A Novel Hybrid Student Model for Personalized Education - Advances in Personalized Web-Based Education - page 73

1, X ≤ 40

1 − X − 40
10

µ UN = , 40 < X < 50

0, X ≥ 50

X − 40
10

, 40 < X < 50

50 ≤ X ≤ 60

1,

µ MKN =

1 − X − 60
10

, 60 < X < 70

0, X ≤ 40 OR X ≥ 70

X − 60
10

, 60 < X < 70

1, 70 ≤ X ≤ 75

µ KN =

1 − X − 75
5

, 75 < X < 80

X ≤ 60 OR X ≥ 80

0,

X − 75
5

, 75 < X < 80

1, 80 ≤ X ≤ 85

µ L =

1 − X − 85
5

, 85 < X < 90

X ≤ 75 OR X ≥ 90

0,

X − 85
5

, 85 < X < 90

µ A = 1, 90 ≤ X ≤ 100

0, X ≤ 85

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 fuzzy rules that are
depicted in Fig. 3.6 (how the knowledge level of Ci j changes according to updates
of the knowledge level of C i ) and Fig. 3.7 (how the knowledge level of Ci i changes
according to updates of the knowledge level of C j ).

3.5.2 Overlay Model

The qualitative values of the fuzzy-weighted qualitative overlay model are the
defined fuzzy sets. In other words, they are the values: 'unknown', 'moderate
known', 'known', 'learned' and 'assimilated'. Therefore, the overlay model uses a
quintet ( μ Un , μ MKn , μ Kn , μ L , μ A ), which expresses the degree in which each of
the above qualitative values are active (Fig. 3.8 ). For example, (0, 0, 0.6, 0.3, 0.1)
declares that the domain concept is 60 % 'known', 30 % 'learned' and 10 % 'assim-
ilated'. Similarly, (0.7, 0.3, 0, 0, 0) declares that the concept is 70 % 'Unknown'
and 30 % 'moderate known'.