\((\lambda,\mu)\)-fuzzy interior ideals of ordered \(\Gamma\)-semigroups

Abstract

For all \(\lambda,\mu\in [0,1]\) such that \(\lambda<\mu\), we first introduced the definitions of \((\lambda,\mu)\)-fuzzy ideals and \((\lambda,\mu)\)-fuzzy interior ideals of an ordered \(\Gamma\)-semigroup. Then we proved that in regular and in intra-regular ordered semigroups the \((\lambda,\mu)\)-fuzzy ideals and the \((\lambda,\mu)\)-fuzzy interior ideals coincide. Lastly, we introduced the concept of a \((\lambda,\mu)\)-fuzzy simple ordered \(\Gamma\)-semigroup and characterized the simple ordered \(\Gamma\)-semigroups in terms of \((\lambda,\mu)\)-fuzzy interior ideals.