TENSOR PRODUCT OF INTUITIONISTIC FUZZY MODULES

P. K. Sharma; Chandni H.R

doi:10.56827/JRSMMS.2023.1101.9

P. K. Sharma P.G. Department of Mathematics, D.A.V. College, Jalandhar, Punjab, INDIA
Chandni H.R Department of Mathematics, Lovely Professional University, Jalandhar, Punjab, INDIA

DOI: https://doi.org/10.56827/JRSMMS.2023.1101.9

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

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 HomTensor adjunction and it establishes a relationship between HomCR-IFM (B⊗A,C) and HomCR-IFM (A,HomCR-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.