AN INVESTIGATION OF F-CLOSURE OF INTUITIONISTIC FUZZY SUBMODULES OF A MODULE

Abstract

In this paper, we introduce the notion of F-closure of intuitionistic fuzzy submodules of a module M. Our attempt is to investigate various characteristics of such an F-closure. If F is a non-empty set of intuitionistic fuzzy ideals of a commutative ring R and A is an intuitionistic fuzzy submodule of M, then the F-closure of A is denoted by ClM F (A). If F is weak closed under intersection, then (1) F-closure of A exhibits the submodule character, and (2) the intersection of F-closure of two intuitionistic fuzzy submodules equals the F-closure of intersection of the intuitionistic fuzzy submodules. If F is weak closed under intersection, then the submodule property of F-closure implies that F is closed. Moreover, if F is inductive, then F is a topological filter if and only if ClM F (A) is an intuitionistic fuzzy submodule for any intuitionistic fuzzy submodule A of M.