Computer Engineering and Applications ›› 2019, Vol. 55 ›› Issue (13): 42-50.DOI: 10.3778/j.issn.1002-8331.1810-0268

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Hesitant Fuzzy Filters of Pseudo BL-Algebras

PENG Jiayin   

  1. School of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641199, China
  • Online:2019-07-01 Published:2019-07-01



  1. 内江师范学院 数学与信息科学学院,四川 内江 641199

Abstract: The concept of hesitant fuzzy filters of pseudo BL-algebras is proposed, the equivalent characterizations of hesitant fuzzy filters are given, and its properties are investigated. Furthermore, several kinds of hesitant fuzzy filters of pseudo BL-algebra are introduced, such as hesitant fuzzy Boolean filter, hesitant fuzzy normal filter, hesitant fuzzy ultrafilter and hesitant fuzzy obstinate filter. Some characterizations of them are discussed and some relations among the above hesitant fuzzy filters are given. By studying the relation between hesitant fuzzy Boolean filter and hesitant fuzzy normal filter in pseudo BL-algebras, it solves an open problem that whether or not every Boolean filter is normal in pseudo BL-algebras.

Key words: pseudo BL-algebra, hesitant fuzzy filter, hesitant fuzzy Boolean filter, hesitant fuzzy normal filter, hesitant fuzzy ultrafilter, hesitant fuzzy obstinate filter

摘要: 提出了伪BL-代数的犹豫模糊滤子的概念,给出它的几个等价刻画,并研究了它的一些性质。进一步,引入了伪BL-代数的几种犹豫模糊滤子,如犹豫模糊Boolean滤子、犹豫模糊正规滤子、犹豫模糊超滤子和犹豫模糊固执滤子,讨论了它们的一些刻画,给出了其间的一些关系。通过研究伪BL-代数中犹豫模糊Boolean滤子与犹豫模糊正规滤子的关系,解决了伪BL-代数中是否每个Boolean滤子都是正规滤子这样一个开问题。

关键词: 伪BL-代数, 犹豫模糊滤子, 犹豫模糊Boolean滤子, 犹豫模糊正规滤子, 犹豫模糊超滤子, 犹豫模糊固执滤子