By using the notion of interval-valued intuitionistic fuzzy relations, we form the poset (IVIR(X), $leq$) of interval-valued intuitionistic fuzzy relations on a given set X. In particular, we form the subposet (IVIE(X), $leq$) of interval-valued intuitionistic fuzzy equivalence relations on a given set X and prove that the poset (IVIE(X), $leq$) is a complete lattice with the least element and greatest element.