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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 24 , Issue 4 , PP: 105-125, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Possibility Fermatean Neutrosophic Soft Set

Shawkat Alkhazaleh 1 , Belal Batiha 2 , Areen Al-khateeb 3 * , Hamzeh Zureigat 4 , Abedallah Al-shboul 5 , Khaldoun Batiha 6

  • 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 - (b.bateha@jadara.edu.jo )
  • 3 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan - (areen.k@jadara.edu.jo)
  • 4 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan; Applied Science Research Center, Applied Science Private University, Al-Arab St. 21, Amman, 11931, Jordan - (hamzeh.zu@jadara.edu.jo)
  • 5 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan - (aalayyoup@yahoo.com)
  • 6 Department of CS, Faculty of IT, Philadelphia University, Amman 19392, Jordan - (kh_batiha@philadelphia.edu.jo)

    • Doi: https://doi.org/10.54216/IJNS.240408

    Received: October 17, 2023 Revised: February 23, 2024 Accepted: May 24, 2024
    Abstract

    In this paper, we introduce the concept of Possibility Fermatean Neutrosophic Soft Set and define some related concepts such as Possibility Fermatean Neutrosophic Soft subset, Possibility Fermatean Neutrosophic Soft null set, and Possibility Fermatean Neutrosophic Soft universal set. Then, we define set-theoretical operations of Possibility Fermatean Neutrosophic Soft Sets such as union, intersection, and complement, and investigate some properties of these operations. We also introduce AND-product and OR-product operations between two Possibility Fermatean Neutrosophic Soft Sets. We propose a decision-making method called the Possibility Fermatean Neutrosophic Soft decision-making method (PFNS-decision-making method) which can be applied to decision-making problems involving uncertainty based on AND-product operation. We finally give a numerical example to display the application of the method that can be successfully applied to the problems.

    Keywords :

    Fuzzy Set, Soft Set , Fuzzy Soft Set , Fermatean Fuzzy Set , Fermatean Fuzzy Soft Set , Intuitionistic Fuzzy Soft Set , Possibility Fuzzy Soft Set , Intuitionistic Possibility Fermatean Fuzzy Soft Set , Possibility Fermatean Neutrosophic Soft Set

    References

    [1] Goguen, J. A. (1973). LA Zadeh. Fuzzy sets. Information and control, vol. 8 (1965), pp. 338–353.-LA Zadeh. Similarity relations and fuzzy orderings. Information sciences, vol. 3 (1971), pp. 177–200. The Journal of Symbolic Logic, 38(4), 656-657.

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

    [3] Atanassov, K. T. (1999). Intuitionistic fuzzy sets. In Intuitionistic fuzzy sets (pp. 1-137). Physica, Heidelberg.

    [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.

    [6] Molodtsov, D. (1999). Soft set theory—first results. Computers & mathematics with applications, 37(4-5), 19- 31.

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

    [8] Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers & Mathematics with Applications, 45(4-5), 555-562.

    [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).

    [13] Broumi, S. (2013). Generalized neutrosophic soft set. Infinite Study.

    [14] P.K. Maji, R. Biswas, A.R. Roy, Intuitionistic fuzzy soft sets, J. Fuzzy Math. 9 (3) (2001) 677–692.

    [15] N. C¸ agman, ˘ S. Karatas¸ , Intuitionistic fuzzy soft set theory and its decision making, J. Intell. Fuzzy Syst. 24 (4) (2013) 829–836.

    [16] M. Agarwal, K.K. Biswas, M. Hanmandlu, Generalized intuitionistic fuzzy soft sets with applications in decision-making, Appl. Soft Comput. 13 (8) (2013) 3552–3566.

    [17] S. Das, S. Kar, Group decision making in medical system: an intuitionistic fuzzy soft set approach, Appl. Soft Comput. 24 (2014) 196–211.

    [18] I. Deli, N. C¸ agman, ˘ Intuitionistic fuzzy parameterized soft set theory and its decision making, Appl. Soft Comput. 28 (2015) 109–113.

    [19] N. C¸ agman, ˘ F. C¸ ıtak, S. Enginoglu, ˘ FP-soft set theory and its applications, Ann. Fuzzy Math. Inf. 2 (2) (2011) 219–226.

    [20] S. Alkhazaleh, A.R. Salleh, N. Hassan, Possibility fuzzy soft set, Adv. Decis. Sci. (2011), http://dx.doi.org/10.1155/2011/479756.

    [21] M. Bashir, A.R. Salleh, S. Alkhazaleh, Possibility intuitionistic fuzzy soft set, Adv. Decis. Sci. (2012),

    [22] Karaaslan, F. Possibility neutrosophic soft sets and PNS-decision making method. Appl. Soft   Comput. 2017, 54, 403–414.

    Cite This Article As :
    Alkhazaleh, Shawkat. , Batiha, Belal. , Al-khateeb, Areen. , Zureigat, Hamzeh. , Al-shboul, Abedallah. , Batiha, Khaldoun. Possibility Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 105-125. DOI: https://doi.org/10.54216/IJNS.240408
    Alkhazaleh, S. Batiha, B. Al-khateeb, A. Zureigat, H. Al-shboul, A. Batiha, K. (2024). Possibility Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science, (), 105-125. DOI: https://doi.org/10.54216/IJNS.240408
    Alkhazaleh, Shawkat. Batiha, Belal. Al-khateeb, Areen. Zureigat, Hamzeh. Al-shboul, Abedallah. Batiha, Khaldoun. Possibility Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science , no. (2024): 105-125. DOI: https://doi.org/10.54216/IJNS.240408
    Alkhazaleh, S. , Batiha, B. , Al-khateeb, A. , Zureigat, H. , Al-shboul, A. , Batiha, K. (2024) . Possibility Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science , () , 105-125 . DOI: https://doi.org/10.54216/IJNS.240408
    Alkhazaleh S. , Batiha B. , Al-khateeb A. , Zureigat H. , Al-shboul A. , Batiha K. [2024]. Possibility Fermatean Neutrosophic Soft Set. International Journal of Neutrosophic Science. (): 105-125. DOI: https://doi.org/10.54216/IJNS.240408
    Alkhazaleh, S. Batiha, B. Al-khateeb, A. Zureigat, H. Al-shboul, A. Batiha, K. "Possibility Fermatean Neutrosophic Soft Set," International Journal of Neutrosophic Science, vol. , no. , pp. 105-125, 2024. DOI: https://doi.org/10.54216/IJNS.240408

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