Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 56

Table 2.8 George's progress
Domain concepts Learner's knowledge

Interaction I ( μ Un , μ MKn ,
μ Kn , μ L , μ A )

Interaction II ( μ Un ,
μ MKn , μ Kn , μ L , μ A )

1.1 Constants and variables (0, 0, 0, 0, 1) (0, 0, 0, 0, 1)

(0,0, 0, 0.08, 0.92) (0,0, 0, 0.08, 0.92)

1.2 Assignment statement

(0, 0, 0, 0, 1) (0, 0, 0, 0, 1)

1.3 Arithmetic operators

1.4 Comparative operators (0,0, 0,0.08, 0.92) (0,0, 0,0.08, 0.92)

(0, 0, 0, 0, 1) (0, 0, 0, 0, 1)

1.5 Logical operators

1.6. Mathematic functions (0, 0, 0, 0, 1) (0, 0, 0, 0, 1)

1.7 Input-output statements (0, 0, 0, 0, 1) (0, 0, 0, 0, 1)

(0, 0, 0, 0, 1) (0, 0, 0, 0, 1)

2.1 A simple program's structure

3.1 If statement (1, 0, 0, 0, 0) (0, 0, 0.4, 0.6, 0)

(1, 0, 0, 0, 0) (0.5, 0, 0.2, 0.3, 0)

3.2 If…else if

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

3.2.1 Finding max, min

3.3 Nested if statement (1, 0, 0, 0, 0) (0.8, 0, 0.08, 0.12, 0)

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

4.1 For statement

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

4.2 Calc. sum in a for loop

4.3 Counting in a for loop (1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

4.4 Calc. avrg in a for loop

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

4.5 Calc. max/min in a for loop

5.1 While statement (1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

5.2 Calc. sum in a while loop

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

5.3 Counting in a while loop

5.4 Calc. avrg in a while loop (1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

5.5 Calc. max/min in a while loop

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

5.6 Do…until

6.1 One-dimension arrays (1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

6.2 Searching

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

6.3 Sorting

6.4 Two-dimensions arrays (1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

6.5 Processing per rows

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

6.6 Processing per column

6.7 Processing of diagonals (1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

(1, 0, 0, 0, 0) (1, 0, 0, 0, 0)

7.1 Functions

According to the FR-CN (Fig. 2.11 ) the concept C 4.2 affects the following concepts
C 4.3 , C 4.4 , C 5.2 , C 5.3 and C 5.4 with “strength of impact” 0.45, 0.81, 1, 0.45 and 0.39
correspondingly. Consequently, applying the fuzzy rule R2 (c) and (d), KL(C 4.3 )
becomes 36 % 'Learned' and 9 % 'Assimilated'. The rest 55 % of the particular
concept remains 'Unknown' (Interaction II of Table 3.2 ). Similarly, applying the
same rules, KL(C 4.4 ) becomes 64.8 % 'Learned' and 16.2 % 'Assimilated' (the rest
19 % of the particular remains 'Unknown'), KL(C 5.2 ) becomes 80 % 'Learned'