Behnam Talaee - Babol Noshirvani University of Technology, Shariati Ave, Babol, Iran.
Mehrnoosh Sobhani - Babol Noshirvani University of Technology, Shariati Ave, Babol, Iran.
Bijan Davvaz - Department of Mathematics, Yazd University, Yazd, Iran.

In this paper, we discuss the structure of intuitionistic fuzzy modules and investigate some fundamental properties of them. Also we study about intuitionistic fuzzy homomorphisms between intuitionistic fuzzy modules.We study about exact sequences, products and co-products, func- tors and relating topics in IFR−Mod and investigate the relationship between them, where IFR−Mod is category whose objects are intu- itionidtic fuzzy modules and morphisms are intuitionistic fuzzy homo-morphisms.For a commutative ring R and two intuitionistic  fuzzy R-modules A=(µA, νA) ≤IF M, B = (µB,  νB) ≤IF N,  we show that  (A, B) = (α, β) is an intuitionistic fuzzy R-module.

Intuitionistic fuzzy modules, Intuitionistic fuzzy projective mod-ules, Intuitionistic fuzzy exact sequences