International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 20 , Issue 4 , PP: 65-77, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

Bipolar fuzzy hypersoft set and its application in decision making

Ashraf Al-Quran 1 * , Faisal Al-Sharqi 2 , Kifayat Ullah 3 , Mamika Ujianita Romdhini 4 , Marwa Balti 5 , Mohammed Alomair 6

  • 1 Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia - (aalquran@kfu.edu.sa)
  • 2 Department of Mathematics, Faculity of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq - (faisal.ghazi@uoanbar.edu.iq)
  • 3 Department of Mathematics, Riphah International University, Lahore Campus, Lahore 54000, Pakistan - (kifayat.khan.dr@gmail.com)
  • 4 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Mataram, 83125,Indonesia - (mamika@unram.ac.id)
  • 5 Department of Mathematics and Statistics,College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia - (mbalti@kfu.edu.sa)
  • 6 Department of Quantitative Methods, College of Business Administration, King Faisal University, Al-Ahsa 31982, Saudi Arabia - (ma.alomair@kfu.edu.sa)
  • Doi: https://doi.org/10.54216/IJNS.200405

    Received: January 04, 2023 Accepted: April 02, 2023
    Abstract

    Smarandache developed the idea of hypersoft set (HSS) theory as an extension of soft set (SS) theory. HSS provides a general mathematical framework for handling data that can be formulated as several trait-valued disjoint sets which blend to various traits. The major goal of this article is to lay the footing for supplying a new model called bipolar fuzzy hypersoft sets (BFHSSs) by linking both fuzzy sets (FSs) and HSSs under bipolarity property. By using positive and negative membership functions and multi-argument functions, these structures work best for testing uncertainty. This makes them better at solving real-world problems, especially ones that have both good and bad sides. This paper also has different operations for BFHSSs, such as absolute BFHSS, null BFHSS, complement, subset, union, intersection, and their related properties. Moreover, operations like OR and AND for BFHSS have been instituted. Some properties are demonstrated, and some numerical examples are given to illustrate the mechanism of using these tools. Finally, these tools are applied in the decision-making process based on an algorithm that is built.

    Keywords :

    Bipolar Fuzzy Set , Fuzzy Set , Fuzzy Soft Set , Fuzzy Hypersoft Set , Hypersoft Set , Soft Set.

    References

    [1] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, pp. 338-353, 1965.

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

    [3] D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex fuzzy sets, IEEE Transactions on Fuzzy Systems,vol.10 , pp. 171-186, 2002.

    [4] A. Al-Quran, A. G. Ahmad, F. Al-Sharqi, A. Lutfi, Q-Complex neutrosophic set, International Journal ofNeutrosophic Science, vol. 20, no. 2, pp. 08-19, 2023.

    [5] F. Smarandache, Neutrosophic probability, set, and logic, American Research Press: Rehoboth, IL, USA,1998.

    [6] D. Molodtsov, Soft set theory, first results, Computers and Mathematics with Applications, vol. 37, no.4-5, pp. 19-31, 1999.

    [7] P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, vol. 9, no. 3, pp.589-602, 2001.

    [8] N. C¸ a˘gman, S. Karatas¸, Intuitionistic fuzzy soft set theory and its decision making, Journal of Intelligentand Fuzzy Systems, vol. 24(4), pp. 829-836, 2013.

    [9] I. Deli, S. Broumi, Neutrosophic soft relations and some properties, Annals of fuzzy mathematics andinformatics, vol. 9(1), pp. 169-182, 2015.

    [10] P. Thirunavukarasu, R. Suresh, V. Ashokkumar, Theory of complex fuzzy soft set and its applications,Int. J. Innov. Res. Sci. Technol, vol. 3(10), pp. 13-18, 2017.

    [11] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Interval-valued neutrosophic soft expert set from real space tocomplex space, Computer Modeling in Engineering and Sciences, vol. 132(1), pp. 267–293, 2022.

    [12] F. Al-Sharqi, A. G. Ahmad, A. Al-Quran, Similarity measures on interval-complex neutrosophic soft setswith applications to decision making and medical diagnosis under uncertainty, Neutrosophic Sets andSystems, vol. 51, pp. 495–515, 2022.

    [13] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Fuzzy parameterized-interval complex neutrosophic softsets and their applications under uncertainty, Journal of Intelligent and Fuzzy Systems, vol. 44 , pp.1453–1477, 2023.

    [14] R. M. Zulqarnain, I. Siddique, M. Asif, S. Ahmad, S. Broumi, and S. Ayaz, Similarity measure for m-Polar interval valued neutrosophic soft set with application for medical diagnoses, Neutrosophic Sets and Systems, vol. 47(1), pp.11, 2021.

