结构元线性生成的模糊值函数的可导性  

The Definite Derivative of Fuzzy Valued Function for Linear Generation of Structural Elements

作　　者：舒天军 莫智文[1] SHU Tianjun;MO Zhiwen(College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan)

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2019年第1期69-76,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11671284);高等学校博士点基金(20135134110003)

摘　　要：用一种模糊距离给出结构元线性生成的模糊值函数极限的一种新定义,然后用这种极限给出结构元线性生成的模糊值函数导数的定义,并用该定义研究结构元线性生成的模糊值函数导数的加法、数乘运算、费马定理、罗尔定理、拉格朗日中值定理、极限定理、介值定理和极限的第一充分条件等基本性质.最后给出结构元线性生成的凸模糊值函数的定义,且探讨其性质.We use a kind of fuzzy distance to give a new definition of the definite integral of fuzzy valued function for linear generation of structural elements.Then the definite integral definition is used to define the derivative of fuzzy valued function for linear generation of structural elements.By using this derivative definition,we study the properties of fuzzy valued function in the linear generation of structural elements.They are addition together with multiplication,Fermat theorem,Rolle theorem,Lagrange mean value theorem,limit theorem,intermediate value theorem,the nature of the first limit,and so on.Finally,the definition of convex fuzzy valued function for linear generation of structural elements is given,and its properties are discussed.

关 键 词：结构元 模糊值函数 模糊距离 导数 

分 类 号：O159[理学—数学]