Journal of Intelligent Learning Systems and Applications, 2012, 4, 29-40
http://dx.doi.org/10.4236/jilsa.2012.41003 Published Online February 2012 (http://www.SciRP.org/journal/jilsa)
29
A Fuzzy Expert System Architecture for Intelligent
Tutoring Systems: A Cognitive Mapping Approach
Mohammad Hossein Fazel Zarandi1, Mahdi Khademian2, Behrouz Minaei-Bidgoli3,
Ismail Burhan Türkşen4
1Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran; 2Department of Computer Engineering &
IT, Amirkabir University of Technology, Tehran, Iran; 3Department of Computer Engineering, Iran University of Science and Tech-
nology, Tehran, Iran; 4Department of Industrial Engineering, TOBB Economy and Technology University, Ankara, Turkey.
Received January 26th, 2011; revised September 25th, 2011; accepted October 9th, 2011
ABSTRACT
An Intelligent Tutoring System (ITS) is a computer based instruction tool that attempts to provide individualized in-
structions based on learner’s educational status. Advances in development of these systems have rose and fell since
their emergence. Perhaps the main reason for this is the absence of appropriate framework for ITS development. This
paper proposes a framework for designing two main parts of ITSs. Besides development framework, the second main
reason for lack of significant advances in ITS development is its development cost. In general, this cost for instructional
material is quite high and it becomes more in ITS development. The proposed method can significantly reduce the de-
velopment cost. The cost reduction mainly is because of characteristics of applied mapping techniques. These maps are
human readable and easily understandable by people who are not aware of knowledge representation techniques. The
proposed framework is implemented for a graduate course at a technical university in Asia. This experiment provides an
individualized instruction which is the main designing purpose of the ITSs.
Keywords: Concept Mapping; Expert and Student Models; Fuzzy Cognitive Maps; Intelligent Tutoring Systems;
Expert Systems
1. Introduction
The idea of using computer for education goes back to 40
years ago with the establishment of Advanced Research
and Projects Agency Net (Arpanet). Contrary to the pur-
pose of the Arpanet, this network is also used for aca-
demic purposes. The reason for this is that the building
blocks of the network were universities and academic
centers in the United States. Current electronic learning
systems have been utilized since 20 years ago with the
development of internet protocols. An individual learner
on the World Wide Web needs the following instruc-
tional helps and supports [1]:
 Access to learning materials;
 Strategies for learning;
 Time to learn;
 Advices on what to learn;
 Feedback on progress;
 Involvement and interactivity.
First generation electronic learning systems can only
satisfy the primary needs of the individual learner, “Ac-
cess to learning materials,” while the others require more
advanced learning systems (good to be named teaching
systems).
By definition, intelligent tutoring systems (ITSs) are
computer based instructional systems that attempt to
gather information about a learner’s learning status and
having this information try to adapt the instruction to fit
the learner’s needs. Based on the definition, ITSs try to
satisfy all needs of an individual learner, especially with
personalization and individualized instruction. However,
cost of ITS development is relatively high [2]. According
to [3], development of one hour of instruction in KAFITS
(an ITS) requires 100 hours of human work and as esti-
mated by Woolf and Cunningham [4] this becomes to the
ratio of 200:1 in average in ITS development, thus me-
thods and framework for rapid development of ITSs are
significantly helpful to increase utilizations of these sys-
tems in the world. For example, recent effort tries to
simplify expert modeling by use of natural language [5].
Or create Example-Tracing Tutors without programming
and just by drag and drop techniques which reduces de-
velopment cost by a factor of 4 to 8 [6]. There are other
efforts for creating ITSs efficiently [7-10] in the recent
years.

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 30
This paper introduces a new method for rapid devel-
opment of ITSs using two well-known cognitive map-
ping techniques, fuzzy cognitive maps and concept map-
ping, and then presents the results of the proposed
method which was experienced in topics relates to two
sessions of a fuzzy course at a technical university in
Asia. The rest of paper is organized as follows: Section 2
presents the backgrounds of the research. The proposed
framework is presented in Section 3. The implemented
system based on the proposed framework with its results
is presented in Section 4. Finally, the conclusions and
future works are presented in Section 5.
2. Background
2.1. Architecture of an ITS
There is no standard architecture for Intelligent Tutoring
Systems (ITSs). However, past experiences suggest four
emerging subsystem for an ITS [11]: Expert Model, Stu-
dent Model, Pedagogical Module, and Communication
Module which are depicted in Figure 1.
Student model stores information about user experi-
ences during working with the system, such as the status
of viewing contents, perceptions about degree of under-
standing of the user, and his/her last activities.
Expert model represents knowledge about the domain
which intends to be presented for the learner. By using
expert model, system makes judgment about learner’s
misconceptions and reasons for these mistakes.
