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Example 3
Nick had learned the sections 1 (the domain concepts 1.1 to 1.7), 2 (the domain
concept 2.1), 3 (the domain concepts 3.1 to 3.3), 4 (the domain concepts 4.1 to
4.5) and some domain concepts 5.1 to 5.5 of the section 5 (Interaction I of
Table
2.10
). He revised the concept C
5.2
. During the revision, he was exam-
ined in the particular domain concept and succeeded 73 %. According to the
above, the value of the defined membership functions for concept C
5.2
become
μ
Un
=
0,
μ
MKn
=
0,
μ
Kn
=
1,
μ
L
=
0 and
μ
A
=
0. According to the FR-CN
(Fig.
2.11
) the concept C
5.2
affects the preceding concepts C
4.2
, C
4.3
, C
4.4
and the following concepts C
5.3
and C
5.4
with “strength of impact” 1, 0.45,
0.81, 0.45 and 0.81 correspondingly. Consequently, applying the fuzzy rule
R8 is:
x
4.2
=
(
1
−
1
)
∗
86
+
MIN[1
∗
86, 1
∗
73]
=
73
. That degree of suc-
cess corresponds to the fuzzy set 'Known' with
μ
Kn
=
1. (Interaction II of
according to the rules R3 and R4 (a), KL(C
5.3
) becomes 45 % 'Known', 15 %
'Learned' and 40 % 'Assimilated' and KL(C
5.4
) becomes 70 % 'Known' and 30 %
'Assimilated' (Interaction II of Table
2.10
).
2.5 Conclusions and Discussion
Learning is a complicated process. It cannot be accurately said that a learner
knows or does not know a domain concept. For example, a new domain concept
may be completely unknown to the learner but in other circumstances it may be
partly known due to previous related knowledge of the learner. On the other hand,
domain concepts, which were previously known by the learner, may be completely
or partly forgotten. Hence, currently they may be partly known or completely
unknown. In this sense, the level of knowing cannot be accurately represented.
Finally, the teaching process itself changes the status of knowledge of a user.
This is happened due to the fact that a learner accepts new concepts while being
taught. Furthermore, the learner's knowledge is a moving target. The knowledge
level of a domain concept is increased when the student's performance is improved.
Alternatively, it is decreased when the student forgets. Improvement of the knowl-
edge level of a domain concept should lead to the increase of the knowledge level
of all the related concepts (prerequisite and following), with his concept. Similarly,
poor performance on a domain concept should lead to decrease of the knowledge
level of all the related concepts with this concept.
In view of the above, an effective adaptive tutoring system has to be responsible
for tracking cognitive state transitions of learners with respect to their progress or
non-progress. The alterations on the state of student's knowledge level are not lin-
ear. They deal with uncertainty. Thus, a solution to represent these is fuzzy logic.
Therefore, the target of this section was to develop a rule-based fuzzy logic system,
which models the cognitive state transitions of learners, such as forgetting, learning
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