D.C.隶属函数模糊集及其应用(II)——D.C.隶属函数模糊集的万能逼近性

Fuzzy Set Based on D.C.Membership Functions and Its Applications(II)——Universal Approximation of D.C.Membership Function Fuzzy Sets

本文是D.C.隶属函数模糊集及其应用系列研究的第二部分。指出在实际问题中普遍选用的三角形、半三角形、梯形、半梯形、高斯型、柯西型、S形、Z形、π形隶属函数模糊集等均为D.C.隶属函数模糊集,建立了D.C.隶属函数模糊集对模糊集的万有逼近性。探讨了D.C.隶属函数模糊集与模糊数之间的关系,给出了用D.C.隶属函数模糊集逼近模糊数的-εC e llina逼近形式,得到模糊数与D.C.函数之间的一个对应算子,指出了用模糊数表示D.C.函数的问题。

This paper is the second part of study for D. C. membership function fuzzy set and its applications. In this paper, we will point out that the fuzzy sets based on triangular, trapezoid, Gauss, Cauchy, S-type, Z-type, π-type membership functions are D.C. membership function fuzzy sets, give the universal approximation of D.C. membership function fuzzy sets, discuss the relations between D.C. membership functipn fuzzy sets and fuzzy numbers, give the ε-Cellina approximation of fuzzy numbers by D.C. membership function fuzzy sets, obtain an operator from fuzzy number space to D. C. function space, point out the representation problem of D. C. function by fuzzy numbers.