Intuitionistic Fuzzy Rings with Operators

International Journal of Algebra, 2011

In this paper we present a new formulation of intuitionistic fuzzy rings based on the notion of intuitionistic fuzzy space. A relation between intuitionistic fuzzy ring based on intuitionistic fuzzy space and ordinary rings is obtained in terms of induction and ...

Transstellar Journal , 2019

In this paper, we introduce the concept of-intuitionistic fuzzy ideal and-intuitionistic fuzzy ideal and study their properties.

JTAM (Jurnal Teori dan Aplikasi Matematika)

In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the value of 1-η∈[0,1]. In its development, new concepts were obtained, namely the η-intuitionistic fuzzy ideal and its properties related to the sum and product operation of η-intuitionistic fuzzy ideals. Furthermore, the η-intuitionistic fuzzy ideals concept can be developed into an η-intuitionistic fuzzy quotient ring, η-intuitionistic fuzzy homomorphism, and its properties on the next research.

MATHEMATICA MONTISNIGRI, 2020

In this paper, we extend the characterizations of Kuroki [17], by initiating the concept of intuitionistic fuzzy left (resp. right, interior, quasi-, bi-, generalized bi-) ideals in a class of non-associative and non-commutative rings (LA-ring). We characterize regular (intra-regular, both regular and intra-regular) LA-rings in terms such ideals.

IJMS, 2012

In this paper, we apply the Yuanli, Zhang, Quanma's idea of intuitionistic anti-fuzzy subgroups to subring and ideal of a ring. We introduce the notion of intuitionistic anti-fuzzy subring and intuitionistic anti-fuzzy ideal of rings, and investigate some related properties.

A JOURNAL OF COMPOSITION THEORY, 2019

In this paper, the notion of intuitionistic fuzzy Bi-Ideal of a ring are defined and discussed. Some of their properties are studied,

SSRN, 2021

The main aim of this paper is to investigate the relationship between the characteristic of a ring and the order of an element in the intuitionistic fuzzy environment. We also characterise the term divisor of zero in a ring and study their connection with the ideal of the ring in the intuitionistic fuzzy setting. Some related results are also analyse.

Journal of Mathematics, 2013

Maji et al. introduced the concept of intuitionistic fuzzy soft sets, which is an extension of soft sets and intuitionistic fuzzy sets. In this paper, we apply the concept of intuitionistic fuzzy soft sets to rings. The concept of intuitionistic fuzzy soft rings is introduced and some basic properties of intuitionistic fuzzy soft rings are given. Intersection, union, AND, and OR operations of intuitionistic fuzzy soft rings are defined. Then, the deffinitions of intuitionistic fuzzy soft ideals are proposed and some related results are considered.

In this paper we introduce the notion of intuitionistic fuzzy polynomial ideal A x of a polynomial ring R[x] induced by an intuitionistic fuzzy ideal A of a ring R, and obtain an isomorphism theorem of a ring of intuitionistic fuzzy cosets of A x. It is shown that an intuitionistic fuzzy ideal A of a ring is an intuitionistic fuzzy prime if and only if A x is an intuitionistic fuzzy prime ideal of R[x]. Moreover, we show that if A x is an intuitionistic fuzzy maximal ideal of R[x], then A is an intuitionistic fuzzy maximal ideal of R but converse is not true.

Pan-American Journal of Mathematics, 2022

The purpose of this paper is to introduce and investigate primary ideal and P-primary ideal in the intuitionistic fuzzy environment and lay down the foundation for the primary decomposition theorem in the intuitionistic fuzzy setting. Also a suitable characterization of intuitionistic fuzzy P-primary ideal will be discussed.