结构元线性生成的模糊值函数的连续性

The Continuity of Fuzzy Valued Function for Linear Generation of Structural Elements

用一种模糊距离给出了结构元线性生成的模糊值函数极限的一种新定义.然后用这种极限定义研究了结构元线性生成的模糊值函数在点连续的局部有界性、局部保号性、加法、减法及数乘运算;在闭区间上连续的有界性、最值定理、根的存在性定理、介值定理、一致连续性等基本性质.同时还全新定义了结构元线性生成的复合模糊值函数、结构元线性生成的反模糊值函数,并探讨其连续性.

A kind of fuzzy distance give is used to a new definition of the limit of fuzzy valued function for linear generation of structural elements. Then the limit definition is used to study the continuous basic properties of fuzzy valued function in the linear generation of structural elements at a certain point of the local boundedness,local preserving number,addition,subtraction and multiplication; the boundedness of continuous function on closed interval,maximum minimum theorem,the existence theorem of root,the intermediate value theorem and identical continuity. Meanwhile,the new compound fuzzy valued function for linear generation of structural elements and inverse fuzzy valued function for linear generation of structural elements are also defined. The continuity of them is discussed as well.