Advances in Fuzzy Mathematics (AFM). 0973-533X Volume 12, Number 1 (2017), pp. 77–91 © Research India Publications http://www.ripublication.com/afm.htm Intuitionistic fuzzy divisible and pure submodule Devanjan Hazarika Department of Mathematics, D.H.S.K. College, Dibrugarh-786001, Assam, India. D.K. Basnet Department of Mathematical Sciences, Tezpur University, Napaam, Tezpur-784028, Assam, India. Abstract In this paper, the concepts of Intuitionistic fuzzy divisible sub-modules and Intu- itionistic fuzzy pure submodules are introduced. The sum, union, intersection etc. of Intuitionistic fuzzy divisible sub-modules as well as Intuitionistic fuzzy pure sub- modules and several other properties are discussed. Also some applications with level subsets ((α,β)-cut) of Intuitionistic fuzzy divisible and pure sub-modules are given. Lastly, the relation between Intuitionistic fuzzy divisible and pure sub- modules is discussed. AMS subject classification: 16D99. Keywords: Fuzzy sub-module, Divisible sub-module, Intuitionistic fuzzy Divisible sub-module, Pure sub-module, Intuitionistic fuzzy Pure sub-module. 1. Introduction Let R be a commutative ring with unity 1,R 0 be the set of all nonzero divisors of R and M be a left module over the ring R. Then M is called a divisible sub-module if ∀y ∈ M and ∀r ∈ R 0 , ∃x ∈ M s.t. y = rx . Yamak, Kazanc and Davvaz [7] defined and investigated some of the properties of Intuitionistic fuzzy divisible and Intuitionistic fuzzy pure subgroups. This leads us to think on the idea of Intuitionistic fuzzy divisible and pure sub-modules. In this article we discuss some of its interesting properties.