(α, β)-fuzzy interior ideals in ordered semigroups

Abstract

In this paper, we introduce the concept of (α, β)-fuzzy interior ideal in ordered semigroups, which is a generalization of a fuzzy interior ideal in ordered semigroup. We investigate the related properties of ordered semigroups in terms of (α, β)-fuzzy interior ideals. The concepts of an (∈,∈ ∨q)-fuzzy interior ideal and (∈,∈ ∨q)-fuzzy ideal coincide in case of regular(resp. intra-regular) ordered semigroups.