Three-Objective Genetic Algorithms for Designing Compact Fuzzy Rule-Based Systems for Pattern Classification Problems

摘要

In this paper, we formulate the design of fuzzy rule-based classification systems as a three-objective optimization problem. Three objectives are to maximize the classification performance of a fuzzy rule-based system, to minimize the number of fuzzy rules, and to minimize the number of features used in the fuzzy rule-based system (i.e., used in the antecedent part of fuzzy rules). The second and third objectives are related to simplicity and comprehensibility of the fuzzy rule-based system. We describe and compare two genetic-algorithm-based approaches for finding non-dominated solutions (i.e., non-dominated fuzzy rule-based systems) with respect to the three objectives. One approach is a rule selection method where a small number of linguistic rules are selected from prespecified candidate rules by a genetic algorithm. The other is a fuzzy partition method, which designs fuzzy rule-based systems by simultaneously determining the number and the shape of the membership function of each fuzzy set from training patterns. These two approaches are compared with each other through computer simulations on some real-world classification problems such as iris data, wine data, and glass data.