Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 51

Fig. 2.13 The membership functions of the fuzzy sets of the programming tutoring system for 'C'

X − 40
10

, 40 < X < 50

1, 50 ≤ X ≤ 60

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

0, X ≤ 60 OR X ≥ 80

X − 75
5

, 75 < X < 80

1, 80 ≤ X ≤ 85

µ L =

1 − X − 85
5

, 85 < X < 90

0, X ≤ 75 OR X ≥ 90

x − 85
5

, 85 < x < 90

µ A =

90 ≤ x ≤ 100 1,

0, x ≤ 85

Therefore, a set ( μ Un , μ MKn , μ Kn , μ L , μ A ) is used to express the student knowl-
edge of a domain concept.
Experts on programming and teachers of the programming language 'C'
have defined the limits of each fuzzy set. In particular, they were asked to deter-
mine the lower and higher values of the degree of success that characterize a
domain concept as 'Unknown', 'Moderate Known', 'Known', 'learned' and
'Assimilated'. The mean values of their answers consist the base for the definition
of the limits of the presented fuzzy sets.