Abstract: It is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are suitable, well-known logics for managing structured knowledge that have gained considerable attention the last decade. The work in this paper is directed towards sophisticated formalisms for reasoning under both fuzzy uncertainty and rough uncertainty in ontologies in the Semantic Web. Ontologies play a central role in the development for the Semantic Web, since they provide a precise definition of shared terms in Web resources. The current research progress and the existing problems of intuitionistic fuzzy rough DLs for the Semantic Web are analyzed. An integration between the theories of intuitionistic fuzzy DLs and rough DLs, i.e., intuitionistic fuzzy rough DLs, has been provided based on (I, T)-intuitionistic fuzzy rough set theory. Concretely, we present the intuitionistic fuzzy rough DL IFRSROIQ(D), which is the extension of the expressive DL SROIQ(D) behind OWL 2. It is proved that the reasoning tasks (knowledge base satisfiability, concept satisfiability, subsumption, logical consequence, ABox consistency, BTCB, and BSB reasoning) in the intuitionistic fuzzy rough DL IFRSROIQ(D) may be reduced to the corresponding reasoning in the fuzzy DL over complete lattices L*-SROIQ(D), respectively.