On intersection graph of intuitionistic fuzzy submodules of a module

Abstract EN

There are some interesting relations between submodules of a module and its intuitionistic fuzzy (IF) submodules.

In this paper we investigate some relationships between submodules of a module and its IF submodules.

Then we introduce a graph structure on IF submodules of a module and obtain some properties of it, that is the main goal of this paper.

We define the intersection graph of submodules of a module M (G ) and we show that a submodule N of M is a center in G ^ -0 if and only if is a center in G - ^.

We get some relationships between IF submodules of a module and their supports, as vertices of IF graph and crisp graph of a module M , respectively.

We show that an IF submodule A of M is center in IF graph of M if and only if A° is a center in crisp graph of M.

In prime ring R, we show that every vertex of intersection graph of IF ideals of R is center.

In general the nature of intersection graph of IF submodules of a module under intersection, homomorphic images, finite sum and other algebraic operations of its vertices, are investigated.