On the intuitionistic fuzzy polynomial ideals of a ring

2016

In this paper we further study the theory of Intuitionistic fuzzy ideals and intuitionistic fuzzy prime ideals. We have investigated these notions and shown a new result using the intu-itionistic fuzzy points and a membership and nonmembership functions.

Notes on Intuitionistic Fuzzy Sets, 2018

In this paper we investigate the radical structure of an intuitionistic fuzzy polynomial ideal A x induced by an intuitionistic fuzzy ideal A of a ring and study its properties. Given an intuitionistic fuzzy ideal B of a ring R and a homomorphism f : R → R , we show that if f x : R[x] → R [x] is the induced homomorphism of f , that is, f x (n i=0 a i x i) = n i=0 (f (a i))x i , then f −1 x [(√ B) x ] = (f −1 (B)) x .

2021

This Paper intends to introduce the notion of prime ideals of Intuitionistic fuzzy normed Rings and to establish basic properties related to it. It investigates these notions and shown anew Result using intuinistic fuzzy points and non membership function incorparating with t-norm and s-norm to show aome results of fuzzy prime ideal.

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.

Creative Mathematics and Informatics, 2023

In this paper, we introduced the notion of intuitionistic fuzzy prime radical of an intuitionistic fuzzy ideal in Γ-rings. We also characterise intuitionistic fuzzy primary ideal of Γ-rings. We also analyse homomorphic behaviour of intuitionistic fuzzy primary ideal and intuitionistic fuzzy prime radical of Γ-rings.

Transstellar Journal , 2019

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

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.

Palestine Journal of Mathematics, 2024

In this paper, we introduce the notion of expansion of intuitionistic fuzzy ideals of a commutative Γ-ring and by using this concept, we develop the notion of intuitionistic fuzzy f-primary ideals (2-absorbing f-primary ideals) which unify the notion of intuitionistic fuzzy prime ideals (2-absorbing ideals) and intuitionistic fuzzy primary ideals (2-absorbing primary ideals) of Γ-ring. A number of important results about intuitionistic fuzzy prime ideals (2-absorbing ideals) and intuitionistic fuzzy primary ideals (2-absorbing primary ideals) are extended into this general frame work.

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.

Creative Mathematics and Informatics, 2022

In this paper, we introduced the notion of intuitionistic fuzzy prime radical of an intuitionistic fuzzy ideal in Γ-rings. We also characterise intuitionistic fuzzy primary ideal of Γ-rings. We also analyse homomorphic behaviour of intuitionistic fuzzy primary ideal and intuitionistic fuzzy prime radical of Γ-rings.