Fuzzy蕴涵代数的素犹豫模糊滤子及其谱空间  

Prime hesitant fuzzy filters in fuzzy implication algebras and its spectral spaces

作　　者：刘春辉 LIU Chunhui(School of Educational Science,Chifeng University,Chifeng 024001,Inner Mongolia,China)

机构地区：[1]赤峰学院教育科学学院,内蒙古赤峰024001

出　　处：《山东大学学报（理学版）》2023年第12期108-117,共10页Journal of Shandong University(Natural Science)

基　　金：内蒙古自治区高等学校科学研究项目(NJZY21138,NJZY22146);赤峰学院一流扶持学科(数学及计算机科学与技术)建设经费资助项目。

摘　　要：运用犹豫模糊集和拓扑学的方法及原理对Fuzzy蕴涵代数的滤子问题做深入研究。首先,引入Fuzzy蕴涵代数的素犹豫模糊滤子概念并考察其性质特征,建立并证明了并半格Fuzzy蕴涵代数的素犹豫模糊滤子定理;其次,在一个给定的Fuzzy蕴涵代数(X,→,0)的全体素犹豫模糊滤子之集PHFil(X)上构造了一个拓扑τ,获得拓扑τ的一个基,证明拓扑空间(PHFil(X),τ)是T_(0)空间。In this paper,filters problem of fuzzy implication algebras is further studied by using the method and principle of hesitant fuzzy sets and topology.Firstly,the notion of prime hesitant fuzzy filter in fuzzy implication algebras is introduced and its properties are investigated.The prime hesitant fuzzy filter theorem is established and proved of upper semilattice fuzzy implication algebras.Secondly,a topology τ is constructed on the set PHFil(X)consisting of all prime hesitant fuzzy filters in a given fuzzy implication algebra(X,→,0),a base is obtained of the topology τ and it is proved that the topological space(PHFil(X),τ)is a T_(0) space.

关 键 词：模糊逻辑 FUZZY蕴涵代数 素犹豫模糊滤子 谱空间 

分 类 号：O141.1[理学—数学] O189.1[理学—基础数学]