If in an interval-valued intuitionistic fuzzy matrix each element is again a smaller interval-valued intuitionistic fuzzy matrix then the interval-valued intuitionistic fuzzy matrix is called interval-valued intuitionistic fuzzy partion matrix (IVIFPMs). In this paper, the concept of interval-valued intuitionistic fuzzy partion matrices (IVIFPMs) are introduced and defined different types of interval-valued intuitionistic fuzzy partion matrices (IVIFPMs). The operations like direct sum, Kronecker sum, Kronecker product of interval-valued intuitionistic fuzzy matrices are presented and shown that their resultant matrices are also interval-valued intuitionistic fuzzy partion matrices (IVIFPMs).