Multiobjective genetic fuzzy rule selection with fuzzy relational rules

Genetic fuzzy rule selection has been frequently used for fuzzy rule-based classifier design. A number of its variants have also been proposed in the literature. In many studies on genetic fuzzy rule selection, each antecedent condition in fuzzy rules is given for a single input variable such as “x<sub>1</sub> is small” and “x<sub>2</sub> is large”. As a result, each antecedent fuzzy set is defined on a single input variable. In this paper, we examine the use of fuzzy relational conditions with respect to the relation between two input variables such as “x<sub>1</sub> is approximately equal to x<sub>2</sub>” and “x<sub>3</sub> is approximately larger than x<sub>4</sub>”. Such a fuzzy relational condition is defined by a fuzzy set on a pair of input variables. We examine the effect of using fuzzy rules with fuzzy relational conditions on the performance of fuzzy rule-based classifiers designed by multiobjective genetic fuzzy rule selection.

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