Fuzzy set approach to ideal theory on Sheffer stroke BE-algebras

Abstract

This paper aims to apply fuzzy set theory to Sheffer stroke BE-algebras. The concepts of fuzzy SBE-ideals and anti-fuzzy SBE-ideals of Sheffer stroke BE-algebras are introduced, and their important properties are investigated. Characterizations of SBE-ideals of SBE-algebras are given in terms of fuzzy SBE-ideals and anti-fuzzy SBE-ideals. Relationships between fuzzy SBEideals and anti-fuzzy SBE-ideals and their level subsets are discussed. We especially characterize fuzzy SBE-ideals and anti-fuzzy SBE-ideals by their level subsets.