Pedagogical module plays a significant role in imple-
menting instruction method. By changing pedagogical
module, the way of teaching can be completely changed.
For example, teaching for K12 students (kindergarten
through twelfth grade) or teaching in higher education is
different from adult learners in many aspects of instruc-
tion (This results in a transition from pedagogical to an-
dragogical approach). Pedagogical module primarily uses
the knowledge of expert model and student model for its
teaching purposes and decisions and actions of the peda-
gogical module relies on this provided knowledge. Thus,
the more accurate and complete expert and student mod-
els results in more precise and effective actions of peda-
gogical module.
Expert Model
Student ModelPedagogical Module
Communication Module
Learner
Figure 1. Four components of an ITS.
Finally, communication module deals with content pre-
sentation and capturing students’ information during the
learning sessions.
2.2. Concept Maps
Concept map is a graphical tool for visual representation
of knowledge in an organized structure. Figure 2 shows
the key features of a concept maps. The nodes of the map
contain the concepts and the links between the nodes
represent the relationship among these concepts.
Concept maps are widely used in various domains,
especially in education; applications such as collabora-
tive learning, learner evaluation and curriculum planning
[12,13]. This is because of theory underlying concept
maps and models about how humans learn new things
based on the old structure of knowledge. Here, the key
point is that the knowledge is stored in a networked
structure and thus, the more organized the network re-
sults in more likelihood in recalling stored information in
the learner’s mind.
2.3. Fuzzy Cognitive Maps
Fuzzy cognitive maps (FCMs) are fuzzy graph structures
for showing causalities between objects. While their
fuzziness allows defining fuzzy degrees between fuzzy
objects, their graph structure allows systematic causal
propagation through the network and also knowledge
base expansion by connecting multiple FCMs [14].
These graphs are developed based on prior work of po-
litical scientist, Robert Axelrod (1982), on cognitive
Figure 2. A concept map describing key features of concept
maps. Concept maps are usually read from the top de-
scending [12].

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 31
maps for representing social scientific knowledge [15].
The main difference between cognitive maps and FCMs
is the use of linguistic variables to define causality be-
tween objects. A simple fuzzy cognitive map related to
automobiles’ accident is illustrated in Figure 3 (extracted
from [16]). The Fuzzy Cognitive Map nodes are Auto
Accidents, Patrol Frequency, Bad Weather, Own Risk
Aversion and Freeway Congestion, and the system out-
put is Own Driving Speed. Relations between the con-
cepts or FCM’s nodes are causal edges and also are fuzzy
values. An example for causal relation is “Bad Weather”
Usually increases “Automobile Accidents”. Both edges
and concept values could be expressed by fuzzy values,
represented with membership functions. In this example
the causality (the edge) is expressed in the forms of lin-
guistic terms and measuring “Bad Weather” or other
concepts (the concept values) could be done by fuzzy
variables.
“The fuzzier the knowledge representation, the easier
the knowledge acquisition and the greater the knowl-
edge-source concurrence” [14]. This statement becomes
more important in soft domains in which system con-
cepts and relationships are basically fuzzy. Examples of
soft domains are: political sciences, military, history and
education. In addition, use of fuzzy knowledge represen-
tation helps us to modify or “tune” our system later just
by modifying membership functions.
3. The Proposed Model
This section explains the proposed aggregated model of
Bad
Weather
Freeway
Congestion
Usually
+
Always
+
Auto
Accidents
Often
+
Patrol
Frequency
A Little
-
Much
-
Own
Driving
Speed
Very Much
-
Some
+
Own Risk
Aversion
Some
-
A Little
+
Always
+
Figure 3. A fuzzy cognitive map which relates some driving
concepts, such as speed, road congestion and accident [16].
ITS. Using the proposed model leads to a repaid devel-
opment and consequently reducing production cost of
ITSs. This rapid development is mainly because that us-
ing cognitive mapping techniques is so simple and easy
for expert and then student modeling; these maps are
expressive and human readable. They easily can be un-
derstood by the domain experts who are not familiar with
more sophisticated knowledge representation techniques.
3.1. Expert Model
Concept maps have been used in various fields of educa-
tion. This paper develops a different application for them.
In the prior experiences, educational knowledge explic-
itly appears in these maps but here a concept map visual-
izes the structure of knowledge to be instructed later. In
other words it works as a meta-knowledge container.
This form of mapping sometimes is called knowledge
structure map [1]. A simple concept map with prerequi-
site relation type is depicted in Figure 4. This map shows
that playing chess requires that the player knows how
chess pieces move. “How Chess Pieces Move” concept is
related to “Play Chess” concept with “is prerequisite for”
stereotype. We call this kind of concepts as instructional
concept and for each domain of instruction, a map of
instructional concepts should be defined to cover all re-
quired instructional materials for an individual learner;
even elementary instructional concepts in contrast to the
learner’s advanced instructional objective.
