An information theoretic approach to generating membership functions from real data

Abstract

In this paper, we propose a framework for using real data to generate fuzzy membership functions which is one of the most challenging issues in the design of fuzzy systems. After modelling fuzzy membership functions by fuzzy partitions, an optimization technique based on a genetic algorithm is presented to find near optimal fuzzy partitions. The fitness function of the genetic algorithm is defined using Shannon entropy and mutual information measures to establish a mapping front real data to fuzzy variables. To generate fuzzy membership functions based on fuzzy partitions, some definitions and assumptions are also introduced. Numerical results are provided to demonstrate the effectiveness of the proposed approach.