Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 35

concepts and the various relations that exist between its concepts (Azadeh et al.
2012; Song et al. 2011; Stula et al. 2010). They are inference networks, using
cyclic directed graphs, for knowledge representation and reasoning (Fig. 2.9 ). In
particular, A FCM consists of nodes (N 1 , N 2 , … N n ), which represent the impor-
tant elements of the mapped system, and directed arcs, which represent the causal
relationships between two nodes (Ni, i , N j ). The directed arcs are labeled with fuzzy
values (f ij ) in the interval [ − 1, 1] that show the “strength of impact” of node Ni i
on node N j . If f ij has a positive value, then it indicates that node Ni i affects posi-
tively node N j . In other words, the positive value on the directed arc that connects
N i with Ni j , means that the increase of the value of Ni i leads to the increase of the
value of Ni j , or the decrease of the value of Ni i leads to the decrease of the value
of N j . Otherwise, If f ij has a negative value, then it indicates that node Ni i affects
negatively node N j . In other words, the negative value on the directed arc that con-
nects N i with Ni j , means that the increase of the value of Ni i leads to the decrease of
the value of Ni j , or the decrease of the value of Ni i leads to the increase of the value
of N j . Therefore, a FCM is a cognitive map whose relations between the nodes
can be used to compute the “strength of impact” of these elements. This property
of FCM makes it able to predict, to make decisions, to generate a more accurate
description of a difficult situation and to explain behaviors, actions and situations
(Codara 1998). That is the reason of their extensive use in a wide range of appli-
cations (Craiger et al. 1996; Kosko 1999; Miao and Liu 2000; Rodriguez-Repiso
et al. 2007; Stylios and Groumpos 2004). Furthermore, according to Papageorgiou
(2011), in the past decade, FCMs have gained considerable research interest
and are widely used to analyze causal systems such as system control, decision-
making, management, risk analysis, text categorization, prediction etc. However,
the contribution of FCMs to the knowledge representation of an adaptive tutoring
system has not been discussed before.
Taking into account the above, there is the need to represent the knowledge
dependency relations between the individual domain concepts of the domain
knowledge. In particular, the knowledge dependencies that exist between the
domain concepts of the learning material, as well as their “strength of impact” on
each other have to be represented. A solution to this is to use a combination of
a network of concepts with Fuzzy Cognitive Maps. In this way, a new approach
of domain knowledge representation derives. That new approach is called Fuzzy
Related-Concept Network (FR-CN).
Fig. 2.9 A fuzzy cognitive
map