Flexibility of the concept maps in defining concepts
and ability to stereotyping them makes these maps as an
ideal tool in expert modeling for ITSs. New concept
types like questions and examples with their relationships
with instructional concepts, “assessed by” and “exempli-
fied by,” may expand expert model to complete its de-
sign purposes which is to be explained in the student
model part.
According to the general model of ITSs, expert model
should assess learners’ understandings and try to diag-
nose and reveals causes which might be the reason for
his/her misconceptions. Assessment concept types such
as placement assessments, diagnostic assessments and
formative assessments perform these tasks1. One assess-
ment concept in the concept map is capable of assessing
multiple instructional concepts with different degrees of
influence. When the learner fails to answer an assessment
Play Chess
How Chess Pieces
Move
is prerequisite for
Figure 4. A simple concept map.
1Appendix 1 of this paper describes four types of assessments.

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 32
concept, its negative effect propagates through the whole
network by its defined relations and on the other hand
his/her success, leads to increasing in system’s belief of
his/her degree of understanding.
Concepts in the concept map are systematically de-
scribed with the use of static and dynamic properties.
Hyperlink address of electronic contents associated with
the instructional concepts is one example of the static
properties. Dynamic properties hold dynamic informa-
tion of the concepts and these properties are used to up-
grade the expert model for modeling the student (student
model). The value of these properties altered by defined
causal relationships between the concepts. In the follow-
ing subsection, this kind of properties and the alteration
mechanism are explained.
3.2. Student Model
The general architecture of ITSs suggests the student
model for holding information about user experiences
during his/her interaction with the system. This model
updates during learning session and dynamic properties
are appropriate containers for this dynamic information.
For example, properties such as “is viewed” and “is com-
pleted” are changed when the learner started to view the
instructional concepts and has completed reading the
concepts. But how and when these properties are changed
in the system?
An effective tool for modeling updates of dynamic
properties is fuzzy cognitive map. FCMs are also called
Qualitative Systems Dynamics or Fuzzy Rule Based
Systems [17]. With FCMs a cause and effect network is
defined over the concept map. This network is responsi-
ble for altering the value of dynamic properties of the
concepts; a causal relationship is defined between an
event of a source concept and a dynamic property of a
target concept(s). For example, as shown in Figure 5,
correct answer to “question 2” causes the increase of sys-
tem’s perception of “degree of understanding” of a spe-
cific learner for “Introduction to Fuzzy Relations” in-
structional concept. In this example, the source and target
concept(s) are “question 2” and “Introduction to Fuzzy
Relations” respectively; a question concept type and an
instructional concept type. Moreover, the event is correct
answer to “question 2” and the dynamic property is sys-
tem’s perception of “degree of understanding” for “In-
troduction to Fuzzy Relations” concept.
Up to now some concepts have been described: expert
model, student model, concept maps, fuzzy cognitive
maps, static properties and dynamic properties. But what
is the exact relationship between them? Despite static
properties, dynamic properties of concepts are assigned
per each learner and the student model acts as a container
for them. In other words, the student model is a data
lowly
highly
highly
highly
relatively
Theory of Classic Sets
Theory of Fuzzy Sets
Introduction to
Fuzzy Relations
question 2
result of wrong answer
result of correct answer
is prerequisite for
degreeof
understanding
list of dynamic properties
instructional
concepts assessments
degreeof
understanding
degree of
understanding
Figure 5. A simple exemplary expert model (and also stu-
dent model—because of dynamic properties) for demon-
strating causal relationship with two types of concepts: 1)
Instructional concepts and 2) Assessments and three types
of relationships: 1) Result of wrong answer, 2) Result of
correct answer and 3) is prerequisite for.
structure for what is happened during the learning ses-
sion and a fuzzy cognitive map is responsible for model-
ing and handling these changes. More precisely, in the
proposed model, the student model is an instance of ex-
pert model which itself is built on a concept map and
changing of dynamic properties of the concept map is
happened by triggered events in the map and the amount
of these changes is defined by causal relationships of
fuzzy cognitive maps.
For each new student, expert model is instantiated with
this new learner’s ID and stored in the system’s knowl-
edge-base. In extensive expert models, the system can
extract concepts which are related to learner’s educa-
tional objective and only make use of these concepts for
expert model instantiation. This extraction eliminates
many irrelevant concepts with their relations and leads to
a significant reduction in size of the expert model and
consequently the student model. As a result, this reduc-
tion in size enhances the performance of system due to
illumination of redundant processing.
