We consider the intuitionistic fuzzification of the concept of interior ideals in a semigroup S , and investigate some properties of such ideals. For any homomorphism f from a semigroup S to a semigroup T , if B = ( μ B , γ B ) is an intuitionistic fuzzy interior ideal of T , then the preimage f − 1 ( B ) = ( f − 1 ( μ B ) , f − 1 ( γ B ) ) of B under f is an intuitionistic fuzzy interior ideal of S .