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Fig. 2.8
A network of
concepts
depended concept C
j
?”; “If the student has misconceptions on the domain concept
C
i
, how will be affected her/his knowledge level of the depended concept Ci,
i
?”.
The domain concepts that constitute the learning material are not independent
from each other. The student's knowledge level of a domain concept usually is
affected by her/his knowledge level of other related domain concepts. 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. Therefore, the knowledge representation
approach has to allow the system to recognize either the domain concepts that
are already partly or completely known for a learner, or the domain concepts that
s/he has forgot, taking into account the learner's knowledge level of the related
concepts. Therefore, the representation of dependencies between the domain con-
cepts of the learning material includes imprecise and uncertain information. As a
result an effective solution for handling this uncertainty is to use fuzzy logic tech-
niques in the representation of the knowledge domain.
A fuzzy logic application, which is used to model the behavior of complex sys-
tems (Leon et al. 2011) and emphasizes the connections and dependencies between
the system's elements, is the Fuzzy Cognitive Map (FCM). Fuzzy Cognitive
Maps (FCMs) constitute a way to represent real-world dynamic systems; in a
form that corresponds closely to the way humans perceive it (Papageorgiou 2011;
Papageorgiou and Iakovidis 2013). They are able to incorporate experts' knowl-
edge (Papageorgiou and Salmeron 2012; Salmeron 2009; Salmeron et al. 2012)
and approach representation of knowledge by emphasizing the connections and
the structure (Lin 2007). A FCM illustrates the whole system as a combination of
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