Now the mechanism for assessing learners’ under-
standing and diagnostic and remedial actions for solving
his/her educational problems is described through the
following example. In Figure 5, three instructional con-
cepts are shown: “Theory of Classic Sets”, “Theory of
Fuzzy Sets” and “Introduction to Fuzzy Relations”. The
first concept is prerequisite for the second one and the
third concept highly depends on the second one.

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 33
Each instructional concept in this figure has just one
dynamic property “degree of understanding” (DOU). DOU,
for example can be measured and traced by a simple
three staged variable or by a more sophisticated meas-
urement such as Bloom’s taxonomy of educational ob-
jective (More information about this taxonomy is pro-
vided in Appendix 2 of this paper). In addition to the
concepts, Figure 5 has three rules and these are pre-
sented in the form of IF-THEN rules as:
 IF student’s answer to “question 2” is wrong THEN
DOU of him for “Theory of Classic Sets” will highly
decrease;
 IF student’s answer to “question 2” is wrong THEN
DOU of him for “Theory of Fuzzy Sets” will slightly
decrease;
 IF student’s answer to “question 2” is correct THEN
DOU of him for “Introduction to Fuzzy Relations”
will highly increase.
When a learner faced with the “question 2” his/her re-
sponse to this question triggers an event which leads to
increase or decrease in system’s perception of his/her
DOU for the corresponding concept. After updating the
value of the associated dynamic properties, the student
model is updated and this leads to a new pedagogical
decision which is the main responsibility of the peda-
gogical module which is discussed in the next part. The
overall operation is shown in the Figure 7. For better
understanding on how these alterations of DOU, as the
most important dynamic property of educational concept,
we should clarify two evidences during learning session:
positive evidence and negative evidence.
Positive evidence. Positive evidence is defined in
terms of any activity of learner which results in increas-
ing the system’s assumption of DOU of him/her. An
example of this could be a correct answer of learner to a
proposed question. Each positive evidence is character-
ized by the level of Bloom’s taxonomy and a confidence
level. Positive evidences in proposed system are:
 Correct response of learner in assessments: When
learner answers the proposed questions correctly, the
system’s assumption of DOU of him should be in-
creased to the specified level of Bloom’s taxonomy
with respect to relation’s confidence level.
 Learner’s study of electronic content of educational
concepts: After reading electronic content by a learner,
the system’s assumption of DOU of him should be
increased by the specified Bloom’s taxonomy level
which is defined inside of electronic content. Here,
the level of confidence is calculated based on reading
allocated time.
 Learner’s study of examples of educational concepts:
Same as learner’s study of educational concept, learner’s
study of examples also results in increasing in his
DOU in all educational concepts which relates to the
example. Moreover, level of confidence also is calcu-
lated based on reading allocated time.
Negative evidence. Conversely, any activity of learner
which results in decreasing the system’s assumption of
DOU of him called negative evidence. Wrong response
of learner in assessments is the only defined negative
evidence in the proposed system.
3.3. Pedagogical Module
Based on the gathered information by the student model,
pedagogical module proposes comprehensive instruction
in agreement with the learner’s need. Most of the ITSs’
pedagogical module operates in the form of procedural
rules [11]. These rules might be fired on certain student
actions or on recognized student model situations which
are defined in the rules. Pedagogical module of the pro-
posed system is designed based on subsumption archi-
tecture [18] in which some instructions’ priority sup-
presses the others from operation. For instance, in a mo-
bile robot in robot path planning, instructions for obstacle
avoidance are much more important than instructions for
following the target. For an example in the educational
domain, instructions for satisfying prerequisite type rela-
tion are more important than instructions for offering
new educational concepts to the learner. Pedagogical mo-
dule of the proposed system consists of five layers of
instructions in a subsumption architecture style. Before
description of each layer, three kinds of educational con-
cepts should be defined for clarification (according to
Figure 6).
Satisfied educational concepts (group 1) are educa-
tional concepts which all of requirements are fully satis-
fied. In Figure 6, “addition” concept is one example for
satisfied educational concept because it requires com-
prehension level of “understanding meaning of numbers”
which is currently in application level and application
level is one layer above comprehension level. In this fig-
ure, “signed numbers” is not a satisfied concept, since it
requires higher level of understanding in “addition” and
“subtraction”.
 Educational concepts which have fully satisfied their
subsequent concepts (group 2) are concepts that their
subsequent concepts do not need higher level of un-
derstanding of them. In Figure 6, “understanding
meaning of numbers” is an example of this group as a
result of its current DOU of application level and sub-
sequent concepts (“addition” and “subtraction”) with
the need of comprehension level.
