BL-代数中的犹豫模糊滤子  

Hesitant fuzzy filters of BL-algebras

作　　者：彭家寅[1] PENG Jiayin(School of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641100,China)

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641100

出　　处：《内江师范学院学报》2020年第4期12-20,27,共10页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11071178,11671284);教育部与四川省“数学与应用数学专业综合改革”项目(ZG0464,01249);四川科技厅重大前沿项目(2017JY0197);四川省教育厅项目(15TD0027)。

摘　　要：初步建立了BL-代数的犹豫模糊滤子理论的基本框架.引入了BL-代数的犹豫模糊滤子(格滤子,素滤子,Boolean滤子,蕴涵滤子,正蕴涵滤子,超滤子和固执滤子)的概念,讨论了它们的相关性质.证明了犹豫模糊滤子、犹豫模糊Boolean滤子和犹豫模糊超滤子分别等价于犹豫模糊格滤子、犹豫模糊蕴涵滤子和犹豫模糊固执滤子.在BL-代数中,每个犹豫模糊Boolean滤子必为犹豫模糊正蕴涵滤子,其逆不真.探明了犹豫模糊正蕴涵滤子成为犹豫模糊Boolean滤波子的条件.The basic framework of the hesitant fuzzy filter theory for BL-algebras is preliminarily established.The concepts of hesitant fuzzy filters(lattice filters,prime filters,Boolean filters,implicative filters,positive implicative filters,ultra filters and obstinate filters)of BL-algebras are introduced and their related properties are also discussed.It is proved that hesitant fuzzy filters,hesitant fuzzy Boolean filters and hesitant fuzzy ultra filters are equivalent to hesitant fuzzy lattice filters,hesitant fuzzy implicative filters and hesitant fuzzy obstinate filters,respectively.In BL-algebra,every hesitant fuzzy Boolean filter must be a hesitant fuzzy positive implicative filter,but the converse may not be true.The condition that the hesitant fuzzy positive implicative filter becomes the hesitant fuzzy Boolean filter is ascertained.

关 键 词：BL-代数 犹豫模糊集 犹豫模糊滤子(格滤子、素滤子、Boolean滤子、蕴涵滤子、正蕴涵滤子、超滤子与固执滤子) 

分 类 号：O153.2[理学—数学]