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In this paper, we consider the intuitionistic fuzzication of the notion of a interior ideal in ordered semigroupS, andinvestigate some properties of such ideals. In terms of intuitionistic fuzzy set, characterizations of intuitionistic fuzzyinterior ideals in ordered semigroups are discussed. Using a collection of interior ideals with additional conditions, anintuitionistic fuzzy interiror ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy interiorideals of an ordered semigroup are investigated. We also give a characterization of a intuitionistic fuzzy simple semigroupin terms of intuitionistic fuzzy interior ideals.