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Fuzzy expert system for evaluation of students and online exams

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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.

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                                                                                       ISSN 1947-5500
                                                                    ournal of Compu Science and Information Sec
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                                                                                                 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
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                                                              [2] Ishiburchi, H., Nozaki, K., and Tanaka, H.
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decision for student follow up.                               Kurdistan Department of Electrical & Computer
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                                                              [7] J. Harris ,"Fuzzy Logic Applications in
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                                                              [8] S. J. Osterlind, "Constructing Test Items:
                                                              Multiple-choice,               Constructed-response,

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                                                                                        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
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Student Classification". Educational Technology &
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