In this paper, we establish the intuitionistic fuzzy version of the Lasker-Noether theorem for a commutative -ring. We show that in a commutative Noetherian -ring, every intuitionistic fuzzy ideal can be decomposed as the intersection of a finite number of intuitionistic fuzzy irreducible ideals (primary ideals). This decomposition is called an intuitionistic fuzzy primary decomposition. Further, we show that in case of a minimal intuitionistic fuzzy primary decomposition of , the set of all intuitionistic fuzzy associated prime ideals of is independent of the particular decomposition. We also discuss some other fundamental results pertaining to this concept.