Intuitionistic Fuzzy Hx 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.

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.

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.

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.

2010

In this paper, we introduce the concept of intuitionistic fuzzy H-ideals in BCK-algebras and investigate some of its properties. Mathematics Subject Classification: 03E72, 03F55, 03G25

researchgate.net

As an abstraction of the geometric notion of translation, author [10 ] has introduced two operators T + and T -called the intuitionistic fuzzy translation operators on the intuitionistic fuzzy set and studied their properties and also investigate the action of these operators on the intuitionistic fuzzy subgroups of a group. Here in this paper we will study the action of these operators on the intuitionistic fuzzy subrings and ideals of a ring. Mathematics Subject Classification: 03F55, 08A72, 20N25.

In this paper, we define the concept of an intuitionistic Q-fuzzy HX group and also define the < α, β > - level subsets of an intuitionistic Q-fuzzy HX group and discussed the relation between a given an intuitionistic Q-fuzzy HX group and its < α, β > - level sub HX groups and investigate the conditions under which a given sub HX group has a properly inclusive chain of sub HX groups. In particular, we formulate how to structure a intuitionistic Q-fuzzy HX group by a given chain of sub HX groups.