Abstract
This paper illustrates how genetic algorithms can be applied to the rule selection problem for constructing a fuzzy-rule-based classification system by a small number of fuzzy if-then rules. First, we briefly describe our former approach where genetic algorithms were applied to the rule selection problem with two objectives : to minimize the number of selected fuzzy if-then rules and to maximize the number correctly classified patterns. Next, we introduce a fuzzy partition method that divides a pattern space into rectangular fuzzy subspaces of different sizes in order to use various combinations of antecedent fuzzy sets in fuzzy if-then rules. Then, it is demonstrated that a small number of fuzzy if-then rules conciding with our intuition are selected by incorporating the new fuzzy partition method into our former approach. It is also demonstrated that the so-called don't care attribute can be handled by treating intervals as antecedent fuzzy sets. Moreover, we show how to construct a fuzzy classification system by fuzzy if-then rules that have linguistic interpretations, i.e., by linguistic rules. Finally, we propose a hybrid algorithm that incorprates a learning procedure of the grade of certainty of each rule into the genetic algorithm. It is shown that the hybrid algorithm improves the performance of a fuzzy-rule-based classification system. In this paper, a modification of the fitness function in our former approach is also introduced by assigning a different weight to each fuzzy if-then rule in order to select general rules that are valid in large subspaces of a pattern space.
