Factors in Assessment Using FIS
6.2 Fuzzy Inference Based on Affective Factors
6.2.3 Results
pre-6.2 Fuzzy Inference Based on Affective Factors 89 Table 6.1Examples of fuzzy rules
No Fuzzy Rules
1 IF (Motivation is High) AND (Attitude is High) AND (Introversion is Low) AND (Extroversion is High) AND (Anxiety is Low) AND (Self-esteem is High) THEN Score is Very Good [1]
2 IF (Motivation is Very Low) AND (Attitude is Very Low) AND (Introversion is Very High) AND (Extroversion is Very Low) AND (Anxiety is Very High) AND (Self-esteem is Very Low) THEN Score is Unsatisfactory [1]
defined rules to produce output in fuzzy values. The inference process uses Mamdani min-max inference method. The Mamdani min-max method is typically is used to model human expert knowledge as has been used in the previous research. The min operator is used as a conjunction in the antecedent part and the max operator is used in the consequent part by aggregating all of the fuzzy sets. Defuzzification methods transform the output in the fuzzy values to the crisp values of student scores. The Center of Gravity (COG) defuzzification method is used to transform to the crisp value.
Fuzzification Inference Engine Rule base
Defuzzification
Crisp value Fuzzy set Fuzzy set Crisp value
Knowledge base
Affective Factors English
Achievement
Figure 6.1Block diagram of FIS
90 Chapter 6 Implementation of Affective Factors in Assessment Using FIS introversion, extroversion, anxiety, and self-esteem to produce a single output of the English score. The input number of the system is regarded as a high dimensional object consisting six-feature values. The visualization is conducted by reducing the dimensionality to visualize pairs of the inputs and the output. As shown in Figure 6.2, the system output is nonlinear with the surface being monotonously non-decreasing (MND).
Figure 6.2Surface plot of FIS Rule Confirmation
Correlation and multivariate regression analysis are conducted to understand the relationship of the affective factors and the student score as well as the contribution of each affective factor to the learning outcome. Table 6.2 summarizes the correlation between affective factors and the student score.
As shown in Table 6.2, there are factors that are significantly correlated with the student score. The tree factors that are significantly correlated with the student
6.2 Fuzzy Inference Based on Affective Factors 91 Table 6.2 Relationship between affective factors and student score
Mot Att Int Ext Anx Sel
Score 0.252∗∗ 0.092 −0.177∗ 0.212∗∗ −0.193∗∗ 0.063 Sig. 2-tailed) 0.001 0.208 0.015 0.004 0.008 0.392
∗∗p <0.01;∗p <0.05
score are motivation (0.252∗∗, p < 0.01), extroversion (0.212∗∗, p < 0.01), anxiety (−193∗∗,p< 0.01), and introversion (.177∗∗, p < 0.05). Two other affective factors of attitude and self-esteem have a low correlation with the student score.
The value of the contribution of each factors is conducted using multivariate re-gression analysis. The contribution of the affective factors can be viewed from the beta(β)value of each of the independent factors. The beta values for each of the af-fective factors are as follows: Two most significant factors contributing to the student score are motivation and extroversion factors with β of 0.087 and 0.058, respectively with p-value < 0.05. Meanwhile, the other beta values for attitude, introversion, anxiety, and self-esteem are, −0.042, −0.040, −0.046, and −0.029, respectively. The summary of the regression analysis is shown in Table 6.3.
Table 6.3Regression analysis result
Model Unstandardized Standardized
t Sig.
β Std. Error β
(Cons.) 0.814 0.033 - 24.62 0.001
Mot 0.087 0.036 0.216 2.40 0.017
Att -0.042 0.039 -0.101 -1.80 0.279
Int -0.040 0.032 -0.094 -1.26 0.209
Ext 0.058 0.029 0.159 1.99 0.048
Anx -0.046 0.030 -0.121 -0.152 0.130
Sel -0.029 0.037 -0.064 -0.765 0.445
92 Chapter 6 Implementation of Affective Factors in Assessment Using FIS Validation and Tuning
This step is to check the construction of the fuzzy inference system by thoroughly checking for pre-defined rules that might violate the monotonic function, and lead to false output. Five sets of cases of inputs were tested on the system output. The first case is zero inputs for all affective factors. The second case is [0.5] input for all of the affective factors. The third case is a high positive value of motivation, attitude, extroversion, and self-esteem, and low value of introversion and anxiety factors. The fourth case is the opposite of the third case, the high input value of introversion and anxiety factors and the low value of motivation, attitude, extroversion, and self-esteem. The first case represents the situation when the student does not possess any affective factor in their learning. The second case represents the condition when the students have moderate affective factors in their learning. The third case represents the context when the students have positive affective factors of motivation, attitudes, extroversion, and self-esteem in their learning. Meanwhile, the last case represents a case of students when they deal with negative affective factors of introversion and anxiety in their learning. The result indicates that the developed system is sufficient to produce reliable output. However, several enhancements could be implemented to make the system more robust.
Simulation
The developed fuzzy inference system is evaluated using the previous survey data [111] and data generated using Monte Carlo simulation. The descriptive statis-tics of both data set are shown in Table 6.4. As shown in the Table 6.4, there is no significant difference of both data in terms of the mean, variance, and standard deviation. Survey data statistics of the mean, variance, and standard deviation values are, 0.669, 0.006, and 0.082, respectively. Meanwhile, the generated data statistics of the mean, variance, and standard deviation are, 0.667, 0.004, and 0.067 respectively.
6.3 Fuzzy Inference Based on Affective-Cognitive Factors 93 These data are then used as inputs to the developed fuzzy inference system. The result of the survey data shows a significant correlation to the student score, while generated data shows a low correlation. The summary of the result from survey data and generated data is shown in Tables 6.5 and 6.6, respectively.
Table 6.4 Descriptive statistics of survey data and generated data
Data Mean Variance Standard Dev.
Real Data 0.669 0.006 0.082
Monte Carlo Sim. 0.667 0.004 0.067
Table 6.5Correlation of survey data and score
Mot Att Int Ext Anx Sel
Score 0.608∗∗ 0.533∗∗ −0.464∗∗ 0.595∗∗ −0.618∗∗ 0.477∗∗
Sig. 2-tailed 0.001 0.001 0.001 0.001 0.001 0.001
∗∗p <0.01;∗p <0.05
Table 6.6 Correlation of generated data and score
Mot Att Int Ext Anx Sel
Score 0.009 0.034 −0.036 0.003 −0.038 0.053 Sig. 2-tailed 0.905 0.648 0.623 0.962 0.606 0.471
∗∗p <0.01;∗p <0.05