Three-objective genetics-based machine learning for linguistic rule extraction

Abstract

Abstract This paper shows how a small number of linguistically interpretable fuzzy rules can be extracted from numerical data for high-dimensional pattern classification problems. One difficulty in the handling of high-dimensional problems by fuzzy rule-based systems is the exponential increase in the number of fuzzy rules with the number of input variables. Another difficulty is the deterioration in the comprehensibility of fuzzy rules when they involve many antecedent conditions. Our task is to design comprehensible fuzzy rule-based systems with high classification ability. This task is formulated as a combinatorial optimization problem with three objectives: to maximize the number of correctly classified training patterns, to minimize the number of fuzzy rules, and to minimize the total number of antecedent conditions. We show two genetic-algorithm-based approaches. One is rule selection where a small number of linguistically interpretable fuzzy rules are selected from a large number of prespecified candidate rules. The other is fuzzy genetics-based machine learning where rule sets are evolved by genetic operations. These two approaches search for non-dominated rule sets with respect to the three objectives.