Intuitionistic fuzzy characteristic of a ring

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.

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 ...

International Journal of Mathematics and Computer Science, 2018

In this paper, we further study the theory of intuitionistic fuzzy rings and give some new concepts such as intuitionistic fuzzy ring with operators, intuitionistic fuzzy ideal with operators , intuitionistic fuzzy quotient ring with operators, etc. while their some elementary properties are discussed.

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.

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.

South East Asian J. of Mathematics and Mathematical Sciences

In this paper, we define the notion of intuitionistic fuzzy characteristic ideal (IFCI) of a Γ-ring which is analogue of a characteristic ideal in the ordinary ring theory and derive various new results. The correlation between the set of all automorphisms of Γ-ring and the corresponding automorphisms of its operator rings have been innovated. Then a one to one correlation between the set of all intuitionistic fuzzy characteristic ideals of Γ-ring and that of its operator ring has been constituted. This is used to obtain a similar bijection for characteristic ideals.

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,

Transstellar Journal , 2019

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

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.

Notes on Intuitionistic Fuzzy Sets

In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we prove that every homomorphic image of a prime ideal of a Γ-ring generated by an Aγ-prime element and translational invariant and f-invariant intuitionistic fuzzy subset is also a prime ideal.