On the Hesitant Fuzzy Commutative Filters and Hesitant Fuzzy Closed Filters in Pseudo BCI-algebras

Firstly, the concept of hesitant fuzzy anti-grouped filter in Pseudo BCI-algebra is proposed, and its properties and equivalent portrayals are given.Secondly, the concepts of hesitant fuzzy commutative filters and hesitant fuzzy closed filters in pseudo BCI-algebras are introduced, and their basic properties and equivalent conditions are investigated.The relationship between hesitant fuzzy commutative filters and hesitant fuzzy anti-grouped filters is discussed.Finally, some necessary and sufficient conditions for a hesitant fuzzy filter to be a hesitant fuzzy closed anti-grouped filter are derived.