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

This paper shows how a small number of linguistically interpretable fuzzy r ules can be extracted from numerical data for high-dimensional pattern clas sification problems. One difficulty in the handling of high-dimensional pro blems by fuzzy rule-based systems is the exponential increase in the number of fuzzy rules with the number of input variables. Another difficulty is t he 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 th e 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 fr om a large number of prespecified candidate rules. The other is fuzzy genet ics-based machine learning where rule sets are evolved by genetic operation s. These two approaches search for non-dominated rule sets with respect to the three objectives. (C) 2001 Elsevier Science Inc. All rights reserved.