Intuitionistic Fuzzy Normed Subrings and Intuitionistic Fuzzy Normed Ideals

Abstract

The main goal of this paper is to introduce the notion of intuitionistic fuzzy normed rings and to establish basic properties related to it. We extend normed rings by incorporating the idea of intuitionistic fuzzy to normed rings, we develop a new structure of fuzzy rings which will be called an intuitionistic fuzzy normed ring. As an extension of intuitionistic fuzzy normed rings, we define the concept of intuitionistic fuzzy normed subrings and intuitionistic fuzzy normed ideals. Some essential operations specially subset, complement, union, intersection and several properties relating to the notion of generalized intuitionistic fuzzy normed rings are identified. Homomorphism and isomorphism of intuitionistic fuzzy normed subrings are characterized. We identify the image and the inverse image of intuitionistic fuzzy normed subrings under ring homomorphism and study their elementary properties. Some properties of intuitionistic fuzzy normed rings and relevant examples are presented.