Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 46

The presented rule-based fuzzy logic module includes the following three steps:

Step 1 Definition of the fuzzy sets:

In the particular step, the definition of the fuzzy sets, which represent the
learner's knowledge level on a domain concept (i.e. {“Unknown”, “Known”,
“Learned”} or {“Unknown”, “Insufficiently Known”, “Known”, “Learned”,
“Assimilated”}), is carried out. Fuzzy sets are used to characterize the change-
able learner's knowledge level. Therefore, FS 1 , FS 2 , …, FS n are the defined
fuzzy sets, for the educational adaptive system.

Step 2 Definition of the membership functions:

In the particular step, the membership functions of the determined fuzzy sets
FS 1 , FS 2 , …, FS n is defined. The membership functions (Fig. 2.12 ) are defined
as follows (x indicates the learner's degree of success on a particular domain
concept; x i-1 , x i , x i + 1 , x i + 2 are thresholds that indicate particular degrees of
success like 0, 50, 100):

1, x ≤ x 1

1 − x − x 1 µ FS 1 =

x 2 − x 1 , x 1 < x < x 2
0,

x ≥ x 2

X − X 2 I − 3

X 2 I − 2 − X 2 I − 3 ,

X 2 I − 3 < X < X 2 I − 2

1, X 2 I − 2 ≤ X ≤ X 2 I − 1

∀ I = 1 ANDI = N µ FSI =

1 − X − X 2 I − 1

X 2 I − X 2 I − 1 , X 2 I − 1 < X < X 2 I

0, X ≤ X 2 I − 3 OR X ≥ X 2 I

x − x 2 n − 3
x 2 n − 2 − x 2 n − 3

x 2 n − 3 < x < x 2 n − 2

µ FSn =

1 x 2 n − 2 ≤ x ≤ x 2 n − 1

x ≤ x 2 n − 3

0

The knowledge level of a domain concept changes in a continuous way. Meaning
that the knowledge level of a domain concept usually passes gradually from the

Fig. 2.12 The membership functions μ FSi