Performance analysis of fuzzy universal approximator based on Gauss-type membership function
Xia Lin-li · Shenyang Gongye Daxue xuebao · 2014
In order to prove that the approximators based on both triangle and Gaussian membership functions can approximate the nonlinear continuous system with arbitrary precision,a design method for the fuzzy approximator based on the Gauss-type membership function was introduced. With the adjustability of parameters,the universal model of membership function was established,which could realize the transform from triangle membership function to Gaussian membership function. A fuzzy approximation system is composed of the Gauss-type membership function,single value fuzzer,product inference and center average defuzzifier,and the approximation accuracy and determination scheme for the number of fuzzy subsets is identified by the universal approximation theorem. Compared with the nonlinear universal approximators such as the neural network,decision tree and wavelet series,the fuzzy system has such unique advantages as the strong interpretability and available language information. Through taking the one-dimensional and two-dimensional nonlinear systems as example,the design and analysis for the fuzzy approximation were carried out. It is noted that the approximation effect exhibits the different control characteristics. Moreover, the rationality and effectiveness for the Gauss-type membership function to be used in representing the fuzzy membership function gets verified.