格蕴涵代数的反犹豫模糊滤子  

The Anti-hesitant Fuzzy Filters in Lattice Implication Algebras

作　　者：傅小波[1] 张建忠[1] FU Xiao-bo;ZHANG Jian-zhong(Wuxi Institute of Technology,Wuxi 214121,China)

机构地区：[1]无锡职业技术学院,江苏无锡214121

出　　处：《模糊系统与数学》2020年第2期34-43,共10页Fuzzy Systems and Mathematics

基　　金：无锡职业技术学院校级科研课题(3116015931)。

摘　　要：本文研究了格蕴涵代数的反犹豫模糊滤子。将反犹豫模糊集应用于格蕴涵代数,提出反犹豫模糊滤子概念,得到了若干等价刻画;给出犹豫模糊集的反扩张定理,并讨论了反犹豫模糊滤子的像与原像的关系;最后定义了犹豫模糊集的反直积,研究了反犹豫模糊滤子与直积格蕴涵代数的反犹豫模糊滤子之间的关系,证明了乘积格蕴涵代数的犹豫模糊子集是反犹豫模糊滤子的必要条件。In this paper,we investigated the anti-hesitant fuzzy filter of lattice implications algebras. By applying the hesitant fuzzy set to lattice implications algebras,we proposed the concept of anti-hesitant fuzzy filter. Some equivalent characterizations of anti-hesitant fuzzy filter were given. The notion of anti-extension principle in hesitant fuzzy set was introduced, and some properties between homomorphic image and homomorphic preimage of anti-hesitant fuzzy filter were discussed. Finally, we defined the concept of anti-direct product in the hesitant fuzzy set. The relationships between anti-hesitant fuzzy filter in direct product lattice implication algebra and anti-hesitant fuzzy filter in lattice implication algebra were studied,and we proved the necessary condition that a hesitant fuzzy subset of the product lattice implication algebra is a anti-hesitant fuzzy filter.

关 键 词：格蕴涵代数 犹豫模糊集 反犹豫模糊滤子 反直积 

分 类 号：O159[理学—数学]