A Simulated Evolution Algorithm for The Synthesis of Trapezoid-Shaped Membership Functions

Abstract

In the past few years, there have been an increasing number of systems based on fuzzy logic in various fields of applications,such as ATM network control, GPS data processing, aircraft flight control, image processing, and so on. In a fuzzy system, the fuzzy rules are characterized by membership function. Therefore, when designing a fuzzy system, the membership functions play a very important role because they are the "brain" in the fuzzy inference process. In order to better control the fuzzy system, we need to have an effective design methodology to synthesize the membership functions. In this paper,we will present a simulated evolution based algorithm for automatic synthesis of the trapezoid-shaped membershop functions, which are based on the repreaentation format presented in [1,2]. Given some test patterns and their desired outputs, the proposed qpproach iteratively improves the membership functions by simulated evolution. Our optimization goal is to find suitable trapezoid-shaped membership functions as the knowledge base such that the total contrla error is minimized. The main distindction of the proposed qpproach is that if fully utilizes the properties inherited in trapezoid-shaped membership functions. As a result, the possibilities of variations in the simulated evolution can be accurately esimated. Experimental data shows that the proposed approach achives very good results and thus is well suitable for the fuzzy logic controller presentedin [1].