Exact sequence of intuitionistic fuzzy G-modules

In this article, we introduce the notion of projectivity and quasi-projectivity of an intuitionistic fuzzy G-module. We also establish a condition on finite dimensional G-modules for which an intuitionistic fuzzy G-module is projective with respect to another intuitionistic fuzzy G-module. We discuss the projectivity of an intuitionistic fuzzy

In this paper, we will introduce the notion of intuitionistic fuzzy G-module by defining the group action of G on the intuitionistic fuzzy set of Z-module M on which G-acts. We obtain the conditions when an intuitionistic fuzzy submodule be an intuitionstic fuzzy G-submodule. Some new notion like intuitionistic fuzzy prime submodule, intuitionistic fuzzy prime G-submodule, intuitionistic fuzzy semi prime submodule, intuitionistic fuzzy G-semi prime submodule, G-invariant intuitionistic fuzzy submodule and G-invariant intuitionistic fuzzy prime submodule of M will be introduced and studied. The homomorphic image and pre-image of intuitionistic fuzzy G-submodules, G-invariant intuitionistic fuzzy submodules and G-invariant intuitionistic fuzzy prime submodules of M will be established.

Advances in Fuzzy Sets and Systems, 2024

In this paper, we study the properties of intuitionistic fuzzy modules from the categorical point of view by proving that the category CR-IFM of intuitionistic fuzzy modules has products, coproducts, equalizers and coequalizers. Then, we show that every intuitionistic fuzzy coretraction (retraction) is an intuitionistic fuzzy equalizer (coequalizer). Further, categorical goodness of intuitionistic fuzzy modules is illustrated by proving that the category of intuitionistic fuzzy modules CR IFM is complete and co-complete.

Notes on Intuitionsitic Fuzzy Sets , 2024

In this paper, we introduce and explore some novel concepts within the frame work of intuitionistic fuzzy module theory. First, we define the notion of an intuitionistic fuzzy chained module as a generalisation of chained modules, establishing it foundational properties. We then characterise intuitionistic fuzzy chained modules, in terms of its level-cut submodules. In addition to this, we describe an intuitionistic fuzzy chained module in terms of its intuitionistic fuzzy cyclic submodules. Finally, we demonstrate that under specific conditions, the intuitionistic fuzzy multiplication module is an intuitionistic fuzzy chained module.

In this paper, we introduce the notion of direct sum of intuitionistic fuzzy submodules of G-module M and discuss some related properties. If B and C are intuitionistic fuzzy submodules of G-module M and G-module N respectively, then we extend the definition of intuitionistic fuzzy submodules B and C to formulate intuitionistic fuzzy submodules of the direct sum M ⊕ N. It is proved that the support of the direct sum of intuitionistic fuzzy submodules B and C is equal to the direct sum of supports of intuitionistic fuzzy submodules B and C. Also we analyze the direct sum of arbitrary family of intuitionistic fuzzy submodules and obtained some results. We also introduce the notion of decomposability and indecomposility of intuitionistic fuzzy G-modules and prove some results. 2010 AMS Classification: 03F55, 16D10

2018

Fuzzy G-modules of fuzzy modules with respect to a t-norm were studied by some authors. Here we introduce the concept of intuitionis- tic fuzzy G-modules with respect to a t-norm and study some properties of them. Based of Atanassov's intuitionistic fuzzy submodule, the rela- tionship between them and t-norms and also t-conorms will be investi- gated in this paper. we will study nature of this kind of intuitionistic fuzzy submodules under algeraic operations.

Mathematics, 2022

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International Journal of Fuzzy Mathematics and Systems., 2012

In this paper, the notion of t-intuitionistic fuzzy cosets of a Intuitionistic fuzzy submodule and t-intuitionistic fuzzy quotient modules are defined and discussed. A homomorphism from a given module onto the set of all tintuitionistic fuzzy quotient module is established. Some related results has been derived.

Annals of Fuzzy Mathematics and Informatics, 2022

In this paper, we introduce and investigate the intuitionistic fuzzy multiplication modules over a commutative ring with non-zero identity. The basic properties of the intuitionistic fuzzy prime submodules of an intuitionistic fuzzy multiplication modules are characterized.

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.