International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 26 , Issue 2 , PP: 41-54, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

On Ranking Algorithms for SV NT′s and NV NT′s

Murad M. Arar 1 *

  • 1 Mathematics Department, Prince Sattam Bin Abdulaziz University-Al Kharj, Saudi Arabia - (m.arar@psau.edu.sa)
  • Doi: https://doi.org/10.54216/IJNS.260205

    Received: December 26, 2024 Revised: February 12, 2025 Accepted: March 10, 2025
    Abstract

    Ranking algorithms are very important tools in decision making. There are two ranking algorithms for nvalued neutrosophic tuplets (Single-Valued MultiNeutrosophic tuplets): The S-ranking algorithm of Single- Valued MultiNeutrosophic tuplets, which is introduced by F.Smarandache in 2023, and the N-ranking algorithm of n-valued neutrosophic tuplets, Which is introduced by V. L. Nayagam and Bharanidharan R. in 2023. In this paper we show (by examples) that these two ranking algorithms are not a total ordering for the set of n-valued neutrosophic tuplets. These algorithms do not taking into account the number of sources, which is a very important factor in neutrosophic n-valued refined sets theory. We introduce two ranking algorithms: The integrated S-ranking algorithm of Single-Valued MultiNeutrosophic tuplets, and the integrated N-ranking algorithm of n-valued neutrosophic tuplets. These algorithms are improvements of the S-ranking algorithm of Single-Valued MultiNeutrosophic tuplets, and the N-ranking algorithm of n-valued neutrosophic tuplets, respectively, and taking the number of sources into account. We construct different examples to show that each step in the integrated ranking algorithms is necessary to make them a total ordering for the set of all n-valued neutrosophic tuplets.

    Keywords :

    Single-Valued MultiNeutrosophic set , n-valued neutrosophic tuplets , S-ranking algorithm , score function , accuracy function , certainty function , membership score , non-membership score , average score

    References

    [1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986),87–96.

    [2] V. L. G. Nayagam and R. Bharanidharan, A Total order on single valued and interval valued neutrosophic triplets, Neutrosophic Sets and Systems, 55 (2023), 2364 - 4974.

    [3] V. L. G. Nayagam and R. Bharanidharan, A Total Ordering on n - Valued Refined Neutrosophic Sets using Dictionary Ranking based on Total ordering on n - Valued Neutrosophic Tuplets, Neutrosophic Sets and Systems, 58 (2023), 379-396.

    [4] A. E. Samuel and R. Narmadhagnanam, Neutrosophic Refined Sets in Medical Diagnosis, International Journal of Fuzz Mathematical Archive, 14(1), 2017, 117-123.

    [5] J. Dai, Z. Xu, and H. Liu, ”A novel approach to multi-attribute decision-making based on neutrosophic sets,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 5, pp. 1208–1221, May 2021.

    [6] M. Ali and F. Smarandache, ”Applications of neutrosophic logic in physics: A concise review,” Journal of Applied Mathematics and Physics, vol. 8, no. 10, pp. 2071–2080, Oct. 2020.

    [7] F. Smarandache, The Score, Accuracy, and Certainty Functions determine a Total Order on the Set of Neutrosophic Triplets (T,I,F), Neutrosophic Sets and Systems, Vol. 38, 2020.

    [8] F. Smarandache, Introduction to the MultiNeutrosophic Sets, Neutrosophic Sets and Systems, Vol. 61, 2023.

    [9] Zadeh, L.A. Fuzzy sets, Information and Control, 8 (1965), 338–353.

     

    Cite This Article As :
    M., Murad. On Ranking Algorithms for SV NT′s and NV NT′s. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 41-54. DOI: https://doi.org/10.54216/IJNS.260205
    M., M. (2025). On Ranking Algorithms for SV NT′s and NV NT′s. International Journal of Neutrosophic Science, (), 41-54. DOI: https://doi.org/10.54216/IJNS.260205
    M., Murad. On Ranking Algorithms for SV NT′s and NV NT′s. International Journal of Neutrosophic Science , no. (2025): 41-54. DOI: https://doi.org/10.54216/IJNS.260205
    M., M. (2025) . On Ranking Algorithms for SV NT′s and NV NT′s. International Journal of Neutrosophic Science , () , 41-54 . DOI: https://doi.org/10.54216/IJNS.260205
    M. M. [2025]. On Ranking Algorithms for SV NT′s and NV NT′s. International Journal of Neutrosophic Science. (): 41-54. DOI: https://doi.org/10.54216/IJNS.260205
    M., M. "On Ranking Algorithms for SV NT′s and NV NT′s," International Journal of Neutrosophic Science, vol. , no. , pp. 41-54, 2025. DOI: https://doi.org/10.54216/IJNS.260205