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International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
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Continuous publication

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Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 25Issue 1PP: 418-427 • 2025

A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers

Rabaa Al-Maita 1*
1Department of Mathematics & Statistics, Mutah University, Al-Karak, Jordan
* Corresponding Author.
Received: January 18, 2024 Revised: April 10, 2024 Accepted: July 7, 2024

Abstract

The objective of this paper is to introduce for the first time the concept of two-fold neutrosophic and fuzzy topological space defined over real numbers, where we combine the two-fold neutrosophic sets with real numbers to get a novel topological space based on them. Also, we present many of its elementary properties and special subsets such as two-fold neutrosophic open sets, two-fold neutrosophic closed sets, and two-fold neutrosophic closure. Many examples and theorems will be provided to clarify the validity of our approach.

Keywords

Two-fold algebra Two-fold neutrosophic topology Two-fold neutrosophic open set Two-fold neutrosophic closed set

References

[1]    Florentine Smarandache. "Neutrosophic Two-Fold Algebra", Plithogenic Logic and Computation, Vol.1, No.1 2024. PP.11-15.

[2]       Mohammad Abobala. "On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations." Galoitica: Journal of Mathematical Structures and Applications, Vol. 10, No. 1, 2023, PP. 17-25. (DOI: https://doi.org/10.54216/GJMSA.0100102).

[3]  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).

[4]  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).

[5]    Abdallah Shihadeh, Khaled Ahmad Mohammad Matarneh, Raed Hatamleh, Randa Bashir Yousef Hijazeen, Mowafaq Omar Al-Qadri, Abdallah Al-Husban. (2024). An Example of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers, Neutrosophic Sets and Systems, Vol. 67.

[6]     Abdallah Shihadeh, Khaled Ahmad Mohammad Matarneh, Raed Hatamleh, Mowafaq Omar Al-Qadri, Abdallah Al-HusbanOn The Two-Fold Fuzzy n-Refined Neutrosophic Rings For 2≤n≤3, Neutrosophic Sets and Systems, Vol. 68, 2024, pp. 8-25. (DOI10.5281/zenodo.11406449).

[7]    Nabil Khuder Salman, On the Special Gamma Function Over the Complex Two-Fold Algebras, Neutrosophic Sets and Systems, Vol. 68, 2024, pp. 26-38. (DOI: 10.5281/zenodo.11406461).

[8]       T.Qawasmeh, A. Qazza, R. Hatamleh, M.W. Alomari, R. Saadeh. (2023). Further accurate numerical radius inequalities. Axiom-MDPI, 12 (8), 801.

[9]       AL-Nafee, A. B., Al-Hamido, R. K., & Smarandache, F. (2019). Separation axioms in neutrosophic crisp topological spaces. Infinite Study.

[10]    M., A. "A Multi-Criteria Decision-Making Approach for Piston Material Selection under Single-Valued Trapezoidal Neutrosophic Sets," Journal of Neutrosophic and Information Fusion, vol. 2, no. 1, pp. 23-43, 2023. (DOI: https://doi.org/10.54216/NIF.020102).

[11]    Al-Husban, A., Amourah, A., & Jaber, J. J. (2020). Bipolar complex fuzzy sets and their properties. Italian Journal of Pure and Applied Mathematics, 43,754-761.

[12]    Mahmoud, H. Abdelhafeez, A. "Spherical Fuzzy Multi-Criteria Decision-Making Approach for Risk Assessment of Natech," Journal of Neutrosophic and Information  Fusion, vol. 2, no. 1, pp. 59-68, 2023. (DOI: https://doi.org/10.54216/NIF.020105).

 [13]   Al-Husban, A., Al-Qadri, M. O., Saadeh, R., Qazza, A., & Almomani, H. H. (2022). Multi-fuzzy rings. WSEAS Trans. Math, 21, 701-706

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Al-Maita, Rabaa. "A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 1, 2025, pp. 418-427. DOI: https://doi.org/10.54216/IJNS.250137
Al-Maita, R. (2025). A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers. International Journal of Neutrosophic Science, Volume 25(Issue 1), 418-427. DOI: https://doi.org/10.54216/IJNS.250137
Al-Maita, Rabaa. "A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers." International Journal of Neutrosophic Science Volume 25, no. Issue 1 (2025): 418-427. DOI: https://doi.org/10.54216/IJNS.250137
Al-Maita, R. (2025) 'A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers', International Journal of Neutrosophic Science, Volume 25(Issue 1), pp. 418-427. DOI: https://doi.org/10.54216/IJNS.250137
Al-Maita R. A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 1):418-427. DOI: https://doi.org/10.54216/IJNS.250137
R. Al-Maita, "A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 1, pp. 418-427, 2025. DOI: https://doi.org/10.54216/IJNS.250137
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