In this paper, we present a novel combination of intuitionistic fuzzy Description Logics with intuitionistic fuzzy logic programs, which yields a more realistic and intelligent hybrid system, which offers the best of both aspects: the extension of Description Logics with intuitionistic fuzzy sets are suitable for describing vague and imprecise concepts in a given domain, on the other hand, intuitionistic fuzzy logic programs suffice for rules with vague atoms. We show that the new formalism remains faithful to both individual intuitionistic fuzzy components, and we provide the decidability and complexity of the framework under some suitable assumptions.