Fuzzy Classifier Design with Different Shapes of Membership Functions for Each Attribute

Abstract

Multi-objective Fuzzy Genetics-Based Machine Learning (MoFGBML) optimizes fuzzy classifiers considering two objectives: maximizing accuracy and minimizing complexity. Generally, a single shape of antecedent conditions is used for fuzzy if-then rules in MoFGBML. However, an appropriate shape of membership functions probably depends on datasets. It is also possible that an appropriate shape is different among attributes even in the same dataset. In this paper, we define six antecedent conditions, combinations of three shapes (i.e., a triangular fuzzy set, a Gaussian fuzzy set, and an interval set) and two types of partitions (i.e., homogeneous and inhomogeneous) and propose MoFGBML simultaneously using these six kinds of antecedent conditions. Through various computational experiments, we discuss the effects of using multiple shapes of antecedent conditions on the accuracy and complexity of the obtained classifiers and analyze the frequency of selected conditions for each attribute.