Volume 25 • Issue 1 • PP: 172-178 • 2025
The Properties of Two-Fold Algebra Based on the n-standard Fuzzy Number Theoretical System
View PDF Abstract
In this paper, we study the two-fold algebra based on the n-standard fuzzy number theoretical system as a special type of two-fold fuzzy algebras, where we study the elementary properties of the algebraic operations defined over this system. Also, we prove many results that describe the relations between two-fold substructures and sub-algebras defined by fuzzy number theoretical systems. On the other hand, we provide many different examples to explain our results.
Keywords
References
[1] Mohammad Abobala. (2023). " 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).
[2] Ahmed Hatip, Necati Olgun. (2023). "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).
[3] 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).
[4] Florentine Smarandache.(2024). "Neutrosophic Two-Fold Algebra", Plithogenic Logic and Computation, 1(1), 11-15.
[5] Abobala, M., Sankari, H., & Zeina, M. (2024). " On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory". Journal of Fuzzy Extension and Applications, 5(1), 69-85. doi: 10.22105/jfea.2024.423818.1321.
[6] ] Hatamleh, R., Zolotarev, V. A., "On Model Representations of Non-Selfadjoint Operators with Infinitely Dimensional Imaginary Component ", ,Zurnal Matematiceskoj Fiziki, Analiza Geometrii, 11(2), 174–186,2015.
[7] Ayman Hazaymeh, Ahmad Qazza, Raed Hatamleh, Mohammad W Alomari, Rania Saadeh, “On Further Refinements of Numerical Radius, Inequalities”, Axiom-MDPI, 12(9),807,2023.
[8] Mayada Abualhomos, Wael Mahmoud M. Salameh, Malik Bataineh, Mowafaq Omar Al-Qadri, Ayman Alahmade, Abdallah Al-Husban. (2024). An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables". International Journal of Neutrosophic Science, 23 ( 4 ), 386-394.
[9] Mohammad Abobala. (2024). On Some Novel Results About Weak Fuzzy Complex Integers, Journal Neutrosophic and Fuzzy Systems, 8 ( 2 ), 15-22. (Doi : https://doi.org/10.54216/JNFS.080202)
[10] Hatamleh, R., Zolotarev, V. A., "Triangular Models of Commutative Systems of Linear Operators Close to Unitary Operators", Ukrainian Mathematical Journal,68(5),791–811,2006.
[11] Noor Edin Rabeh, Othman Al-Basheer, Sara Sawalmeh, Rozina Ali. (2023). " An Algebraic Approach to n-Plithogenic Square Matrices For 18 ≤ n ≤ 19". Journal of Neutrosophic and Fuzzy Systems, 7 ( 2 ), 08-23 (Doi : https://doi.org/10.54216/JNFS.070201).
[12] T.Qawasmeh,R.Hatamleh,(2023). "A new contraction based on H-simulation functions in the frame of extended b-metric spaces and application", International Journal of Electrical and Computer Engineering 13 (4),4212-4221.
[13] Rashel Abu Hakmeh, Murhaf Obaidi. (2024). " On Some Novel Results About Fuzzy n-Standard Number Theoretical Systems and Fuzzy Pythagoras Triples".,Journal of Neutrosophic and Fuzzy Systems, 8 ( 1 ), 18-22 (Doi : https://doi.org/10.54216/JNFS.080102).
[14] Abdallah Al-Husban, Abdul Razak Salleh, & Nasruddin Hassan.2015. Complex fuzzy normal subgroup." THE 2015 UKM FST POSTGRADUATE COLLOQUIUM: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2015 Postgraduate Colloquium. Vol. 1678. AIP Publishing 2015. Pages. 060008-060015.
[15] Hazaymeh, Ayman, (2023). "Time Effective Fuzzy Soft Set and Its Some Applications with and Without a Neutrosophic. International", Journal of Neutrosophic Science 23(.2), 129-29.
[16] Shihadeh, A., Matarneh, K. A. M., Hatamleh, R., Hijazeen, R. B. Y., Al-Qadri, M. O., & Al- Husban, A. (2024). "An Example of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers", Neutrosophic Sets and Systems, 67, 169-178.
[17] Ayman Hazaymeh, Rania Saadeh, Raed Hatamleh, Mohammad W Alomari, Ahmad Qazza, ( 2023). " A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp Error Estimates", Axioms-MDPI,12(9),803.
[18] Abdallah Al-Husban & Abdul Razak Salleh 2015. " Complex fuzzy ring. Proceedings of 2nd International Conference on Computing, "Mathematics and Statistics. Pages. 241-245. Publisher: IEEE 2015.
[19] Heilat, A. S., Zureigat, H., Hatamleh, R., Batiha, B., “New Spline Method for Solving Linear Two-Point Boundar Value Problems”, European Journal of Pure and Applied Mathematics, 14(4), 1283–1294,2021.
[20] Abdallah Al-Husban & Abdul Razak Salleh( 2015), " Complex Fuzzy Hyperring Based on Complex Fuzzy Spaces", Proceedings of 2nd Innovation and Analytics Conference & Exhibition (IACE). Vol. 1691. AIP Publishing 2015. Pages 040009-040017.
[21] Hatamleh, R., Zolotarev, V. A., " On Two-Dimensional Model Representations of One Class of Commuting Operators", Ukrainian Mathematical Journal, 66(1), 122–144,2014.
[22] Jaradat, A., & Al-Husban, A. (2021). The multi-fuzzy group spaces on multi-fuzzy space. J. Math. Comput. Sci., 11(6), 7535-7552
[23] Al-Husban, A., Al-Qadri, M. O., Saadeh, R., Qazza, A., & Almomani, H. H. (2022). " Multi-fuzzy rings", WSEAS Trans. Math, 21, 701-706.
[24] Abobala, M., " n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules", International Journal of Neutrosophic Science, 2020.
[25] Alkhazaleh, S., & Hazaymeh, A. A. (2018), "N-valued refined neutrosophic soft sets and their applications in decision making problems and medical diagnosis", Journal of Artificial Intelligence and Soft Computing Research, 8(1), 79-86.
[26] Hazaymeh, A. A., Abdullah, I. B., Balkhi, Z. T., & Ibrahim, R. I. (2012), "Generalized fuzzy soft expert set", Journal of Applied Mathematics, 2012, 1-22.
[27] Batiha, I. M., Alshorm, S., Al-Husban, A., Saadeh, R., Gharib, G., & Momani, S. (2023). The n-point composite fractional formula for approximating Riemann–Liouville integrator. Symmetry, 15(4), 938.
[28] Al-Husban, A., Djenina, N., Saadeh, R., Ouannas, A., & Grassi, G. (2023). A new incommensurate fractional-order COVID 19: modelling and dynamical analysis. Mathematics, 11(3), 555.
Cite This Article
Choose your preferred format