On the Algebraic Attributes of (α, β)-Pythagorean Fuzzy Subrings and (α, β)-Pythagorean Fuzzy Ideals of Rings

Supriya Bhunia,Qin Xin,Muhammad Gulzar,Ganesh Ghorai

doi:10.1109/access.2022.3145376

Abstract

<inline-formula> <tex-math notation="LaTeX">$(\alpha,\beta)$ </tex-math></inline-formula>-Pythagorean fuzzy set is a very efficient way of dealing with uncertainty. In this article, we have introduced the notions of <inline-formula> <tex-math notation="LaTeX">$(\alpha,\beta)$ </tex-math></inline-formula>- Pythagorean fuzzy subring and <inline-formula> <tex-math notation="LaTeX">$(\alpha,\beta)$ </tex-math></inline-formula>- Pythagorean fuzzy ideal of a ring. Further, we have briefly described various results related to it. Also, we have discussed the level subring of an <inline-formula> <tex-math notation="LaTeX">$(\alpha,\beta)$ </tex-math></inline-formula>- Pythagorean fuzzy subring. Moreover, we have studied the direct product and ring homomorphism of <inline-formula> <tex-math notation="LaTeX">$(\alpha,\beta)$ </tex-math></inline-formula>- Pythagorean fuzzy subrings.

Highlights

I N classical ring theory, the concepts of subring and ideal are extremely important
We face a significant problem in dealing with errors in decision-making situations
In 1965, Zadeh [18] established the concept of a fuzzy set to deal with ambiguity in real-world situations, breaking the usual conception of yes or no

Summary

Introduction

I N classical ring theory, the concepts of subring and ideal are extremely important. S. Bhunia et al.: On the Algebraic Attributes of (α, β)-Pythagorean Fuzzy Subrings and (α, β)-Pythagorean Fuzzy Ideals of Rings 3) To describe (α, β)-Pythagorean fuzzy level subring of a ring 4) To discuss the direct product and ring homomorphism of (α, β)-Pythagorean fuzzy subring.

Results

Conclusion