International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 19 , Issue 3 , PP: 85-94, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators

M. Palanikumar 1 * , Aiyared Iampan 2 , Said Broumi 3

  • 1 Department of Mathematics, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India - (palanimaths86@gmail.com)
  • 2 Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand - (palanimaths86@gmail.com)
  • 3 Laboratory of Information Processing, Faculty of Science Ben MSik, University of Hassan II, Casablanca, Morocco;Regional Center for the Professions of Education and Training (C.R.M.E.F), Casablanca-Settat, Morocco - (broumisaid78@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.190308

    Received: June 28, 2022 Accepted: November 13, 2022
    Abstract

    In this study, we presented a new generalization of the Fermatean interval valued fuzzy soft set (FIVFSS) and

    the neutrosophic interval valued soft set called the neutrsophic Fermatean interval valued soft set (NSFIVSS).

    The NSFIVSS decision matrix aggregated operations are the topic of our current discussion. Strong points of

    view for the generalization of the interval valued fuzzy soft set (IVFSS) known as multi-criteria group decision

    making (MCGDM) are the TOPSIS and VIKOR techniques. We discuss a score function that combines

    TOPSIS, VIKOR, and NSFIVSS-positive ideal solution (PIS) and NSFIVSS-negative ideal solution (NIS)

    techniques. The TOPSIS and VIKOR methods also offer decision-making weights. The nearness condition

    is used to determine the best alternative. An educational trust intends to give some money to those underdeveloped

    schools since they lack amenities like restrooms, a campus environment that is favorable to learning,

    sports equipment, and classroom furnishings like desks and lights. In order to lower the factor, they declared

    a payment to be made in the amounts of 30, 25, 20, 15, and 10. Find the top five under performing schools in

    the state.

    Keywords :

    NSFIVSS , TOPSIS , VIKOR , aggregation operator

    References

    [1] Ahmed B. AL-Nafee, Said Broumi, Luay A. Al Swidi, n-valued refined neutrosophic crisp sets. International

    Journal of Neutrosophic Science, 17(2), 2021, 87-95.

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

    [3] F.E. Boran, S. Genc, M. Kurt and D. Akay, A multi-criteria intuitionistic fuzzy group decision making

    for supplier selection with TOPSIS approach, Expert Systems with Applications 36(8), (2009), 11363-

    11368.

    [4] S. Eraslan and F. Karaaslan, A group decision making approach based on TOPSIS under fuzzy soft

    environment, Journal of New Theory, 3, (2015), 30-40.

    [5] F. K. Gundoodu and Cengiz Kahraman, A novel fuzzy TOPSIS method using emerging interval-valued

    spherical fuzzy sets, Engineering Applications of Artificial Intelligence, 85, (2019), 307323.

    [6] C.L. Hwang, K. Yoon, Multiple Attributes Decision Making Methods and Applications, Springer, Berlin

    Heidelberg, 1981.

    [7] C. Jana and M. Pal, Multi criteria decision making process based on some single valued neutrosophic

    Dombi power aggregation operators, Soft Computing, 25(7), (2021), 5055-5072.

    [8] C. Jana, M. Pal, F. Karaaslan and J. Q. Wang, Trapezoidal neutrosophic aggregation operators and their

    application to the multi-attribute decision making process, Scientia Iranica, 27(3), (2020), 1655-1673

    [9] M. Lathamaheswari, Said Broumi, Florentin Smarandache, S. Sudha, Neutrosophic perspective of neutrosophic

    probability distributions and its application, International Journal of Neutrosophic Science,

    17(2), 2021, 96-109.

    [10] D. Liang and Z. Xu, The new extension of TOPSIS method for multiple criteria decision making with

    hesitant Pythagorean fuzzy sets, Applied Soft Computing, 60, (2017), 167-179.

    [11] P.K. Maji, R. Biswas and A.R. Roy, Fuzzy Soft Set, Journal of Fuzzy Mathematics, 9(3), (2001), 589-602.

    [12] P.K. Maji, R. Biswas and A.R. Roy, On intuitionistic Fuzzy Soft Set, Journal of Fuzzy Mathematics, 9(3),

    (2001), 677-692.

    [13] Palanikumar,M.; Arulmozhi, K.; On vague subbisemirings of bisemirings, Bulletin of the International

    Mathematical Virtual Institute, 2022; Vol. 11(3). pp. 419-428.

    [14] Palanikumar,M.; Iampan, A.; Lejo J. Manavalan; M-Bi-base generator of ordered gamma-semigroups,

    2022; ICIC Express Letters Part-B, Vol. 13(8). pp. 795-802.

