Soft set theoretical approach to pseudo-BCI algebras

Abstract

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 a generalization of pseudo-BCK algebra which is close connection with various non-commutative fuzzy logic algebras. The concept of soft set is introduced by Molodtsov, it can be seen as a new mathematical tool for dealing with uncertainty. In this paper, soft set theory is applied to pseudo-BCI algebras, the new notions of soft pseudo-BCI algebras and filteristic soft pseudo-BCI algebras are introduced. The relationships between soft pseudo-BCI algebras and soft non-commutative residuated lattices are presented. The union, intersection, int-product, uni-product and difference operations of (filteristic) soft pseudo-BCI algebras are investigated. Finally, another application of soft set to pseudo-BCI algebras is discussed, the new concept of int-soft filters in pseudo-BCI algebras is introduced, and related properties are proved.