### 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

### 伪BL-代数的犹豫模糊滤子

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.