Statistical method based membership function optimization for fuzzy logic controller

Abstract

Designing a proficient fuzzy logic system is governed by a number of design parameters which include: controller architecture, fuzzification method, membership function formulation, rule base, inference engine, and defuzzification method. Proposed research work focuses on the design of optimized membership function by utilizing statistical attribute of the system. As the notion of fuzzy logic is based on uncertainty, an idea of having an empirical formula to determine membership function defies with the generalized applicability of fuzzy logic system. Optimization of membership function has always been a field of research in fuzzy logic systems; however, majority of literature emphases on optimization of the “mathematical function” (shape) of the membership function and not the “support” of fuzzy sets in a membership function. In view of this proposed optimization algorithm is focused on obtaining the optimizing support for a fuzzy membership function and not on its shape (mathematical function). The proposed algorithm utilizes “entropy function” and “standard deviation” to obtain the optimization objective function for previously characterized membership functions. These predefined sets are distributed uniformly over the fuzzy variable’s universe of discourse. The support of these predefined sets is modified by using the standard deviation, thus forming a variable membership function. Entropy for these displaced sets is optimized to obtain maximum combined entropy using genetic algorithms.