Abstract

In this paper, we introduce the concept of tensor product between intuitionistic fuzzy submodules. We establish a formal framework for the tensor product operation, examining its properties and applications within the context of intuitionistic fuzzy modules. We then establish a relationship between the Hom functor and the tensor product in the category of intuitionistic fuzzy modules. The connection between tensor products and hom-functors in some algebraic structures, such as modules, is made possible via a natural isomorphism known as the Hom-Tensor adjunction and it establishes a relationship between $\textbf{Hom}_{\textbf{C}_\textbf{R-IFM}}(B\otimes A, C)$ and $\textbf{Hom}_{\textbf{C}_\textbf{R-IFM}}(A, \textbf{Hom}_{\textbf{C}_\textbf{R-IFM}}(B, C))$. An application of tensor product of intuitionistic fuzzy modules can be used in decision-making processes by embracing ambiguity and vagueness, making it a valuable tool when exact data is lacking.

Keywords and Phrases

Hom functor, Tensor product, Category, Intuitionistic fuzzy $R$-homomorphism.

A.M.S. subject classification

03F55, 16D90, 18F22.

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