 Educational concepts which are candidates for pres-
entation (candidates): We define these concepts as
concepts which are ready for presentation and extrac-
tion of them is done by the following method. Set of
group 2 concepts subtracts from set of all concepts in
group 1; result is candidates set.

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 34
basic mathematical
operation (addition)
understanding
meaning of numbers
(application level)
(comprehension level)
basic mathematical
operation
(multiplication)
(unknown)
basic mathematical
operation (subtraction)
(comprehension level)
basic mathematical
operation (division)
(unknown)
signed numbers
(unknown)
is prerequisite
(comprehension level)
is prerequisite
(comprehension level)
is prerequisite
(application level)
is prerequisite
(analysis level)
is prerequisite
(analysis level)
is prerequisite
(analysis level)
Figure 6. A simple student model (an instance of expert
model).
In any cycle of learner interactions with the system,
learner specifies an educational concept as learning ob-
jective. Then system extracts all required educational
concepts and their related other concepts in the expert
model. Based on this extraction, a new student model is
instantiated and can be added to the old student model.
Information in the old student model helps pedagogical
module to prevent instructing previously learner known
materials. Now the goal of pedagogical module is to take
the learner to his chosen learning objective. For this pur-
pose, pedagogical module uses the following layers of
instruction (in a cycle of instruction, if student model
meets the criteria of a specific layer then the instructions
of that layer followed and pedagogical module stops at
that layer):
1) If there is no candidate in the candidates set, then
the learner is reached to his educational objective.
2) Select (and then inquire) the most preferred place-
ment assessment from set of unanswered placement as-
sessments which has relationship with not shown candi-
dates (from the candidates set). The most preferred place-
ment assessment is the one with maximum relationship
level to all related educational concepts. The main goal
of this step is to eliminate system from presenting al-
ready known materials to the learner.
3) Select (and then show) the most preferred educa-
tional concept from not shown candidates of the candi-
dates set. Here, the most preferred concept has the maxi-
mum need of DOU to become as a group 2 concept. At
this level, Primary learning is done because the new
educational concepts are presented to the learner.
4) From examples related to previously displayed
candidates, select (and then show) the most preferred
one. Here, the most preferred example has the maxi-
mum positive evidence in related educational concepts.
The aim of this level is to present additional illustration
for educational concept to upgrade them into group 2
concepts.
5) From unanswered formative assessments which
have relation with previously displayed candidates, select
(and then ask) the most preferred one. The most pre-
ferred assessment has the maximum relationship with
educational concepts. This level assesses the learner and
adapts instruction to meet his needs. Adaptation in in-
struction is done by altering DOU in related educational
concepts which itself is the result of positive and nega-
tive evidences of assessment. After changing in DOU,
group 1, group 2, and as the result, candidates set are
modified.
6) Selection of assessments, examples, or educational
concepts offered to the learner.
According to the strategy of tutoring system, learner,
at any time, could choose learning materials and assess-
ments himself which leads to updating the student model.
Updates in student model causes changing in elements of
group 1, group 2, and then candidates set which means
an adaptation according to learner’s action.
Pedagogical module serves other actions during learn-
ing session. One important example of this is “termina-
tion suggestion”. If a learner allots more time than speci-
fied required time for an educational concept, the system
suggests termination. If the learner terminates reading the
educational concept, “is viewed” status will be altered to
true. In next cycle of operation of pedagogical module,
another educational concept might be nominated for
presentation (operation of level 2) or an example for pre-
vious educational concept, if it is available, will be pre-
sented (operation of level 3).
3.4. Communication Module
In the proposed system, communication module has two
responsibilities. It visualizes student and expert model
for learners and captures environment variables like
learner’s allotted time for studying a specific content.
When a learner finishes his/her studying of a specific
content this environment variable acts as an event and
changes the dynamic property of related concept(s) which
means update in student model. Pedagogical module by
use of the updated student model presents new educa-
tional material for the learner, offers teaching sugges-
tions or assesses the learner. After this, the student model
updates again and this cycle continues. Figure 7 illus-
trates the overall operation of the system.

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 35
Updates in
student model
Operation of
pedagogical
module
Offer suggesstions
Content presentation
Learner Assessment
Learner
Figure 7. The overall operation of system.
4. Implementation and Results
Implementation of the system and its properties based on
proposed model is described in this section. For expert
and student models, the domain of instruction for ITSs
impact on selecting types of concepts, properties and re-
lations, however, this difference is not as much as one
which is dominated in designing other advanced teach-
ing/learning systems like cognitive tutors. This is the
reason why other types of advanced teaching/learning
systems like cognitive tutors are domain based and could
not be made in a general domain. Therefore, the expert
team should decide on types of concepts, properties and
relations and grouping them into essential elements. In
the proposed system, four types of concepts are defined:
instructional concepts, placement assessments, formative
assessments and examples. Two types of causal relation-
ship and one simple stereotype relates the concepts to
each other. All concepts have two common dynamic pro-
perties, “is viewed” and “is completed,” and instructional
concepts have another dynamic property by title of “de-
gree of understanding.” Degree of understanding is ad-
justed by causal relationships which exist between as-
sessments, examples, and concepts. Concepts also con-
tain five static properties: title, color, position, radius and
hyperlink. First four static properties are used for visual
representation purposes in the communication model and
the last one, the hyperlink, is used for content presenta-
tion.
