**6. Conclusion**

In this study, fuzzy inference models provide an efficient way to reason about a student's learning achievement in quantitative way. In this work, a complete fuzzy rule base are formed using ANFIS approach, where all possible input conditions of the fuzzy rules are being generated apart from the 18 human experts' rules that are considered certain. By training the neural network with selected 18 conditions that are certain, the ANFIS is able to recognize other decisions that are previously not complete, in both the antecedents and consequent parts of the fuzzy rules. However, some of the decisions are found misclassified and inconsistent. In addition, it is realized that the number of fuzzy rules formed is directly related to the number of fuzzy term sets defined at the antecedents. As the number of fuzzy term sets increases, the fuzzy rules will also increases and will affect the computation time and space. Besides that, when there are too many rules, some of the rules may be found not significant. Therefore, this work proposes the Rough-Fuzzy approach that able to reduce the complete fuzzy rule base into a concise fuzzy rule base. This approach able to determine the selection of important attributes that can be used to represent the fuzzy rule base system. Therefore, the condition space is reduced by taking only a few conditions to achieve a reasonable size of the condition subspace. Moreover, the proposed concise fuzzy rule base is said to be reliable, due to the fact that it is covered, consistent and have full certainty.

#### **7. Acknowledgment**

80 Fuzzy Inference System – Theory and Applications

**RS RSupp RA CA DC RL**  *R1* 27 1 27/81= 0.333333 27/45= 0.6 1 *R2* 27 1 27/81= 0.333333 27/45= 0.6 1 *R3* 9 1 9/81= 0.111111 9/33= 0.272727 2 *R4* 9 1 9/81= 0.111111 9/33= 0.272727 2 *R5* 9 1 9/81= 0.111111 9/33= 0.272727 2 *R6* 3 1 3/81= 0.037037 3/3=1 3 *R7* 3 1 3/81= 0.037037 3/33= 0.090909 3 *R8* 3 1 3/81= 0.037037 3/33= 0.090909 3

RS – Rule Sets, RSupp – Rule Support, RA – Rule Accuracy, CA – Conditional Coverage, DC – Decision

Coverage gives a measure of how well the objects describe the decision class. The conditional coverage is measured by the ratio of the number of rules that fulfil the conditional part of the rules to the overall number of rules in the sample. Meanwhile, the decision coverage is measured by the ratio of the number of rules that give decision rules to the overall number of rules in the sample. Accuracy gives a measure of how trustworthy the rule is in the condition. It is the probability that an arbitrary object belonging to Class *C* is covered by the description of the reduct (Grzymala-Busse, 1991). According to Pawlak (1998), an accuracy value of 1 indicates that the classes have been classified into decision

For example, there are 27 objects that fulfil the conditional part of the rule *R1*, compared with the overall 81 rules in the sample. Therefore, the conditional coverage of this rule is about 0.3333. In addition, the decision for the performance and learning efficiency with the value of not mastered is used once in the fuzzy rule base and it is only given to rule *R1*. Therefore, the decision coverage for this rule is 1. Finally, the accuracy value of this rule is 1, which means that this rule belongs to Class *C1* and is covered. Thus, it is said to have full certainty and is consistent. In conclusion, because all of the rules in Table 10 have accuracy values of 1, the concise fuzzy rules are reliable because they are covered, have full certainty,

In this study, fuzzy inference models provide an efficient way to reason about a student's learning achievement in quantitative way. In this work, a complete fuzzy rule base are formed using ANFIS approach, where all possible input conditions of the fuzzy rules are being generated apart from the 18 human experts' rules that are considered certain. By training the neural network with selected 18 conditions that are certain, the ANFIS is able to recognize other decisions that are previously not complete, in both the antecedents and consequent parts of the fuzzy rules. However, some of the decisions are found misclassified and inconsistent. In addition, it is realized that the number of fuzzy rules formed is directly related to the number of fuzzy term sets defined at the antecedents. As the number of fuzzy term sets increases, the fuzzy rules will also increases and will affect the computation time and space. Besides that, when there are too many rules, some of the rules may be found not

*Legend:* 

Coverage, RL – Rule Length

and are consistent.

**6. Conclusion** 

Table 10. Rule Generation Analysis

classes with full certainty and consistency.

The authors are especially grateful to the members of the Soft Computing Research Group (SCRG), Faculty of Computer Science and Information Systems, University of Technology Malaysia, for their encouraging support to this work. The authors would also like to thank Universiti Teknologi Malaysia (UTM) for their financial support under Research University Grant Vot. No. Q.J130000.7128.01H82 and Q.J130000.7128.02J57 as well as the FRGS Grant - Vot No. 4F026(NT:2000957).

### **8. References**


**Section 3** 

**Application to Mechanical and** 

**Industrial Engineering Problems** 

