A novel structure of $ q $-rung orthopair fuzzy sets in ring theory

Dilshad Alghazzwi; Arshad Ali; Ahmad Almutlg; E. A. Abo-Tabl; A. A. Azzam; Dilshad Alghazzwi; Arshad Ali; Ahmad Almutlg; E. A. Abo-Tabl; A. A. Azzam

doi:10.3934/math.2023422

AIMS Mathematics

2023, Volume 8, Issue 4: 8365-8385. doi: 10.3934/math.2023422

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A novel structure of $ q $-rung orthopair fuzzy sets in ring theory

1.
Department of Mathematics College of Science & Arts, King Abdulaziz University, Rabigh, Saudi Arabia
2.
Department of Mathematics, National College of Business Adminstration and Economics, Lahore, Pakistan
3.
Department of Mathematics, College of Science and Arts, Methnab, Qassim University, Buraidah 51931, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt
5.
Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
6.
Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt

Received: 30 October 2022 Revised: 15 January 2023 Accepted: 16 January 2023 Published: 03 February 2023
MSC : 05C25, 11E04, 20G15

The q-rung orthopair fuzzy atmosphere is an innovative approach for handling unclear circumstances in a range of decision making problems. As compare to intuitionistic fuzzy sets, this one is more appropriate and adaptable because it evaluates the significance of ring theory while retaining the features of q-rung orthopair fuzzy sets. In this study, we characterize $ q $-rung orthopair fuzzy subring as a modification of the pythagorean fuzzy subring. We introduce the novel idea of $ q $-rung orthopair fuzzy subring and investigate the algebraic characteristics for the $ q $-rung orthopair fuzzy subrings. Furthermore, we establish the concept of $ q $-rung orthopair fuzzy quotient ring and $ q $-rung orthopair fuzzy left and right ideals. Also, we describe the $ q $-rung orthopair fuzzy level subring and associate axioms. Finally, we investigate how ring homomorphism influences the q-rung orthopair fuzzy subring and investigate there pre-images homomorphism on $ q $-ROFSR and different aspects of images.
- fuzzy ideal,
- orthopair,
- quotient ring,
- fuzzy level subring
Citation: Dilshad Alghazzwi, Arshad Ali, Ahmad Almutlg, E. A. Abo-Tabl, A. A. Azzam. A novel structure of $ q $-rung orthopair fuzzy sets in ring theory[J]. AIMS Mathematics, 2023, 8(4): 8365-8385. doi: 10.3934/math.2023422

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Abstract

The q-rung orthopair fuzzy atmosphere is an innovative approach for handling unclear circumstances in a range of decision making problems. As compare to intuitionistic fuzzy sets, this one is more appropriate and adaptable because it evaluates the significance of ring theory while retaining the features of q-rung orthopair fuzzy sets. In this study, we characterize $ q $-rung orthopair fuzzy subring as a modification of the pythagorean fuzzy subring. We introduce the novel idea of $ q $-rung orthopair fuzzy subring and investigate the algebraic characteristics for the $ q $-rung orthopair fuzzy subrings. Furthermore, we establish the concept of $ q $-rung orthopair fuzzy quotient ring and $ q $-rung orthopair fuzzy left and right ideals. Also, we describe the $ q $-rung orthopair fuzzy level subring and associate axioms. Finally, we investigate how ring homomorphism influences the q-rung orthopair fuzzy subring and investigate there pre-images homomorphism on $ q $-ROFSR and different aspects of images.

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