Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 52

Step 3 Definition of the fuzzy rules:

Concerning two domain concepts Ci i and C j where C i is taught before Ci j , the
knowledge level of the concepts can change according to the following rules
( μ D (C i , C j ) and μ D (C j , C i ) indicate the “strength of impact” of Ci i on C j and of
C j on C i correspondingly. Their values are the values of the arcs that depict the
“knowledge dependencies” relations between the concepts of the learning material
in the FR-CN (Sect. 3.1.1 Fig. 2.11 )):

• Based on updates of the KL(Ci), i ), the KL(C j ) is improved according to:
Subtract the value (new μ x (C j )—previous μ x (C j )) from the others μ y (C j )
sequentially until µ Un + µ MKn + µ Kn + µ L + µ A = 1 , where x = {MKn, Kn,
L, A} and y = {Un, MKn, Kn, L} with y < x.

R1: If the same fuzzy sets are active for both Ci i and Cj, then:
- If KL A (C j ) > 0: µ A

C j = MAX µ A C j , µ A ( C i ) ∗ µ D C i , C j

- Else If KL L (C j ) > 0: µ L C j = MAX µ L C j , µ L ( C i ) ∗ µ D C i , C j

- Else If KL Kn (C j ) > 0: µ KN C j = MAX µ KN C j , µ KN ( C i ) ∗ µ D C i , C j

- Else If KL MKn (C j ) > 0: µ MKN C j = MAX µ MKN C j , µ MKN ( C i ) ∗ µ D C i , C j

R2:

(a) If KL(Ci) j ) = Un and KL(C i ) = MKn, then KL(C j ) = MKn with

µ MKN C j = µ MKN ( C i ) ∗ µ D C i , C j

(b) If KL(Ci) j ) = Un and KL(C i ) = Kn, then KL(C j ) = Kn with

µ KN C j = µ KN ( C i ) ∗ µ D C i , C j

(c) If KL(Ci) j ) = Un and KL(C i ) = L, then KL(C j ) = L with

µ L C j = µ L ( C i ) ∗ µ D C i , C j

(d) If KL(Ci) j ) = Un and KL(C i ) = A, then KL(C j ) = A with

µ A C j = µ A ( C i ) ∗ µ D C i , C j

(e) If KL(Ci) j ) = MKn and KL(C i ) = Kn, then KL(C j ) = Kn with

µ KN C j = µ KN ( C i ) ∗ µ D C i , C j

(f) If KL(Ci) j ) = MKn and KL(C i ) = L, then KL(C j ) = L with

µ L C j = µ L ( C i ) ∗ µ D C i , C j

(g) If KL(Ci) j ) = MKn and KL(C i ) = A, then KL(C j ) = A with

µ A C j = µ A ( C i ) ∗ µ D C i , C j

(h) If KL(Ci) j ) = Kn and KL(C i ) = L, then KL(C j ) = L with

µ L C j = µ L ( C i ) ∗ µ D C i , C j