基于类高斯隶属函数的模糊万能逼近器性能分析

为了验证由三角形和高斯型隶属函数构造的逼近器均能以任意精度逼近非线性连续系统，引入了一种基于类高斯隶属函数的模糊逼近器设计方法，借助参数可调性来构造隶属函数的“泛模型”，从而实现三角形到高斯型两类隶属函数的切换.由类高斯隶属函数、单值模糊器、乘积型推理和中心平均解模糊器构成模糊逼近系统，并由万能逼近定理指出逼近精度及模糊子集数目的确定方法.与神经网络、决策树和小波级数等非线性万能逼近器相比，模糊系统具有可解释性强和可利用语言信息的独特优势.分别以一维和二维非线性系统为例进行模糊逼近设计与分析，逼近效果体现了不同的控制特性，证明了类高斯函数用于模糊隶属函数表示的合理性和有效性.

Performance analysis of fuzzy universal approximator based on Gauss type membership function

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.