International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 25 , Issue 1 , PP: 418-427, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

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

Rabaa Al-Maita 1

  • 1 Department of Mathematics & Statistics, Mutah University, Al-Karak, Jordan - (rabaamaita@mutah.edu.jo)
  • Doi: https://doi.org/10.54216/IJNS.250137

    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

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    [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).

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    Cite This Article As :
    Al-Maita, Rabaa. A Note on Two-Fold Neutrosophic and Fuzzy Topological Space Based on Real Numbers. International Journal of Neutrosophic Science, vol. , no. , 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, (), 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 , no. (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 , () , 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. (): 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, vol. , no. , pp. 418-427, 2025. DOI: https://doi.org/10.54216/IJNS.250137