inf-α_R合成Fuzzy关系方程的解集  

inf-α_R Composition Fuzzy Relation Equation

作　　者：杨雪 吴莉 王学平[1] YANG Xue;WU Li;WANG Xueping(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan;College of Mathematics and Computer Science,Aba Teachers University,Wenchuan 623002,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 [2]阿坝师范学院数学与计算机科学学院,四川汶川623002

出　　处：《四川师范大学学报（自然科学版）》2018年第6期729-734,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(61573240)

摘　　要：讨论定义在[0,1]上的inf-αR合成Fuzzy关系方程,即对给定的Fuzzy关系R∈F(X×Y)和A∈F(Y),讨论是否存在X,使RαRX=A,其中,aαRb={MR, a≤b,b,否则,MR为R的最大元.给出inf-αR合成Fuzzy关系方程RαRX=A有解的充要条件,并给出了它的解集.This paper deals with infαR composition fuzzy relation equation over[0,1].That is,for a given fuzzy relation R∈F(X×Y)and a fuzzy set A∈F(X),determine the existence of X with RαR X=A is determined,where aαR b=MR, a≤b,{b, otherwise,MR is the greatest element of R.It gives necessary and sufficient conditions that the infαR composition fuzzy relation equation has solutions,and describes the set of all X which satisfy RαR X=A.

关 键 词：模糊关系 inf-αR合成模糊关系方程 解集 

分 类 号：O159[理学—数学]