Fuzzy蕴涵代数的犹豫模糊滤子格  

The Lattice of Hesitant Fuzzy Filters in a Given Fuzzy Implication Algebra

作　　者：刘春辉 LIU Chun-hui(School of Mathematics and Computer Science,Chifeng University,Chifeng 024001,China)

机构地区：[1]赤峰学院数学与计算机科学学院,内蒙古赤峰024001

出　　处：《模糊系统与数学》2021年第4期30-39,共10页Fuzzy Systems and Mathematics

基　　金：内蒙古自治区高等学校科学研究项目(NJZY18206)。

摘　　要：对Fuzzy蕴涵代数的犹豫模糊滤子问题作进一步深入研究。引入了由Fuzzy蕴涵代数上的一个犹豫模糊集生成的犹豫模糊滤子概念,给出了其基本性质并建立了其表示定理。证明了一个Fuzzy蕴涵代数(X,→,0)的全体犹豫模糊滤子之集HFil(X)在犹豫模糊包含序?H下构成一个分配的连续(代数)格,从而构成一个Frame.In this paper, the problem of hesitant fuzzy filters in Fuzzy implication algebras is further studied. The notion of hesitant fuzzy filter which is generated by a hesitant fuzzy set on Fuzzy implication algebras is introduced and its representation theorem is established. It is proved that the set HFil(X) consisting of all hesitant fuzzy filters in a given Fuzzy implication algebra(X,→,0), under hesitant fuzzy inclusion order ?H forms a distributive continuous(algebraic) lattice, and particularly forms a frame.

关 键 词：FUZZY蕴涵代数 犹豫模糊滤子 生成犹豫模糊滤子 连续格 代数格 FRAME 

分 类 号：O141[理学—数学] O153[理学—基础数学]