Abstract
In this thesis, the intuitionistic fuzzy injective act and intuitionistic fuzzy quasi-injective act have been introduced. We gave our motivation to introduce this concept by giving a commutative diagram which intuitionistic fuzzy injective S-act, intuitionistic fuzzy quasi-injective S-act and mentioned definitions of this concept. The notion of the subact of the intuitionistic fuzzy injective S-act and subact of intuitionistic fuzzy quasi-injective S-act have been introduced and we gave an example show that subact of intuitionistic fuzzy quasi-injective S-act need to be intuitionistic fuzzy quasi-injective S-act. Thus we investigated some kinds of intuitionistic fuzzy subact which inherit the intuitionistic fuzzy quasi-injective S-act property such as (intuitionistic fuzzy retract subact, intuitionistic fuzzy fully invariant subact) also intuitionistic fuzzy quasi-injective S-act has been defined and discussed its relationships with direct sum. The intuitionistic fuzzy exact sequence on S-act and the intuitionistic fuzzy functor homomorphism Hom (A,B) will be introduced and investigated.
