The lattice generated by hesitant fuzzy filters in pseudo-BCI algebras

Abstract

The notion of hesitant fuzzy set is introduced by V. Torra, which is a very useful tool to express peoples' hesitancy in daily life. The notion of pseudo-BCI algebra is introduced by W. A. Dudek and Y. B. Jun, which is a kind of nonclassical logic algebra and close connection with various non-commutative fuzzy logic algebras. In this paper, hesitant fuzzy theory is applied to pseudo-BCI algebras. The new concepts of hesitant fuzzy filter and anti-grouped hesitant fuzzy filter in pseudo-BCI algebras are proposed, and their characterizations are presented. Also, the relationships between fuzzy filters and hesitant fuzzy filters are discussed. Moreover, by introducing the notion of tip-extended pair of hesitant fuzzy filters, a new union operation (generated by the union of two hesitant fuzzy filters) is defined and it is proved that the set of all hesitant fuzzy filters in pseudo-BCI algebras forms a bounded distributive lattice about intersection and the new union.