具有广义线性隶属函数的典型模糊系统的通用逼近性*

设计了一种将三角形和梯形隶属函数作为特例的广义线性隶属函数，推导了输入采用广义线性隶属函数的典型Mamdani模糊系统的解析结构，证明了典型模糊系统是单调、递减的有界连续函数；在此基础上证明了该类模糊系统能以任意精度逼近任意连续实函数，最后仿真实例证明了本设计的有效性。

Universal approximation of typical fuzzy systems with generalized linear membership function

This paper designed a kind of membership function named generalized linear membership function, and triangle and trapezoid shaped membership function were as its special cases. Deduced the analytical structure of the Mamdani fuzzy system whose input sets were with generalized linear membership function and manifested that the output of the fuzzy systems were monotonical, decreasing, continuous and bounded. On the basis of the analytical structure, it was proven that the fuzzy system could approximate any real continuous function. Finally, gave some simulations to manifest the effect of the design.