基于结构元理论的复Fuzzy数及运算

模糊结构元理论在模糊数、模糊值函数及模糊数四则运算方面取得了丰硕的研究成果,而在复模糊数研究方面尚属起步阶段,只是借助模糊结构元理论,相继研究了结构元线性生成的复模糊数及其运算,得到一些有价值的结论。在此基础上给出基于结构元理论的一般复Fuzzy数的定义,并借助模糊数相关理论定义了2个复模糊数的距离、大小关系、上下界及四则运算,同时对结构元生成的复Fuzzy数四则运算进行了探讨,确定了复Fuzzy数四则运算的隶属函数的表达式并给予证明。

Study on Double Fuzzy Numbers and Operations Based on Structural-element Theory

There have been many achievements in fuzzy structural-element theory about fuzzy numbers,fuzzy value functions and operations of fuzzy numbers.But it is still at its initial stage.Some studies are made about liner double fuzzy numbers and operations on the basis of fuzzy structural-element,and some results are achieved.Then,some definitions are given for the distance,size relations,upper and lower bound and four arithmetic operations between two double fuzzy numbers.At the same time,the four arithmetic operations of double fuzzy numbers is discussed.At last,the subordinate function expression of four arithmetic operation of double fuzzy numbers is given and proved.