is fail
fuzzy output is translated to a crisp value[9] shown
R2: If x1 is low and y1 is medium Then x4 is fail
in (figure 5).
R3: If x1 is low and y1 is high Then x4 is pass
The center of gravity is calculated as follow:
R4: If x1 is low and y1 is very high Then x4 is pass
µA . ,
COG = = = 62.5
µA . . R5: If x1 is medium and y1 is low Then x4 is fail
R6: If x1 is medium and y1 is medium Then x4 is
pass
R7: If x1 is medium and y1 is high Then x4 is good
R8: If x1 is medium and y1 is very high Then x4 is
good
R9: If x1 is high and y1 is low Then x4 is pass
R10: If x1 is high and y1 is medium Then x4 is pass
R11 If x1 is high and y1 is high Then x4 is good
R12: If x1 is high and y1 is very high Then x4 is
excellent
R13: If x1 is very high and y1 is low Then x4 is
pass
R14: If x1 is very high and y1 is medium Then x4 is
Figure5. Defuzzification Result for Exam good
Evaluation R15: If x1 is very high and y1 is high Then x4 is
excellent
Then the exam level is "Moderate".
B. Evaluating students R16: If x1 is very high and y1 is very high Then x4
is excellent
We consider two fuzzy input variables as exam
TABLE 2. Fuzzy Rules for student evaluation
grade x3 (figure 6.a) and difficulty level of exam y1
Low Medium High Very High
(figure 6.b) and the output will be the student level
(x4). Membership function of x3, y1 and x4 should Low Fail Fail Pass Pass
be as follows (0 ≤ µ≤ 1).
Mediu Fail Pass Good Good
Fig 6-a m
Low Moderate High Very High
1 high Pass Pass Good Excellent
Very Pass Good Excellent Excellent
High
0 20 40 60 80 100 For student "student ID 1008":
Fig 6-b 1- Exam grade for this student is :
Low Moderate High Very High
Student grade = 77%
1
2-Exam difficulty level
Exam difficulty level = 62%
First we can apply fuzzification where a crisp input
is translated into a fuzzy value,
By applying Triangle Membership Function for Fig
6-a
0 20 40 60 80 100 µA(x1) = 10% µA (y1) = 85%
Figure 6. Membership function of student grade µB(x1) = 90% µB (y1) = 15%
(x1) and difficulty level (y1) By applying inference mechanism
if µA(x1) = 10% and µA(y1) = 85% then
µA(x4) = 10%
.
128 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 8, November 2010
if µA(x1) = 10% and µB(y1) = 15% then TABLE 4. Results for student evaluation
µA(x4) = 10%
if µB(x1) = 90% and µA(y1) = 85% then Student ID Grade Level
µA(x4) = 85% 1006 63% Good
if µB(x1) = 90% and µB(y1) = 15% then
µA(z2) = 15% 1007 87% Excellent
1008 77% Excellent
Second: Rule Evaluation, where the fuzzy output
truth values are computed. 1009 52% Pass
According to fuzzy based rule, we can use 1011 38% Fail
∆x4 = µA(x4) = 10% "Excellent" Rule 16
∆x4 = µB(x4) = 85% "Excellent" Rule 12 1014 83% Excellent
1052 60% Good
Third: We will apply defuzzification where the
fuzzy output is translated to a crisp value. 1062 30% Fail
COG = 78
Then the student level is "Excellent".
CONCOLUSION
V. FEEDBACK FOR EVALUATING
Fuzzy expert system and fuzzy rule based is a great
SRUDENTS AND ONLINE EXAM step forward for the adaptation of the accessible
knowledge for the student according to the feedback
We can classify exams according to our obtain from the evaluating system.
expert system in to 3 levels: Easy, Moderate and It's also considered a good reference for instructor to
Difficult.[10] Then we have exam store for evaluate the exam level and the quality assurance
Pharmacy students for Mansoura University so we organization is benefit from this evaluation.
can evaluate this exams and give the feedback to the
instructor to be a good reference for exam
evaluation, so the results is as follow in Table[3] : ACKNOWLEDGMENT
First of all, I thank Allah for achieving this paper
and giving me the ability to finish it. Second, I
TABLE3. Results for exam evaluation would like to express my appreciation to my
Course Level supervisor Dr. Sherief Barakat for his continuous
support and encouragement during the research
Cartilage and Bone Online Exam Difficult study in this thesis. He really influenced my way of
Cytology for Clinical Pharmacy Exam Difficult thinking and developing the research ideas adopted
in this thesis. I am very grateful for his effort and
Group I Online Exam of Immune Easy his highly useful advice throughout the development
System of this work.
REFRENCES
CVS Online Exam Moderate
[1] Henry Nasution, "Design methodology of fuzzy
Urinary, Male, and Female Online Moderate logic control", Journal Teknos-2k, Universitas Bung
Hatta, Vol.2, No.2, December (2002).
Exam
[2] Ishiburchi, H., Nozaki, K., and Tanaka, H.
Online Exam of Muscular Tissue Easy “Distributed Representation of Fuzzy Rules and Its
Application to Pattern Classification. Fuzzy Sets
Modifications, Glands & CT Exam Difficult and Systems”, Vol. 52,pp. 21-32. 1992.
Med-Term Exam for Clinical Moderate [3] Zadeh, L. A. “Fuzzy sets. Information and
Control”, Vol. 8, pp. 338-353. 1965.
Pharmacy [4] Takagi,T. and Sugeon, "Fuzzy identification of
Second Med-Term Exam for CP Difficult System and Its Applications to Modeling and
Control", vol. 15, no. 1, 116-132, 1985.
[5] GAO Xinbo (1) XIE Weixin(2)," Advances in
theory and applications of fuzzy clustering",
The student assessment is very important because a Institute of Electronic Engineering, China, 2000.
good assessment let the instructor to have a correct [6] H.Bevrani, "Defuzzification", University of
decision for student follow up. Kurdistan Department of Electrical & Computer
Eng, Spring Semester, 2009.
We classify student in to 4 levels: fail, pass, good
[7] J. Harris ,"Fuzzy Logic Applications in
and excellent. [11] So according to "Cyptology"
Engineering Science", vol 29,2003.
Course the students level are as shown in Table
[8] S. J. Osterlind, "Constructing Test Items:
Multiple-choice, Constructed-response,
.
129 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 8, November 2010
Performance, and Other Formats", London, United
Kingdom: Springer, 1998.
[9] Sudarshan, Pavankiran, Swetha Krishnan and G
Raghurama, "Fuzzy Logic Approach for
Replacement Policy in Web Caching", Indian,
December 2005, ISBN: 0-9727412-1-6, pp 2308-
2319.
[10] Arriaga, F. de, Alami, M. El., & Arriaga, A,
"Evaluation of Fuzzy Intelligent Learning Systems".
Spain, November 2005.
[11] Nykänen, "Inducing Fuzzy Models for or
Student Classification". Educational Technology &
Society, vol 2, pp 223-234, 2006.
.
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