区间值模糊集中蕴涵算子基于重叠和分组函数的分配性  

Distributivity of Implication Operator on Overlap and Grouping Functions in Interval-Valued Fuzzy Set

作　　者：吴涛 赵彬[1] WU Tao;ZHAO Bin(School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China)

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《吉林大学学报（理学版）》2019年第5期1014-1022,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11531009;11971286)

摘　　要：用区间值模糊集的方法和原理,通过引入可表示的区间值重叠函数和分组函数的概念,在边界条件下给出以下4种方程及类似方程的解:I(x,O1(y,z))=O2(I(x,y),I(x,z));I(Ox,y,z)=G(I(x,z),I(y,z));I(G(x,y),z)=OI(x,z),I(y,z);I(x,G1(y,z))=G2(I(x,y),I(x,z)).并说明t-可表示的连续Archimedean三角模(三角余模)分配性方程的解类似于上述结果.Using the method and principle of interval-valued fuzzy set,we introduced the concepts of representable interval overlap and grouping functions,under the boundary conditions,the solutions to the following four functional equations and the like were given:I(x,O1(y,z))=O2(I(x,y),I(x,z));I(Ox,y,z)=G(I(x,z),I(y,z));I(G(x,y),z)=OI(x,z),I(y,z);I(x,G1(y,z))=G2(I(x,y),I(x,z)).It was shown that the solutions of the distributivity equations about t-representable and continuous Archimedean t-norms(t-conorms)were similar to the above results.

关 键 词：区间值模糊集 模糊蕴涵 分配性 重叠函数 分组函数 函数方程 

分 类 号：O159.1[理学—数学]