In this paper, we establish the intuitionistic fuzzy version of the Lasker-Noether theorem for a commutative \Gamma-ring. We show that in a commutative Noetherian \Gamma-ring, every intuitionistic fuzzy ideal A 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 A, the set of all intuitionistic fuzzy associated prime ideals of A is independent of the particular decomposition. We also discuss some other fundamental results pertaining to this concept.



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 Lata, Hem,  Sharma, P. K., Bhardwa, Nitin