Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 38

Therefore, a FR-CN that is used to represent the knowledge domain of the
learning material is a 6-tuple (C, ORD, PART, IMPACT, KL, f), where:
• C = {C 1 , C 2 , … C n } is the set of concepts of the knowledge domain.
• ORD: (C i , C j ) ₒ {0, 1} is a matrix, which denotes that the concept Ci i is
delivered to the learner before the concept C j (the value of the corresponding
matrix's cell—line i, column j—is 1). If the value of the corresponding matrix's
cell is 0, then it denotes that there is no “precedes” relation between the two
domain concepts.
• PART: (C i , C j ) ₒ {0, 1} is a matrix, which denotes that the concept Ci i is part-
of the concept Ci j (the value of the corresponding matrix's cell—line i, column
j—is 1). If the value of the corresponding matrix's cell is 0, then it denotes that
there is no “part-of” relation between the two domain concepts.
• IMPACT: (C i , C j ) ₒ w ij is a matrix, where w ij is a weight of the directed arc
from Ci i to C j , which denotes the “strength of impact” of the concept Ci i on the
concept C j (the value w ij is inserted in the cell that corresponds to line i and
column j). If w ij = 0, then it denotes that Ci i and C j are not knowledge related
concepts.
• KL is a function that at each concept C i associates the sequence of its activa-
tion degree. In other worlds, KL i (t) indicates the value of a concept's knowledge
level at the moment t.
• f is a transformation function. For the deinition of the transformation
function the following limitation has to be taken into account. Only the
knowledge level of the most recently read concept affects the knowl-
edge level of a domain concept, each time. The reason for this is the fact
that the learner's knowledge level is affected either by the new knowledge
that s/he has obtained, or by the knowledge that s/he has forgot, each time.
Consequently, the KL value of a concept is affected only by the KL value of
the most recently read concept, regarding the weight of the directed arc that
connects them. Therefore, the transformation function for a FR-CN, which is
used to represent the knowledge domain of the learning material, is defined
as: KL i (t + 1) = f(KL i (t) w ji *p j *KL i (t)/100), where p j is the percentage of
the difference on the value of the knowledge level of the most recently read
concept C j , with p j = (KL j (t + 1) − KL j (t))*100/KL j (t). Also, the + is used
in case of increase and the − is used in case of decrease.
For example, the matrixes ORD (Table 2.1 ), PART (Table 2.2 ) and IMPACT
(Table 2.3 ) for the FR-CN that depicts in Fig. 2.10 are the following:
At the ORD matrix the value of the cell ORD [i, j], which corresponds to the
line i and column j, can be 1, although there is no a direct arc in the corresponding
FR-CN that connects the node-concept C i with the node-concept Ci j and
declares “precedes” relation between the particular concepts. The reason for that
is the fact that an indirect relation of type “precedes” can be exist between the par-
ticular concepts. For example, in the FR-CN of Fig. 2.10 , the concept C 3 precedes
the concept C 2 due to the fact that the concept C 7 precedes the concept C 2 and the