Annals of Fuzzy Mathematics and Informatics Volume 12, No. 6, (December 2016), pp. 805–823 ISSN: 2093–9310 (print version) ISSN: 2287–6235 (electronic version) http://www.afmi.or.kr @FMI c  Kyung Moon Sa Co. http://www.kyungmoon.com 1 2 3 Injectivity of intuitionistic fuzzy G-modules 4 P. K. Sharma, Simpi Chopra 5 Received 24 February 2016; Revised 20 June 2016; Accepted 24 June 2016 6 7 8 Abstract. In this article, we introduce the notion of injectivity and quasi injectivity of an intuitionistic fuzzy G-module. We also establish a condition on finite dimensional G-modules for which an intuitionistic fuzzy G-module is injective with respect to another intuitionistic fuzzy G-module. We discuss the injectivity of an intuitionistic fuzzy G-module with respect to the quotient intuitionistic fuzzy G-module of another G-module. Some important properties of injectivity of intuitionistic fuzzy G-modules with regards to direct sum of intuitionistic fuzzy G-modules are also studied. A relationship between injectivity and quasi injectivity of intuitionistic fuzzy G-modules is also obtained. 9 2010 AMS Classification: 03F 55, 13C11 10 Keywords: Intuitionistic fuzzy G-modules, G-module homomorphism, Injective 11 modules, Quasi-injective modules, Relatively injective modules. 12 Corresponding Author: P.K.Sharma (pksharma@davjalandhar.com) 13 14 15 1. Introduction 16 The concept of injectivity of modules was introduced by Eckmann and Schopf 17 [8]. Banaschewski [5] extended this work of injective and projective modules. Af- 18 ter this, many authors tried to generalize the concept of injective modules, for ex- 19 ample, Johnson and Wong [14] introduced quasi-injective modules. The notion of 20 M-injective modules was introduced by Azumaya in [4]. Singh [21] introduced the 21 notion of Pseudo injective modules. After the introduction of fuzzy sets by Zadeh 22 [23], the researchers have been carrying out research in various concepts of abstract 23 algebra in fuzzy setting. Rosenfeld [17] was the first one to define the concept of 24 fuzzy subgroups of a group. The literature of various fuzzy algebraic concepts have 25 been growing rapidly. In particular, Nagoita and Ralescu [15] introduced and ex- 26 amined the notion of fuzzy submodule of a module. Zahedi and Ameri [22] studied 27 about the fuzzy projectivity and fuzzy injectivity of modules. Fernadez introduced 28