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

This paper shows how a small number of linguistically interpretable fuzzy rules can be extracted from numerical data for high-dimensional pattern classi®cation problems. One diculty 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 diculty 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 classi®cation ability. This task is formulated as a combinatorial optimization problem with three objectives: to maximize the number of correctly classi®ed 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 inter-pretable fuzzy rules are selected from a large number of prespeci®ed 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.