Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 45

For example, the domain concept C 1 is delivered before concept C 2 and concept
C 4.2 is delivered before the domain concept C 4.4 . That is derived from the values of
the cells ORDER [1, 9] (Table 1.8 a ) and ORDER [18, 20] (Table 1.8 b ), which are 1
both. On the other hand, the ORDER [18, 21] = 0 (Table 1.8 b ) denotes that the con-
cept C 4.2 is not necessary to be taught before the concept C 4.5. Furthermore, C 3.2.1
belongs to the concepts C 3 and C 3.2 as PART [14, 11] = 1 and PART [14, 13] = 1
(Table 2.1 a). In addition, the learner's knowledge level on the concept C 4.4 affects
the particular learner's knowledge level on the previously delivered concepts C 4.2 ,
C 4.3 , C 5.2 , C 5.3 and C 5.5 . This information is derived from the matrix IMPACT.
In particular, the values IMPACT [20, 18] = − 1 and IMPACT [20, 19] = − 0.45
(Table 2.2 b) denote that the knowledge level of concept C 4.4 affects the knowledge
level of C 4.2 and C 4.3 , and its “strength of impact” on C 4.2 and C 4.3 are 1 and 0.45
correspondingly. Similarly, the values IMPACT [20, 24] = + 1, IMPACT [20,
25] = + 0.45 and IMPACT [20, 26] = + 0.52 (Table 2.2 b) denote that the knowledge
level of concept C 4.4 affects the knowledge level of the following concepts C 5.2 , C 5.3
and C 5.5 , and its “strength of impact” on the particular concepts are 1, 0.45 and 0.52
correspondingly. However, the value IMPACT [20, 21] = 0 (Table 2.2 b) denote that the
knowledge level of concept C 4.4 does not affect the knowledge level of the concept C 4.5 .
2.4 A Novel Rule-Based Fuzzy Logic System
for Modeling Automatically the Learning
or Forgetting Process of a Student
Learning is not a “black or white” process. The definition of the learner's knowledge
level is a moving target. In other words, it is not a straightforward task to define for
each learner which concepts are unknown, known or assimilated and at what degree.
The particular process is confronted with uncertainty and human subjectivity. One
possible approach to deal with this is fuzzy set techniques, with their ability to nat-
urally represent human conceptualization. That is the reason for the integration of
fuzzy logic techniques into the student model.
Fuzzy logic is the solution for recognizing and modeling the increase and/or
decrease of the learner's knowledge level on a domain concept in relation with
her/his performance on other related domain concepts of the learning material. In
particular, the presented rule-based fuzzy logic module is responsible for identifying and
updating the student's knowledge level of all the concepts of the knowledge domain.
Its operation is based on the Fuzzy Related-Concepts Network that is used to
represent the structure of the learning material and the dependencies that exist
between the domain concepts. It uses fuzzy sets to represent the student's knowl-
edge level and a mechanism of rules over the fuzzy sets, which is triggered after a
change has occurred on the student's knowledge level of a domain concept. This
mechanism updates the student's knowledge level of all related with this concept,
concepts. With this approach the alterations on the state of student's knowledge
level, such as forgetting or learning are represented.