Picture fuzzy filters of pseudo-BCI algebras

Abstract

The notion of picture fuzzy set is introduced by B. C. Cuong, which is a common extension of fuzzy set and intuitionistic fuzzy set. The notion of pseudo-BCI algebra is introduced by W. A. Dudek and Y. B. Jun, it is a kind of non-classical logic algebra and close connection with various non-commutative fuzzy logic algebras. In this paper, picture fuzzy theory is applied to pseudo-BCI algebras. The new concepts of picture fuzzy filter and anti-grouped picture fuzzy filter in pseudo-BCI algebras are proposed, and their characterizations are presented. Moreover, the relationships between fuzzy filters and picture fuzzy filters are discussed.