Pedagogical module is designed based on Brook’s ar-
chitecture [18] and consists of five suppressive layers. By
applying the expert and student models, suggested mate-
rials and instructions are individualized for learners and
each learner is able to experience a different navigation
path regarding the others. Six layers of instruction me-
thod in the pedagogical module are described in section
3.3 of this paper (Pedagogical Module). In these six lay-
ers the most preferred concept selected by calculations
on its relation degree with related concepts. Detailed
calculations for this most preferred concept selection is
not presented here because it is outside the scope of this
paper and the implemented pedagogical module is just
used as an example in our experienced system.
Based on the strategy of tutoring system (pedagogical
module), the learner, at any time, is able to choose learn-
ing materials and assessments, himself which leads to
update in the student model and consequently resuming
systems work (Look at Figure 7).
Our system can facilitate communications by the use
of Microsoft Silverlight and Microsoft Agent technolo-
gies. Using the Silverlight technology the student model
is visually represented in a colored graph with fuzzy
links and various shapes and the learner can submit his/
her request with this graph. Learner can also see his/her
model anytime during his/her interactions with the sys-
tem. Part of visual representation of the expert model for
implemented system is demonstrated in Figure 8. In this
figure three types of concepts are represented: instruc-
tional concepts, questions and examples and relations
between them are demonstrated with fuzzy links. For
example “butterfly example”, a well-known example in
the fuzzy clustering, is closely related to the “Fuzzy
Clustering” and “Bezdek Algorithm” concepts. In this
map, also, “question 12” is a question type concept which
cannot significantly assess “Fuzzy Clustering” instruc-
tional concept but it can assess the “Crisp Clustering”
concept. The whole experienced network consists of
more than 40 concepts.
The pedagogical instructions and suggestions are de-
monstrated by an agent character with Microsoft Agent
Technology and agent uses text to speech synthesizers
Figure 8. Extracted part of visual representation of expert
model of the implemented system.

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 36
(TTS Engine) for auditory communications. Agent also
can hear learner’s predefined requests and process learner’s
voice with its speech recognition Engine.
4.1. First Prototype: Teaching Fuzzy Clustering
The proposed ITS model in which expert and student
models are created by cognitive mapping methods, is
constructed for concepts are related to two sessions of
graduate fuzzy course by the title of fuzzy clustering.
The implemented system is an open web based ITS for
learning fuzzy pattern recognition and fuzzy clustering.
Elementary required instructional concepts such as the
concepts with topic of mathematical sets, fuzzy sets and
algorithms are embedded in the system which makes it
an ideal tool for learning advanced graduate topics in
fuzzy theory for undergraduate students.
Expert model’s map of implemented system consists
of 20 assessments, three examples and 20 instructional
concepts. The whole network constructed with more than
200 well-defined relationships. Each assessment node
has one related multiple choice question and can assess
three concepts simultaneously in average. Examples and
instructional concepts have their electronic resource of
educational content in the form of web pages.
The pedagogical module has five layers of defined in-
struction method which is briefly defined in this paper
and the communication module facilitates communica-
tion by the use of two technologies, Microsoft Agent and
Silverlight technologies.
Construction of whole network and electronic concepts
takes about 150 hours of human work and the system pro-
vides about 200 minutes of individualized instruction
(with related prerequisites). This means that the ratio of
45:1 for system development in the selected graduate
course is obtained. Even though this experience is just one
instance, the course is an advanced graduate course and
this is a significant time reduction in ITS development.
This time reduction mainly is due to the use of concept
maps and especially fuzzy cognitive maps in dealing
with this soft domain (education) for expert and student
modeling. In this methodology, the experts of a specific
domain are able to sketch the expert model and put this
model into the implemented system, using the recom-
mended pattern. Therefore, this approach also can reduce
the development time of ITSs with no loss of productiv-
ity. Using this methodology, expert and student models
are separated from the codes. Development of two other
parts of the system and their expansion can be done with
no hard-coding, but just by expanding these models them-
selves with use of a simple GUI application as an editor.
This methodology could also be applied for covering
other fuzzy pattern recognition subjects, such as image
processing and expert systems development with fuzzy
clustering for future work. This expansion can be done
just by defining and inserting the required concepts and
the related electronic contents into the implemented sys-
tem without any hard-coding.
