Constructing Fuzzy Membership Function Subjected to GA based Constrained Optimization of Fuzzy Entropy Function

This paper presents a Genetic Algorithm based optimization algorithm for fuzzy logic system. The proposed algorithm employs fuzzy entropy function as optimization bound(s) parameter. Membership function formation plays a key role in performance of a fuzzy system, as an improperly designed MF may lead to an inefficient system. Majority of literature focuses on optimization of shape of a MF and not the support. Proposed optimization method focuses on optimizing support of MF and not on its shape. For this optimization process predefined membership functions are used, the support of these membership functions these predefined sets are varied using standard deviation of the system data obtained by simulation or real-time analysis of the system. The support of these membership functions these predefined sets are varied using standard deviation of the system data obtained by simulation or real-time analysis of the system. Entropy for each displaced Fuzzy Set is maximized subjective to constraint optimization and thus optimized value of support is obtained. The proposed algorithm optimizes the support of Fuzzy Sets and hence can be combined with any other optimization tool for obtaining even better results.