Group action on intuitionistic fuzzy ideals of near rings
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This article investigates the effect of group action on the intuitionistic fuzzy ideals of a near ring $\mathcal{N}$. We establish a connection between intuitionistic fuzzy $\mathcal{G}$-prime ideals and intuitionistic fuzzy prime ideals of $\mathcal{N}$. Specifically, we show that the largest $\mathcal{G}$-invariant intuitionistic fuzzy ideal contained in an intuitionistic fuzzy prime ideal, is an intuitionistic fuzzy $\mathcal{G}$-prime ideal of $\mathcal{N}$. Additionally, we demonstrate that for every intuitionistic fuzzy $\mathcal{G}$-prime ideal $Q$ of $\mathcal{N}$, there exists an intuitionistic fuzzy prime ideal $P$ of $\mathcal{N}$ such that $P^{\mathcal{G}} = Q$ where $P$ is unique up to $\mathcal{G}$-orbits. The article also explores the relationship between intuitionistic fuzzy $\mathcal{G}$-prime ideals and their level cuts under group action. Moreover, we provide a characterization of intuitionistic fuzzy $\mathcal{G}$-prime ideals of $\mathcal{N}$ in terms of intuitionistic fuzzy points of $\mathcal{N}$ under this group action. Lastly, we examine the behavior of intuitionistic fuzzy $\mathcal{G}$-prime ideals of a near ring under $\mathcal{G}$-homomorphisms.
Abstract
This article investigates the effect of group action on the intuitionistic fuzzy ideals of a near ring $\mathcal{N}$. We establish a connection between intuitionistic fuzzy $\mathcal{G}$-prime ideals and intuitionistic fuzzy prime ideals of $\mathcal{N}$. Specifically, we show that the largest $\mathcal{G}$-invariant intuitionistic fuzzy ideal contained in an intuitionistic fuzzy prime ideal, is an intuitionistic fuzzy $\mathcal{G}$-prime ideal of $\mathcal{N}$. Additionally, we demonstrate that for every intuitionistic fuzzy $\mathcal{G}$-prime ideal $Q$ of $\mathcal{N}$, there exists an intuitionistic fuzzy prime ideal $P$ of $\mathcal{N}$ such that $P^{\mathcal{G}} = Q$ where $P$ is unique up to $\mathcal{G}$-orbits. The article also explores the relationship between intuitionistic fuzzy $\mathcal{G}$-prime ideals and their level cuts under group action. Moreover, we provide a characterization of intuitionistic fuzzy $\mathcal{G}$-prime ideals of $\mathcal{N}$ in terms of intuitionistic fuzzy points of $\mathcal{N}$ under this group action. Lastly, we examine the behavior of intuitionistic fuzzy $\mathcal{G}$-prime ideals of a near ring under $\mathcal{G}$-homomorphisms.