Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 27

Fig. 2.1 Fuzzy sets and their partitions. a Fuzzy sets for age; b Fuzzy sets for knowledge level;
c Fuzzy sets for height
Fuzzy logic variables have a truth-value that ranges in degree between 0 and 1.
That value declares the degree in which the particular variable belongs to a fuzzy
set. For example, if x is a fuzzy logic variable that describes the student's knowl-
edge level and its value is 0.6 for the fuzzy set 'novice', then it means that the
particular student is considered to be 60 % novice. This value is called degree of
membership or membership value and is symbolized with μ . A fuzzy logic ele-
ment can belong to two adjacent fuzzy sets at the same time, but with different
membership degrees. For example, if a person's height is 1.72 cm, then according
to the fuzzy sets that are depicted in Fig. 2.1 c, the particular person is considered
to be 80 % tall (the membership degree for the fuzzy set 'tall' is 0.8) and 20 %
medium (the membership degree for the fuzzy set 'medium' is 0.2).
Taking into account the above, the definition of a fuzzy set follows (Fig. 2.2 ).
Let S be a set of values that represent an element (i.e. S = {1.20, …, 2.10} for
Fig. 2.2 Definition of fuzzy set