In this paper, we discuss and study certain properties of interval-valued intuitionistic fuzzy sets and their level subsets. We introduce a special class of interval-valued intuitionistic fuzzy ideals of a ring having the same tip and prove that it forms a complete sublattice of the lattice of interval-valued intuitionistic fuzzy ideal of a ring. Further a sub-class of the interval-valued intuitionistic fuzzy ideals with the same tip is introduced and shows that it forms a complete modular sublattice of the lattice of interval-valued intuitionistic fuzzy ideal of a ring.

interval-valued intuitionistic fuzzy set, level sets, strong level sets, interval-valued intuitionistic fuzzy subrings, interval-valued intuitionistic fuzzy ideals, modular lattice.