4.2. A Tutoring System for Teaching RLC
Circuits
After successful prototype of the proposed model in
summer 2007, the authors decide to integrate the system
with a CMS for establishing another real experiment of
system in autumn 2008. This time a section of electric
circuits’ course by the title of “The Complete Response
of Circuits with Two Energy Storage Elements” is se-
lected for the expert model domain. The system attached
to Masir CAMP, a content management system, which
enables establishing a dynamic web-site with user regis-
tration, interaction with web-controls, establishing exams
and surveys with advanced logging system. The expert
model is designed with a graphical drag-drop tool and
consists of about 45 nodes. In this experiment students of
two groups of electric circuits’ course are encouraged to
attend and about 40 students were registered in the sys-
tem and about 32 of them continuously and actively at-
tended in the planned programs.
5. Conclusions and Future Works
In this paper, a methodology for designing expert and
student models of an ITS with the use of cognitive map-
ping techniques has been presented. The aim of present-
ing this approach is to provide a systematic way of de-
signing expert and student models of general domain
ITSs.
The implemented system with its expert model was
used for teaching two sessions of a graduate course and
the course instructor never taught these materials again
for the course students. Oral discussion with the students
reveals that they are satisfied with this way of learning
especially that they are able to navigate the contents and
review them repeatedly while the system remembers
each learner’s status in their student models. The students
also are able to read and practice the course problems
and experience completely different sessions based on
their needs. This experimental study shows that the pro-
posed model is demonstrated to successfully improve
efficiency of ITS construction that provides individual-
ized instruction based on the learners’ needs.
As it is mentioned in the result part of this paper, this
method also was applied for a second experience related
to electric circuits’ course. The results of final survey of
this experience shown that more than 95% of the students
have benefited from the system and they believe that this
experiment helps them in their final exam of their course.
In addition 92% of them believe that the system works

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 37
well on prerequisite consideration while about 80% of
this group thinks that they experience different sequence
of contents from their friends. The detailed questionnaire
results are presented in the Appendix 3 of this paper.
As a final word, it is noticeable that the described
methodology is in its childhood steps and it requires
more and more investigation and experience. Although,
the authors believe that this first step is able to speed up
ITS development growth in the world. Moreover, the
authors suggest the following developments as the future
work and completion of this research:
 Expanding the expert model to support educational
concepts in a hierarchical manner for including broader
scientific domains. In other words, develop a model
to define relationships between educational concepts
in different levels in a hierarchy;
 Develop more advanced pedagogical module by ap-
plying advanced human behavior modelers such as
SOAR, architecture for human cognition;
 Develop methods for extracting expert models in a
collaborative manner in which experts of a specific
domain work together to form an expert model col-
laboratively.
6. Acknowledgements
The authors would like to thank Masir Ltd. for its coop-
eration in integrating Masir CAMP and the implemented
system in the second experience. In addition the authors
gratefully acknowledge the support of electric circuits’
expert S. J. Mousavi during the design of the expert mo-
del of the second experience and Mr. H. P. Sadjad for
providing electronic contents. In this project some parts
of electric circuits’ and differential equation course ma-
terials of MIT open courseware were used which en-
riched the electronic contents. The authors thank the MIT
open courseware for providing such great source of edu-
cational materials. Finally authors thank students who
attended in our experience actively and energetically.
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A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 38
Appendix 1. Types of Assessments
In a process of teaching usually there are four types of
assessments which are taking place; placement assess-
ments, formative assessments, diagnostic assessments
and summative assessments. New students are assessed
by placement assessments in order to determine where
they should start in the instructional sequence. Before
starting a specific topic and especially during instruction,
teachers use formative assessments to evaluate whether
the topic is covered completely and accurately and if
formative assessment does not reveals problems which
may occur in certain instructional objectives, diagnostic
assessments are used. This type of assessment involves
diagnostic instruments as well as observation techniques
and usually only one student is under investigation to
determine his problems. Diagnostic assessment searches
for root causes resulting in learning problems and offer
remedial advices. Finally, summative assessments are
taken at the end of an instructional unit to grade students
and specify how well they have attained the instructional
objectives. Educators believe that teachers commonly
use this type of assessment while other tree types have
significant effect for improving students’ achievements
in learning.
Appendix 2. Bloom’s Taxonomy of
Educational Objectives
In 1956, a group of educational psychologists and uni-
versity examiners presented a classification system in
learning. This classification is named Bloom’s taxonomy
of educational objectives. In this taxonomy, educational
objectives are primarily categorized in three major
classes: objectives in cognitive, affective, and psycho-
motor domains.
