Volume 8 , Issue 1 , PP: 18-22, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Rashel Abu Hakmeh 1 * , Murhaf Obaidi 2
Doi: https://doi.org/10.54216/JNFS.080102
The main goal of this work is to study the solutions of linear congruencies in the standard and n-standard fuzzy number theoretical systems, where we present necessary and sufficient conditions for fuzzy congruence to be solvable in these systems. Also, we provide the conditions of fuzzy nilpotency and fuzzy invertibility modulo integers with many illustrated examples. On the other hand, we suggest an algorithm to generate fuzzy Pythagoras triples and fuzzy Pythagoras quadruples in the standard fuzzy number theoretical system.
standard fuzzy number theoretical system , n-standard system , fuzzy Pythagoras triple , fuzzy nilpotent element , fuzzy invertible element
[1] Akram M, Naz S (2019) A novel decision-making approach under complex Pythagorean fuzzy environment. Math Comput Appl 24(3):73
[2] Marashdeh MF, Salleh AR (2011) Intuitionistic fuzzy rings. Int J Algebra 5(1):37–47.
[3] Öztürk MA, Jun YB, Yazarli H (2010) A new view of fuzzy gamma rings. Hacet J Math Stat 39(3):365–378.
[4] Ashraf S, Abdullah S, Mahmood T, Ghani F, Mahmood T (2019c) Spherical fuzzy sets and their applications in multi-attribute decision-making problems. J Intell Fuzzy Syst 36(3):2829–2844.
[5] Murat Ozcek. (2023). The Intersections Based on Joint Observables In Fuzzy Probability. Galoitica: Journal of Mathematical Structures and Applications, 5 ( 2 ), 17-26 (Doi : https://doi.org/10.54216/GJMSA.050203).
[6] Mohammad Abobala. (2023). On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations. Galoitica: Journal of Mathematical Structures and Applications, 10 ( 1 ), 17-25 (Doi : https://doi.org/10.54216/GJMSA.0100102).
[7] Mohammad Abobala. (2024). On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System. Journal of Neutrosophic and Fuzzy Systems, 7 ( 2 ), 24-29 (Doi : https://doi.org/10.54216/JNFS.070202).
[8] Ahmed Hatip, Necati Olgun. (2024). On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules. Journal of Neutrosophic and Fuzzy Systems, 7 ( 2 ), 46-52 (Doi : https://doi.org/10.54216/JNFS.070205)
