On Adaptive Fuzzy Systems with Sinusoidal Membership Functions

摘要

An adaptive fuzzy system with a singleton fuzzifier, a product inference, a centroid defuzzifier, and a sinusoidal membership function is proposed in this paper. First, fuzzy basis function expansions of fuzzy systems with sinusoidal membership functions are given in order to describe the input-output relationships of fuzzy systems. Then, it is shown that such fuzzy systems are capable of uniformly approximating any continuous function on a compact set to a desired degree of accuracy using the well-known Stone-Weierstrass theorem. Learning algorithms for tuning both network weights and parameters of sinusoidal membership functions are discussed. Finally, a simulation example of nonlinear system identification is provided to demonstrate the effectiveness of fuzzy systems.