Relation between Pareto-Optimal Fuzzy Rules and Pareto-Optimal Fuzzy Rule Sets

Evolutionary multiobjective optimization (EMO) has been utilized in the field of data mining in the following two ways: to find Pareto-optimal rules and Pareto-optimal rule sets. Confidence and coverage are often used as two objectives to evaluate each rule in the search for Pareto-optimal rules. Whereas all association rules satisfying the minimum support and confidence are usually extracted in data mining, only Pareto-optimal rules are searched for by an EMO algorithm in multiobjective data mining. On the other hand, accuracy and complexity are used to evaluate each rule set. The complexity of each rule set is often measured by the number of rules and the number of antecedent conditions. An EMO algorithm is used to search for Pareto-optimal rule sets with respect to accuracy and complexity. In this paper, we examine the relation between Pareto-optimal rules and Pareto-optimal rule sets in the design of fuzzy rule-based systems for pattern classification problems. More specifically, we check whether Pareto-optimal rules are included in Pareto-optimal rule sets through computational experiments using multiobjective genetic fuzzy rule selection. A mixture of Pareto-optimal and non Pareto-optimal fuzzy rules are used as candidate rules in multiobjective genetic fuzzy rule selection. We also examine the performance of selected rules when we use only Pareto-optimal rules as candidate rules