In this article, we introduce the notion of projectivity and quasi-projectivity of an intuitionistic fuzzy G-module. We also establish a condition on finite dimensional G-modules for which an intuitionistic fuzzy G-module is projective with respect to another intuitionistic fuzzy G-module. We discuss the projectivity of an intuitionistic fuzzy G-module with respect to the quotient intuitionistic fuzzy G-module of another G-module. Some important properties of projectivity of intuitionistic fuzzy G-modules with respect to the direct sum of intuitinistic fuzzy G-modules are also studied. A relationship between projectivity and quasi-projectivity of intuitionistic fuzzy G-modules is also obtained.

G-module, intuitionistic fuzzy G-module, intuitionistic fuzzy projectivity, self projectivity.