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-aşgebras are introduced, and several properties are investigated. The relations among betweena biploar-valued fuzzy set, a biploar-valued fuzzy filter, a biploar-valued fuzzy  quasi-subalgebra and a biploar-valued fuzzy ultra filer are studied and necassasy and sufficiendt conditions are given. We prove that every biploar-valued fuzzy filter is a biploar-valued fuzzy quasi-subalgebra.