Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 48

had read previously, is improved when s/he performs better in following
concepts. In this way Kav LJi LJ's work deals only with how learning progresses.
In her work there are no rules that imply the possible decrease of knowledge
via the student's forgetting of some previously learned concepts. Moreover,
another important problem that is not dealt with in Kav LJi LJ's work is the
fact that in static educational systems, students are often required to repeat
previously known concepts thought the following chapters. However, this
practice is quite generic and does not take into account individual features
of a student such as how fast they learn or how well they remember previ-
ously taught concepts. As such, educational systems do not adapt their pace
on individual students. In view of the above, in the presented rule-based
fuzzy module, Kav LJi LJ's rules have been expanded to deal with the above
problems. The rules with these novelties that lead to the dynamic personali-
zation of teaching are presented below. In the following rules, FS x , FS y are
fuzzy sets that represent knowledge levels with FS x < FS y , and KL() denotes
the “Knowledge Level of”.

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

R1: If the same fuzzy sets are active for both Ci i and C j , then KL(C j ) = FS x with

µ FS y ( C j ) = MAX [µ FS X ( C i ) , µ FS X ( C i ) ∗ µ D ( C i , C j )

where FS x is the last active fuzzy set. Subtract the value (new μ FSx (C j )— previous
μ FSx (C j )) from the others μ FSy (C j ) (FSy < FSx) sequentially until

µ FSi = 1 .

R2: If KL(Ci) j ) = FS x and KL(C i ) = FS y , then KL(C j ) = FS y with

µ FS y ( C j ) = µ FS y ( 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) = FS n , then
if µ FS 1 C j + µ FS 2 C j + +µ FSn − 1 C j <µ FSi ( C i ) ∗ µ D C i , C j , where

i < n, then the corresponding value is subtracted by μ FSn (Cj)

else it does not change.

R4: If KL(Ci) j ) = FS y and KL(C i ) = FS x , then KL(C j ) = FS x with

µ FS X C j = µ FS X ( 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 C j , then KL(C j ) = FS x with

µ FS X ( C i ) = MAX [µ FS X ( C i ) , µ FS X C j ∗ µ D C i , C j ]

where FS x is the last active fuzzy set. Subtract the value (new μ FSx (C i )— previous
μ FSx (C i )) from the others μ FSy (C i ) (FSy < FSx) sequentially until

µ FSi = 1

R6: If KL(Ci) i ) = FS x and KL(C j ) = FS y , then KL(C i ) = FS y with

µ FS Y ( C i ) = µ FS Y ( C j ) ∗ µ D ( C j , C i )