具有任意形状隶属函数的分层模糊系统逼近性能研究

首先证明了对任意给定的矩阵A和正数c, 一定存在向量b, 使得方程Ax=b有非负解, 且b和解的范数均小于c. 在此基础上证明了具有任意形状隶属函数的分层模糊系统对紧集上连续函数的逼近性质, 为使用分层模糊系统进行辨识或控制以避免模糊规则数目随系统变量个数呈指数增长提供了理论依据.

Study on universal approximation of hierarchical fuzzy systems with arbitrary membership functions

It is first shown that for any given matrix A and constant c>0 there exists a vector b such that Ax = b has a non-negative solution, and both the norms of b and this solution are less than c. Based on this fact it is proved that the hierarchical fuzzy systems with arbitrary membership functions are capable of approximating any continuous function on a compact set. Thus, the theoretical foundation is established for applying hierarchical fuzzy systems to identification and control such that the problem that the number of fuzzy rules increases exponentially with the number of system variables can be avoided.