模糊值函数积分的结构元表示及其性质

Calculus of fuzzy-valued function and its property based on structured element

针对模糊值函数黎曼积分应用模糊结构元理论进行研究.给出了限定运算的拓广定义并研究了其性质,利用模糊结构元理论,定义了模糊数值函数的积分,得到了模糊值函数的积分的解析表达式.研究结果表明:模糊数函数的积分具有限定可加性,不具有一般意义上的可加性,这是模糊积分与经典积分的关键区别.研究结论初步突破了对传统的模糊值函数积分的认识,同时运算比较简捷,解决了很多模糊值函数不可积和积分表述式难以解析表达的问题.

Based on the study on the Riemann integral of fuzzy-valued function by using the fuzzy structured element,this paper gave the extensional definition of the limited operations and its property,defined the calculus of fuzzy-valued function by using fuzzy structured element theory,and obtained the analytical expression of fuzzy-valued function integral.The results show that the fuzzy number function integral has limited additivity,and it does not have the general sense of the additive,and this is the key difference with the classical integral fuzzy integral.The conclusion breakout the traditional understanding of fuzzy-valued integrals initially,and the operation is simpler,it solves a lot of problems of fuzzy-valued functions which are not integrable and difficult to resolve with integral expressions.