Category of Intuitionistic Fuzzy Modules

Poonam Kumar Sharma, Chandni and Nitin Bhardwaj
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Poonam Kumar Sharma: Department of Mathematics, D.A.V. College, Jalandhar 144008, India
Chandni: Research Scholar, Department of Mathematics, Lovely Professional University, Jalandhar 144402, India
Nitin Bhardwaj: Department of Mathematics, Lovely Professional University, Jalandhar 144402, India

Mathematics, 2022, vol. 10, issue 3, 1-14

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

Keywords: intuitionistic fuzzy modules; intuitionistic fuzzy R -homomorphism; category; covariant functor; contravariant functor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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