Category of Intuitionistic Fuzzy Modules

Abstract

We study the relationship between the category of R-modules (CR-M) and the category of intuitionistic fuzzy modules (CR−IFM). We construct a category CLat(R−IFM) of complete lattices corresponding to every object in CR−M and then show that, corresponding to each morphism in CR−M, there exists a contravariant functor from CR−IFM to the category CLat (=union of all CLat(R−IFM), corresponding to each object in CR−M) that preserve infima. Then, we show that the category CR−IFM forms a top category over the category CR−M. Finally, we define and discuss the concept of kernel and cokernel in CR−IFM and show that CR−IFM is not an Abelian Category.

Keywords

• intuitionistic fuzzy modules
• intuitionistic fuzzy <i>R</i>-homomorphism
• category
• covariant functor
• contravariant functor