This paper presents a general framework for the study of (I, T)-interval-valued intuitionistic fuzzy rough sets integrating the intuitionistic rough set with the interval-valued fuzzy set theory by axiomatic approaches. Some primary properties of interval-valued fuzzy logical operators are first introduced and a pair of lower and upper interval-valued intuitionistic fuzzy rough approximation operators w.r.t. an arbitrary interval-valued intuitionistic fuzzy relations is then defined. Finally, an operator-oriented characterization of interval-valued intuittionistic fuzzy rough sets is proposed in the axiomatic approach, and some results about approximation operators are obtained.