(λ, μ)-fuzzy interior ideals of ordered Г-semigroups

Abstract

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