基于正则模糊划分的模糊系统及其逼近性质

Fuzzy Systems Based on Regular Vague Partitions and Their Approximation Properties

文中讨论了带有不同模糊基函数的模糊系统的逼近问题。首先,基于一维正则模糊划分和重叠函数建立多维正则模糊划分,以划分中的元素为模糊基函数设计模糊系统,应用Weierstrass逼近定理证明了该模糊系统是通用逼近器,给出了模糊系统的逼近误差界。其次,提出了多项式型、指数型和对数型模糊系统,并给出了带有隶属函数参数的逼近误差界。最后,通过数值实验对不同模糊系统的逼近能力进行了比较,实验结果进一步验证了理论分析的正确性。

This paper is devoted to investigating the approximation problem of fuzzy systems based on different fuzzy basis functions.Firstly,the multi-dimensional regular vague partitions are established based on one-dimensional regular vague partitions and overlap functions,and the fuzzy systems are designed by taking the elements in the partition as the fuzzy basis functions.With the help of the Weierstrass approximation theorem,the conclusion that the fuzzy systems are universal approximators is obtained,and the corresponding approximation error bounds are presented.Secondly,this paper proposes the polynomial,exponential and logarithmic fuzzy systems,and gives their approximation error bounds with the parameters of membership functions.Finally,experiments are designed to compare the approximation capability of different fuzzy systems.Experimental results further verify the correctness of the theoretical analysis.