    [15] Palanikumar,M.; Arulmozhi, K.; (α, β)-neutrosophic subbisemiring of bisemiring, 2022; Neutrosophic

    Sets and Systems, Vol. 48, pp. 368-385.

    [16] Palanikumar,M.; Arulmozhi, K.; On New Ways of various ideals in ternary semigroups, 2020; Matrix

    Science Mathematic, Vol. 4(1). pp. 06-09.

    [17] Palanikumar,M.; Arulmozhi, K.; On Various Tri-ideals in ternary Semirings, 2021; Yulletin of the International

    Mathematical Virtual Institute, Vol. 11(1). pp. 79-90.

    [18] Palanikumar,M.; Arulmozhi, K.; On intuitionistic fuzzy normal subbisemiring of bisemiring, 2021; Nonlinear

    Studies, Vol. 28(3). pp.717-721.

    [19] M. Palanikumar, K. Arulmozhi, and C. Jana, Multiple attribute decision-making approach for

    Pythagorean neutrosophic normal interval-valued aggregation operators, Comp. Appl. Math. 41(90),

    (2022), 1-27.

    [20] M.Palanikumar and Aiyared Iampan, Spherical fermatean interval valued fuzzy soft set based on multi

    criteria group decision making, International Journal of Innovative Computing, Information and Control,

    18(2), (2022), 607-619.

    [21] M.Palanikumar and Aiyared Iampan, A novel approach to decision making based on type-II generalized

    fermatean bipolar fuzzy soft sets, International Journal of Innovative Computing, Information and

    Control, 18(3), (2022), 769-781.

    [22] X.D. Peng, Y. Yang, J.P. Song, Pythagorean fuzzy soft set and its application, Computer Engineering,

    41(7), (2015), 224-229.

    [23] T. Senapati, R.R. Yager, Fermatean, fuzzy sets. J. Ambient Intell. Humaniz. Comput. 11, (2020), 663-

    674.

    [24] Souhail Dhouib, Said Broumi, M. Lathamaheswari, Single valued trapezoidal neutrosophic travelling

    salesman problem with novel greedy method, the dhouib matrix TSP1, International Journal of Neutrosophic

    Science, 17(2), 2021, 144-157.

    [25] G.H. Tzeng, C.W. Lin, S. Opricovic, Multi-criteria analysis of alternative-fuel buses for public transportation,

    Energy Policy, 33, (2005) 1373-1383.

    [26] Z. Xu and X. Zhang, Hesitant fuzzy multi-attribute decision-making based on TOPSIS with incomplete

    weight information, Knowledge-Based Systems, 52, (2013), 53-64.

    [27] R.R. Yager, Pythagorean membership grades in multi criteria decision making, IEEE Trans. Fuzzy Systems,

    22, (2014), 958-965.

    [28] L. A. Zadeh, Fuzzy sets, Information and control 8(3),(1965), 338-353.

    [29] R.M. Zulqarnain , Xiao Long Xin , Muhammad Saqlain and Waseem Asghar Khan, TOPSIS method

    based on the correlation coefficient of interval valued intuitionistic fuzzy soft sets and aggregation operators

    with their application in decision making, Journal of Mathematics, (2021), 1-16.

     

    Cite This Article As :
    Palanikumar, M.. , Iampan, Aiyared. , Broumi, Said. MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators. Journal of International Journal of Neutrosophic Science, vol. 19, no. 3, 2022, pp. 85-94. DOI: https://doi.org/10.54216/IJNS.190308
    Palanikumar, M. Iampan, A. Broumi, S. (2022). MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators. Journal of International Journal of Neutrosophic Science, 19( 3), 85-94. DOI: https://doi.org/10.54216/IJNS.190308
    Palanikumar, M.. Iampan, Aiyared. Broumi, Said. MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators. Journal of International Journal of Neutrosophic Science 19, no. 3 (2022): 85-94. DOI: https://doi.org/10.54216/IJNS.190308
    Palanikumar, M. , Iampan, A. , Broumi, S. (2022) . MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators. Journal of International Journal of Neutrosophic Science , 19( 3) , 85-94 . DOI: https://doi.org/10.54216/IJNS.190308
    Palanikumar M. , Iampan A. , Broumi S. [2022]. MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators. Journal of International Journal of Neutrosophic Science. 19( 3): 85-94. DOI: https://doi.org/10.54216/IJNS.190308
    Palanikumar, M. Iampan, A. Broumi, S. "MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators," Journal of International Journal of Neutrosophic Science, vol. 19, no. 3, pp. 85-94, 2022. DOI: https://doi.org/10.54216/IJNS.190308