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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 25 , Issue 3 , PP: 469-488, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Fermatean Neutrosophic Soft Set

Shawkat Alkhazaleh 1 , Hamzeh Zureigat 2 , Belal Batiha 3 , Areen Al-khateeb 4 , Abedallah Al-shboul 5

  • 1 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan - (s.alkhazaleh@jadara.edu.jo)
  • 2 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan - (hamzeh.zu@jadara.edu.jo)
  • 3 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan - (b.bateha@jadara.edu.jo)
  • 4 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan - (areen.k@jadara.edu.jo)
  • 5 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan - (aalayyoup12@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.250339

    Received: March 28, 2024 Revised: June 27, 2024 Accepted: November 12, 2024
    Abstract

    This paper aims to introduce a new concept which is Fermatean Neutrosophic Soft Set (FNSS), which is a combination of the Neutrosophic soft sets and Fermatean Fuzzy Sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of FNSS is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the most attractive laptop based on a computer simulation report. Finally, a comparative analysis between the initiated FNSS model and some existing approaches is provided to show its reliability.

    Keywords :

    Fuzzy Set , Soft Set , Fuzzy Soft Set , Fermatean Fuzzy Set , Fermatean Fuzzy Soft Set , Neutrosophic Set , Neutrosophic Soft Set , Fermatean Neutrosophic Set

    References

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    [2] Turksen, I. B. (1986). Interval valued fuzzy sets based on normal forms. Fuzzy sets and systems, 20(2), 191- 210.

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    [4] Neutrosophy, S. F. (1998). Neutrosophic probability, set, and logic, ProQuest Information & Learning. Ann Arbor, Michigan, USA, 105, 118-123.

    [5] Smarandache, F. (2002). Neutrosophic set–a generalization of the intuitionistic fuzzy set. In University of New Mexico.

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    [7] Maji, P. K., Biswas, R. K., & Roy, A. (2001). Fuzzy soft sets.

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    [9] Majumdar, P., & Samanta, S. K. (2010). Generalised fuzzy soft sets. Computers & Mathematics with Applications, 59(4), 1425-1432.

    [10] Sezgin, A., & Atagün, A. O. (2011). On operations of soft sets. Computers & Mathematics with Applications, 61(5), 1457-1467.

    [11] Maji, P. K. (2013). Neutrosophic soft set. Infinite Study.

    [12] Sahin, R., & Küçük, A. (2014). Generalised Neutrosophic Soft Set and its Integration to Decision Making Problem. Applied Mathematics & Information Sciences, 8(6).

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    Cite This Article As :
    Alkhazaleh, Shawkat. , Zureigat, Hamzeh. , Batiha, Belal. , Al-khateeb, Areen. , Al-shboul, Abedallah. Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 469-488. DOI: https://doi.org/10.54216/IJNS.250339
    Alkhazaleh, S. Zureigat, H. Batiha, B. Al-khateeb, A. Al-shboul, A. (2025). Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science, (), 469-488. DOI: https://doi.org/10.54216/IJNS.250339
    Alkhazaleh, Shawkat. Zureigat, Hamzeh. Batiha, Belal. Al-khateeb, Areen. Al-shboul, Abedallah. Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science , no. (2025): 469-488. DOI: https://doi.org/10.54216/IJNS.250339
    Alkhazaleh, S. , Zureigat, H. , Batiha, B. , Al-khateeb, A. , Al-shboul, A. (2025) . Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science , () , 469-488 . DOI: https://doi.org/10.54216/IJNS.250339
    Alkhazaleh S. , Zureigat H. , Batiha B. , Al-khateeb A. , Al-shboul A. [2025]. Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science. (): 469-488. DOI: https://doi.org/10.54216/IJNS.250339
    Alkhazaleh, S. Zureigat, H. Batiha, B. Al-khateeb, A. Al-shboul, A. "Fermatean Neutrosophic Soft Set," International Journal of Neutrosophic Science, vol. , no. , pp. 469-488, 2025. DOI: https://doi.org/10.54216/IJNS.250339

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