基于结构元理论的复模糊值和函数及泰勒级数

Research on sum function and Taylor series of complex fuzzy value based on structural element theory

借助于结构元理论给出了复模糊值和函数定义及级数存在和函数的充要条件,对和函数的连续性、可微性及可积性进行了探讨,得到了相关的定理并给出证明.在定义结构元线性生成的泰勒级数和麦克劳林级数基础上,给出了复模糊值函数展成泰勒级数的充要条件.所得结论对进一步完善模糊复分析理论将起到一定的促进作用.

The definition of sum function of complex fuzzy value and the necessary and sufficient condition of sum function existence of series was given on the base of structural element theory. The continuity, differentiability and integration of the sum function was discussed, and related theory was proposed and proved. The necessary and sufficient conditions of complex fuzzy value functions developing into Taylor series was given on the base of the definition of Taylor series and Macuaurin series which are linely generated by structural element. These conclusions will promote the further development of the fuzzy complex analysis theory.