Fuzzy modeling using genetic algorithms with fuzzy entropy as conciseness measure

In this paper, a fuzzy modeling method using genetic algorithms (GAs) with a conciseness measure is presented. This paper introduces De Luca and Termini's fuzzy entropy to evaluate the shape of a membership function, and proposes another measure to evaluate the deviation of a membership function from symmetry. A combined measure is then derived from these two measures, and a new conciseness measure is de®ned for evaluation of the shape and allocation of the membership functions of a fuzzy model. Numerical results show that the new conciseness measure is e€ective for fuzzy modeling formulated as a multi-objective optimization problem. Ó 2001 Published by Elsevier Science Inc.