Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 53

(i) If KL(C j ) = Kn 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

(j) If KL(C j ) = L 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

• Based on updates of the KL(Ci) i ), the KL(C j ) is deteriorated according to:

R3: If KL(Cj) = A, then
- if µ Un , where

x = {Un, MKn, Kn, L}, then the corresponding value is subtracted by μ A (Cj)
- else it does not change.

C j + µ MKn C j + µ Kn C j + µ L C j <µ x ( C i ) ∗ µ D C i , C j

R4:

(a) If KL(Ci) j ) = L 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

(b) If KL(Ci) j ) = L 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

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

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

(d) If KL(Ci) j ) = Kn 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

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

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

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

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

• Based on updates of the KL(Ci) j ), the KL(C i ) is improved according to:

R5: If the same fuzzy sets are active for both Ci i and Cj, then:
- If KL A (C i ) > 0: µ A ( C i ) = MAX µ A ( C i ) , µ A C j ∗ µ D C j , C i

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

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

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

Subtract the value (new μ x (C i )—previous μ x (C i )) from the others μ y (C i )
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.