The goals in cognitive domain relates to intellectual
skills involving acquisition, process, reasoning, and use
of knowledge in application areas. Bloom’s team identi-
fies six classes in this domain which they are also di-
vided into subclasses. Knowledge, comprehension, ap-
plication, analysis, synthesis, and evaluation are six
classes within the cognitive domain. Success in each
class in this domain requires students’ achievement in
inferior classes. For example, successful utilization of
specific knowledge never happens without its compre-
hension.
The affective domain mainly focuses on attitudes and
feelings and is categorized into five classes: receiving,
responding, valuing, organization, and characterization.
For example, if a teacher is worried about learner's lack
of interest in physics, his concern relates to affective
domain.
The psychomotor domain deals with the physical ac-
tivities of students. However, Blooms and his colleagues
have not been made any taxonomy for this domain, but
several taxonomies of this domain have been extracted
over the years since the original books of Bloom.
Current intelligent tutoring systems mainly deal with
the cognitive domain rather than the two others. This
means that educational objectives of these systems might
be designed with consideration of defined stages in the
cognitive domain. A linear representation of stages in the
cognitive domain is demonstrated in Figure 9. The ex-
pert and student models of the proposed system employ
stages in the cognitive domain for measuring learners’
understanding of the specific topic or educational mate-
rial which will be explained in the next section.
Figure 9. Linear representation of stages in cognitive do-
main.

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach39
Appendix 3. The Second Experience’s Questionnaire and Its Results
Question title and choices # Total 26 %
Your opinion about the exam’s time and duration?
 Appropriate and adequate
 It needs more time
18
7
70%
27%
Your opinion about the difficulty of the exam’s questions?
 Hard
 Appropriate according to contents
 Easy
13
13
0
50%
50%
0%
Exam questions’ relativity to system’s content:
 They are quite relative.
 They are not designed uniformly according to content.
19
7
73%
27%
Your opinion about the website accessibility and availability:
 It was available and accessible with suitable speed.
 It was unavailable in many times.
 The web-site was too slow.
18
6
2
70%
23%
7%
Your opinion about the user-interfaces:
 I feel well while working with the system.
 It has appropriate design by considering it as an academic project.
 It has a poor design.
 It has problem in my web-browser/operating system.
5
7
12
2
19%
27%
46%
8%
Bandwidth requirement for multimedia contents:
 I didn’t see multimedia contents.
 My experience was great and I have high speed internet connection.
 My experience was not bad and I have dial-up connection.
 My experience was bad and I have dial-up connection.
15
8
3
0
58%
31%
11%
0%
Your overall opinion about the website:
 Very good
 Good
 Not bad
 Bad
2
14
10
0
8%
54%
38%
0%
You opinions about the website’s help and support:
 It was good.
 I have asked questions but I didn’t get any answer from the support team.
 The support was good but there was latency in answers.
15
1
2
58%
4%
8%
Do you think you have benefited from the course?
 Yes. I think.
 I have benefited from some part of it.
 No, I haven’t.
7
17
1
27%
65%
4%
Do you suggest other students to take the course?
 Yes
 Yes, definitely. But after the system improvement.
 No
9
16
1
35%
61%
4%
Do you think that taking this course may help you in final exam of your electric circuits course?
 Yes
 No
19
7
73%
27%
Your opinion about the contents:
 Adequate and appropriate
 The contents of this course are too much.
 It needs more multimedia contents
10
3
10
39%
12%
39%
Do you think that the project would be succeeded in the future versions according to its significant
objective (to be a real ITS)?
 Yes
 No
25
1
96%
4%

A Fuzzy Expert System Architecture for Intelligent Tutoring Systems: A Cognitive Mapping Approach 40
Continued
Do you think that step-by-step learning helps students in learning educational subjects?
 Yes
 It depends on learning materials.
 No
13
13
0
50%
50%
0%
Overall, how much interested have you been about the project?
 I am interested in the project.
 I take part in this activity because of its extra mark.
 It was a waste of time.
16
10
0
62%
38%
0%
The early day’s feedbacks show that the system works-well on prerequisite consideration for content
viewing. Do you agree with this?
 Yes
 No. I saw materials which I didn’t pass their prerequisite contents.
24
2
92%
8%
Do you think that other students might saw contents in different sequence according to their answers
to the placement assessments?
 Definitely no.
 Yes
3
20
11%
77%
What is your overall opinion about the functionality of the system (as an ITS)?
 I think the system was good.
 I think it needs more improvements but it would be a great educational tool later.
 I think it was a failed project.
5
21
0
20%
80%
0%
The last question, your opinion about this questionnaire?
 I think that questions are phrased wisely and precisely.
 It has too many questions.
 It doesn’t have appropriate choices.
17
0
9
65%
0%
35%