    [15] M. M. Abed, A. F. Al-Jumaili, F. G. Al-Sharqi, Some mathematical structures in a topological group, Journal of Algebra and Applied Mathematics, vol. 16(2), pp. 99-117, 2018.

    [16] M. Palanikumar, K. Arulmozhi, A. Iampan, S. Broumi, Medical diagnosis decision making using type- II generalized Pythagorean neutrosophic interval-valued soft sets, International Journal of Neutrosophic Science, Vol. 20, No. 1, pp. 85-105, 2023.

    [17] F. Al-Sharqi, A.G. Ahmad, A. Al-Quran, Mapping on interval complex neutrosophic soft sets, International Journal of Neutrosophic Science, vol. 19(4), pp. 77-85, 2022.

    [18] C. Jana, G. Muhiuddin and M. Pal, Multi-criteria decision-making approach based on SVTrN Dombi aggregation functions, Artificial Intelligence Review, vol. 54(4), pp. 3685-3723, 2021.

    [19] K. Naeem, M. Riaz, D. Afzal, Fuzzy neutrosophic soft σ-algebra and fuzzy neutrosophic soft measure with applications, Journal of Intelligent and Fuzzy Systems, vol. 39(1), pp. 277-287, 2020.

    [20] F. Smarandache, Extension of soft set of hypersoft set, and then to plithogenic hypersoft set, Neutrosophic Sets Syst., vol. 22, pp. 168-170, 2018.

    [21] M. Saeed, A. U. Rahman, M. Ahsan, F. Smarandache, An inclusive study on fundamentals of hypersoft set, Theory and Application of Hypersoft Set, vol. 1, pp. 1-23, 2021.

    [22] A. Yolcu, T. Y. Ozturk, Fuzzy hypersoft sets and it’s application to decision-making, Theory and application of hypersoft set, vol. 50, 2021.

    [23] W. R. Zhang, YinYang, Bipolar fuzzy sets, In Proceedings of the IEEE International Conference on Fuzzy Systems Proceedings and the IEEE World Congress on Computational Intelligence (FUZZ-IEEE’98),Anchorage, AK, USA, vol. 1, pp. 835–840, 4–9 May 1998.

    [24] M. Naz, M. Shabir, On fuzzy bipolar soft sets, their algebraic structures and applications, Journal of Intelligent and Fuzzy Systems, vol. 26(4), pp.1645-1656, 2014.

    [25] S. Y. Musa, B. A. Asaad, Bipolar hypersoft sets, Mathematics, vol. 9(15), pp. 1826, 2021.

    Cite This Article As :
    Al-Quran, Ashraf. , Al-Sharqi, Faisal. , Ullah, Kifayat. , Ujianita, Mamika. , Balti, Marwa. , Alomair, Mohammed. Bipolar fuzzy hypersoft set and its application in decision making. International Journal of Neutrosophic Science, vol. , no. , 2023, pp. 65-77. DOI: https://doi.org/10.54216/IJNS.200405
    Al-Quran, A. Al-Sharqi, F. Ullah, K. Ujianita, M. Balti, M. Alomair, M. (2023). Bipolar fuzzy hypersoft set and its application in decision making. International Journal of Neutrosophic Science, (), 65-77. DOI: https://doi.org/10.54216/IJNS.200405
    Al-Quran, Ashraf. Al-Sharqi, Faisal. Ullah, Kifayat. Ujianita, Mamika. Balti, Marwa. Alomair, Mohammed. Bipolar fuzzy hypersoft set and its application in decision making. International Journal of Neutrosophic Science , no. (2023): 65-77. DOI: https://doi.org/10.54216/IJNS.200405
    Al-Quran, A. , Al-Sharqi, F. , Ullah, K. , Ujianita, M. , Balti, M. , Alomair, M. (2023) . Bipolar fuzzy hypersoft set and its application in decision making. International Journal of Neutrosophic Science , () , 65-77 . DOI: https://doi.org/10.54216/IJNS.200405
    Al-Quran A. , Al-Sharqi F. , Ullah K. , Ujianita M. , Balti M. , Alomair M. [2023]. Bipolar fuzzy hypersoft set and its application in decision making. International Journal of Neutrosophic Science. (): 65-77. DOI: https://doi.org/10.54216/IJNS.200405
    Al-Quran, A. Al-Sharqi, F. Ullah, K. Ujianita, M. Balti, M. Alomair, M. "Bipolar fuzzy hypersoft set and its application in decision making," International Journal of Neutrosophic Science, vol. , no. , pp. 65-77, 2023. DOI: https://doi.org/10.54216/IJNS.200405