多种模糊值函数微分定义的统一表述

Unified Definition of Differentials of Fuzzy-valued Functions

针对模糊值函数微分有多种定义,并且在形式难以得到统一的现状,提出了模糊数的广义限定性运算。在此基础上,利用[-1,1]上同序标准单调函数类与模糊实数空间的同胚性质,给出了广义限定差意义下的模糊值函数微分定义,并证明了这个定义与借助于扩张原理形式、借助于Hukuhara差形式和借助于模糊结构元形式的三种模糊值函数微分定义是等价的,进而得到了基于模糊结构元方法的模糊值函数微分定义的统一表述。

In this paper we present the concept of generalized fuzzy arithmetic with requisite constraints, in order to solve the problems that differential of fuzzy-valued function have various definitions and difficult to be uniformed. Accordingly, apply the homeomorphic property between the family of standard function with same monotonic formal on [-1, 1] and fuzzy real number space, we put forward a definition of differential of fuzzy-valued function based on generalized subtractive operation with requisite constraints. At the same time, the paper shown this definition is equal to differential of fuzzy-valued function definitions which is based on extension principle, H-subtraction and Fuzzy structured element respectively.