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

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