Ultra filters and quasi-subalgebras of Sheffer stroke BL-algebras based on the bipolar-valued fuzzy environment

Abstract

The notion of bipolar-valued filters and quasi-subalgebras of Sheffer stroke BL-algebras are introduced, and several properties are investigated. The relations among between a bipolar-valued fuzzy set, a bipolar-valued fuzzy filter, a bipolar-valued fuzzy quasi-subalgebra and a bipolar-valued fuzzy ultra filer-valued fuzzy ultra filer are studied and necassasy and sufficiendt conditions are given. We prove that every bipolar-valued fuzzy filter is a bipolar-valued fuzzy quasi-subalgebra.