Intuitionistic L-fuzzy essential and closed submodules

Advances in Fuzzy Sets and Systems, 2020

The aim of this paper is to study the concept of intuitionistic L-fuzzy submodules of an R-module M. In this direction, definitions and properties like intersection, sum, product and Cartesian product of two intuitionistic L-fuzzy submodules are defined and discussed. We also introduce the notion of intuitionistic L-fuzzy quotient R-module. The effect of lattice homomorphisms

South East Asian J. of Mathematics and Mathematical Sciences, 2023

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 Cl M 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 Cl M F (A) is an intuitionistic fuzzy submodule for any intuitionistic fuzzy submodule A of M .

In this paper, we introduce the concept of intuitionistic fuzzy supplement submodules of a module. We attempt to investigate various properties of such submodules. Also we define an intuitionistic fuzzy coclosed submodules and study the relationship with intuitionistic fuzzy supplement submodules.

researchgate.net

The Author has introduced the notion of intuitionistic anti-fuzzy subring and ideal in a ring and studied their properties in . In this paper, the notion of intuitionistic anti-fuzzy submodule of a module is introduced and some of their properties has been discussed.

Let R be a commutative ring and B be an intuitionistic fuzzy submodule (IFSM) of an R-module M. Then an IFSM A of M is called B-essential in M provided for each IFSM C of M , A∩C ⊆ B implies that C ⊆ B. Further, for IFSMs A, B, C of M , the IFSM C is called B-complement to A if C is maximal with respect to the property that A ∩ C ⊆ B. We study these mentioned notations which are generalization of the intuitionistic fuzzy essential (compliment) submodules, introduced by Basnet in [5]. Here we shall study some related results.

Malaya Journal of Matematik, 2020

In the present manuscript, we introduce and study the notion of primary submodules as well as P-primary submodules of a module in the intuitionistic L-fuzzy environment. Apart from investigating basic properties of these submodules, we explore some foundational results analogous to corresponding submodules. A suitable characterization of intuitionistic L-fuzzy primary (P-primary) submodules in terms of primary (P-primary) submodules are presented.

In this paper, we introduce the concept of intuitionistic fuzzy small submodule with respect to an arbitrary intuitionistic fuzzy submodule of an R-module M. We derive the condition when an intuitionistic fuzzy submodule to be a small submodule with respect to another intuitionistic fuzzy submodule with the crisp small submodule of the R-module M. It is also shown that the sum of two intuitionistic fuzzy small submodules with respect to a fixed intuitionistic fuzzy submodule is again an intuitionistic fuzzy submodule with respect to the same fixed intuitionistic fuzzy submodule. This result can be extended to an arbitrary sum of intuitionistic fuzzy submodules. Further, we prove that the homomorphic image of an intuitionistic fuzzy small submodule with respect to a fixed intuitionistic fuzzy submodule is again an intuitionistic fuzzy small submodule with respect the homomorphic image of the fixed intuitionistic fuzzy submodule.

Information Sciences, 2006

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to H v -modules. The notion of an intuitionistic fuzzy H v -submodule of an H vmodule is introduced, and some related properties are investigated. Characterizations of intuitionistic fuzzy H v -submodules are given.

CiiT International Journal of Fuzzy Systems, 2017

Let M be an R-module, A and B are intuitionistic fuzzy submodules of M with A  B. Then A is called an intuitionistic fuzzy cosmall submodule of B in M if B / A << IF M /A (=  (M) / A *). In this paper an attempt has been to study intuitionistic fuzzy cosmall submodules and investigate various properties of such intuitionistic fuzzy submodules. The notion of an intuitionistic fuzzy hollow module is also introduce and a relationship of this with the intuitionistic fuzzy indecomposable module and the factor module are established.

In this paper we try to study the intuitionistic-fuzzy aspects of socle of modules over rings. We demonstrate some properties of a socle of intuitionistic-fuzzy submodules and their relations with intuitionistic-fuzzy essential submodules and a family of intuitionistic-fuzzy complemented submodules of a module. Some related results are also established.