Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory

somendebnath

Full Length Article

•

Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory

somendebnath ^*

mail

* Corresponding Author.

DOI

format_quote Cite this article

View PDF open_in_new

Abstract

In this article, we use the notion of an intuitionistic neutrosophic set(INS) proposed by Bhoumik et al. Later on, Broumi et al. extend this concept by introducing intuitionistic neutrosophic soft set(INSS). Based on INSSs and their properties, we define two-person intuitionistic neutrosophic soft games(TP-INS-games). We then define some definitions and properties associated with TP-INS-games. Also, we extend the TP-INS-games to N-person INS-games. In the end, to validate this concept, we give a concrete application which shows that this concept can be used successfully in real decision-making problem.

Keywords

Soft set Neutrosophic soft set Intuitionistic neutrosophic soft set Intuitionistic neutrosophic soft payoff

References

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

[2] B. C. Cuong,” Picture fuzzy sets”, Journal of Computer Science and Cybernetics, Vol 30, pp. 409-420, 2014.

[3] P. A. Ejegwa,” Pythagorean fuzzy set and its application in career placement based on academic performance using max-min-max composition”, Complex and Intelligent Systems, Vol 5, pp. 165-175, 2019.

[4] K. T. Atanassov, “ Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol 20, pp. 87-96, 1986.

[5] K. T. Atanassov and G. Gargov,” Interval valued intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol 31, pp. 343-349, 1989.

[6] M. Gorzalczany,” A method of inference in approximate reasoning based on interval-valued fuzzy sets”, Fuzzy Sets and Systems, Vol 21, pp. 1-17, 1987.

[7] F. Smarandache,” Pilthogenic set, an extension of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets-revisited”, Neutrosophic Sets and Systems, Vol 21, pp. 153-166, 2018.

[8] D. Molodtsov, ”Soft set theory-first-results”, Computers and Mathematics with Applications, Vol 37, pp. 19-31, 1999.

[9] P. K. Maji, A. R. Roy and R. Biswas,” An application of soft sets in a decision making problem”, Computers and Mathematics with Applications, Vol 44, pp. 1077-1083, 2002.

[10] S. Yuksel, T. Dizman, G. Yildizdan and U. Sert,” Application of soft sets to diagnose the prostate cancer risk”, Journal of Inequalities and Applications, DOI: https://doi.org/10.1186/1029-242X-2013-229.

[11] A. R. Roy and P. K. Maji,” A fuzzy soft set theoretic approach to decision making problems”, Journal of Computational and Applied Mathematics, Vol 203, pp. 412-418, 2007.

[12] I. Deli and N. Cagman,” Intuitionistic fuzzy parameterized soft set theory and its decision making”, Applied Soft Computing, Vol 28, pp. 109-113, 2015.

[13] P. K. Maji, R. Biswas and A. R. Roy,” Intuitionistic fuzzy soft sets”, Journal of Fuzzy Mathematics, Vol 12, pp. 669-683, 2004.

[14] X. B. Yang, T. Y. Lin, J. Y. Yang, Y. Li and D. Yu,” Combination of interval-valued fuzzy set and soft set”, Computers and Mathematics with Applications, Vol 58, pp. 521-527, 2009.

[15] Y. Jiang, Y. Tang, Q. Chen, H. Liu and J. Tang,” Interval valued intuitionistic fuzzy soft sets and their properties”, Computers and Mathematics with Applications, Vol 60, pp.906-918, 2010.

[16] F. Smarandache, “A unifying field in logics: neutrosophic logic in philosophy”, American Research Press, pp. 1-141, 1999.

[17] F. Smarandache,” Neutrosophic set-a generalization of the intuitionistic fuzzy set”, International Journal of Pure and Applied Mathematics, Vol 24, pp. 287-297, 2005.

[18] H. Wang, F. Smarandache, Y. Q. Zhang and R. Sunderraman,” Single valued neutrosophic sets”, Review of the Air Force Academy, Vol 1, pp. 10-14, 2010.

[19] P. K. Maji,” Neutrosophic soft set”, Annals of Fuzzy Mathematics and Informatics, Vol 5, pp. 157-168, 2013.

[20] H. Zhang, J. Wang and X. Chen,” Interval neutrosophic sets and their application in multicriteria decision making problem”, The Scientific World Journal, Vol 2014, https://dx.doi.org/10.1155/2014/645953.

[21] G. Shahzadi, M. Akram and A. Saeid,” An application of single-valued neutrosophic sets in medical diagnosis”, Neutrosophic Sets and Systems, Vol 18, pp. 80-88, 2017.

[22] F. Karaaslan,” Neutrosophic soft sets with applications in decision making”, International Journal of Information Science and Intelligent System, Vol 4, pp. 1-20, 2015.

[23] J. V. Neumann and O. Morgenstern,” The theory of games and economic behaviour”, Princeton University Press, 1944.

[24] N. Cagman and I. Deli, “Soft games”, https://arxiv.org/abs/1302.4568, 2013.

[25] I. Deli and N. Cagman,” Application of soft sets in decision making based on game theory”, Annals of Fuzzy Mathematics and Informatics, Vol 11, pp. 425-438, 2016.

[26] I. Deli,” Applications of soft and fuzzy soft sets to game theory(in Turkish) Ph.D thesis, Gaziosmanpasa University”, Graduate School of Natural and Applied Science, 2013.

[27] I. Deli and N. Cagman,” Fuzzy soft games”, Filomat, Vol 29, pp. 1901-1917, 2015.

[28] A. Mukherjee and S. Debnath,” Intuitionistic fuzzy soft game theory”, Songklanakarin Journal of Science and Technology, Vol 40, pp. 409-417, 2018.

[29] A. Mukherjee and S. Debnath, “Generalized fuzzy soft sets in decision making based on game theory and their applications”, Bulletin of Calcutta Mathematical Society, Vol 108, pp. 431-448, 2016.

[30] S. Debnath, “Application of interval-valued neutrosophic soft sets in decision making based on game theory”, Songlanakarin Journal of Science and Technology SJST-2020-0290.R1, in press.

[31] T. Maeda,” On characterization of equilibrium strategy of two person zero-sum games with fuzzy payoffs”, Fuzzy Sets and Systems, Vol 139, pp. 283-296, 2003.

[32] I. Deli and N. Cagman,” Probabilistic equilibrium solution of soft games”, Journal of Intelligent and Fuzzy Systems, Vol 30, pp. 2237-2244, 2016.

[33] M. Bhowmik and M. Pal,” Intuitionistic neutrosophic set”, Journal of Information and Computing Science, Vol 4, pp. 142-152, 2009.

[34] B. Said and F. Smarandache,” Intuitionistic neutrosophic soft set”, Journal of Information and Computing Science, Vol 8, pp. 130-140, 2013.

Cite This Article

Choose your preferred format

format_quote

, somendebnath. "Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory." International Journal of Neutrosophic Science, vol. , no. , , pp. . DOI:

, s. (). Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory. International Journal of Neutrosophic Science, (), . DOI:

, somendebnath. "Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory." International Journal of Neutrosophic Science , no. (): . DOI:

, s. () 'Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory', International Journal of Neutrosophic Science, (), pp. . DOI:

s. Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory. International Journal of Neutrosophic Science. ;():. DOI:

s. , "Application of Intuitionistic Neutrosophic Soft Sets in Decision Making Based on Game Theory," International Journal of Neutrosophic Science, vol. , no. , pp. , . DOI:

Digital Archive Ready