Matrix Game with Payoffs Represented by Triangular Dual Hesitant Fuzzy Numbers
Keywords:
matrix game, hesitant fuzzy set, triangular dual hesitant fuzzy numbers, multiobjective programmingAbstract
Matrix Game with Payoffs RepresentedDue to the complexity of information or the inaccuracy of decision-makers’ cognition, it is difficult for experts to quantify the information accurately in the decision-making process. However, the integration of the fuzzy set and game theory provides a way to help decision makers solve the problem. This research aims to develop a methodology for solving matrix game with payoffs represented by triangular dual hesitant fuzzy numbers (TDHFNs). First, the definition of TDHFNs with their cut sets are presented. The inequality relations between two TDHFNs are also introduced. Second, the matrix game with payoffs represented by TDHFNs is investigated. Moreover, two TDHFNs programming models are transformed into two linear programming models to obtain the numerical solution of the proposed fuzzy matrix game. Furthermore, a case study is given to to illustrate the efficiency and applicability of the proposed methodology. Our results also demonstrate the advantage of the proposed concept of TDHFNs.References
Afzali, A.; Rafsanjani, M. K.; Saeid, A. B. (2016). A fuzzy multi-objective linear programming model based on interval-valued intuitionistic fuzzy sets for supplier selection, International Journal of Fuzzy Systems, 18(5), 864-874, 2016. https://doi.org/10.1007/s40815-016-0201-1
Aggarwal, A.; Mehra, A.; Chandra, S. (2012). Application of linear programming with i-fuzzy sets to matrix games with i-fuzzy goals, Fuzzy Optimization and DecisionMaking, 11(4), 465-480, 2012. https://doi.org/10.1007/s10700-012-9123-z
An, J. J.; Li, D. F. (2019). A linear programming approach to solve constrained bi-matrix games with intuitionistic fuzzy payoffs, International Journal of Fuzzy Systems, 21(3), 908-915, 2019. https://doi.org/10.1007/s40815-018-0573-5
An, J. J.; Li, D. F.; Nan, J. X. (2017). A mean-area ranking based non-linear programming approach to solve intuitionistic fuzzy bi-matrix games, Journal of Intelligent Fuzzy Systems, 33(1), 563-573, 2017. https://doi.org/10.3233/JIFS-162299
Atanassov, K. T. (1999). Intuitionistic fuzzy sets, Springer, New York, USA, 1999. https://doi.org/10.1007/978-3-7908-1870-3
Aubin, J. P. (1981). Cooperative fuzzy games, Mathematics of Operations Research, 6(1), 1-13, 1981. https://doi.org/10.1287/moor.6.1.1
Bector, C. R.; Chandra, S. (2005). Fuzzy mathematical programming and fuzzy matrix games, Germany, Berlin, Springer-Verlag.
Bhaumik A.; Roy S. K. (2019). Intuitionistic interval-valued hesitant fuzzy matrix games with a new aggregation operator for solving management problem, Granular Computing, 2019. https://doi.org/10.1007/s41066-019-00191-5
Bhaumik, A.; Roy, S.K.; Li, D.F. (2017). Analysis of triangular intuitionistic fuzzy matrix games using robust ranking, Journal of Intelligent Fuzzy Systems, 33(1), 327-336, 2017. https://doi.org/10.3233/JIFS-161631
Bhaumik, A.; Roy, S.K.; Weber, G.W. (2020). Hesitant interval-valued intuitionistic fuzzylinguistic term set approach in Prisoners' dilemma game theory using TOPSIS: a case study on Human-trafficking, Central European Journal of Operations Research, 28, 797-816, 2020. https://doi.org/10.1007/s10100-019-00638-9
Borkotokey, S.; Neog, R. (2014). Dynamic resource allocation in fuzzy coalitions: a game theoretic model, Fuzzy Optimization and Decision Making, 13(2), 211-230, 2014. https://doi.org/10.1007/s10700-013-9172-y
Collins, W. D.; Hu, C. (2008). Studying interval valued matrix games with fuzzy logic, Soft Computing, 12(2), 147-155, 2008. https://doi.org/10.1007/s00500-007-0207-6
Fei, W.; Li, D.F. (2016). Bilinear programming approach to solve interval bimatrix games in tourism planning management, International Journal of Fuzzy Systems, 18(3), 504-510, 2016. https://doi.org/10.1007/s40815-015-0082-8
Figueroa-GarcÃa, J. C.; Mehra, A.; Chandra, S. (2019). Optimal solutions for group matrix games involving interval-valued fuzzy numbers, Fuzzy Sets and Systems, 362(1), 55-70, 2019. https://doi.org/10.1016/j.fss.2018.07.001
Gao, J.; Liu, Z.Q.; Shen, P. (2009). On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game, Soft Computing, 13(1), 127-132, 2009. https://doi.org/10.1007/s00500-008-0310-3
Gao, J.; Yu Y. (2013). Credibilistic extensive game with fuzzy payoffs, Soft Computing, 17(4), 557-567, 2013. https://doi.org/10.1007/s00500-012-0928-z
Ishibuchi, H.; Tanaka, H. (1990). Multiobjective programming in optimization of the interval objective function, European Journal of Operational Research, 48(2), 219-225, 1990. https://doi.org/10.1016/0377-2217(90)90375-L
Jana, J.; Roy, S. K. (2019). Dual hesitant fuzzy matrix games: based on new similarity measure, Soft Computing, 23(18), 8873-8886, 2019. https://doi.org/10.1007/s00500-018-3486-1
Li, D. F. (2012). A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers, European Journal of Operational Research, 223(2), 421-429, 2012. https://doi.org/10.1016/j.ejor.2012.06.020
Li, D. F.; Hong, F. X. (2013). Alfa-cut based linear programming methodology for constrained matrix games with payoffs of trapezoidal fuzzy numbers, Fuzzy Optimization and Decision Making, 12(2), 191-213, 2013. https://doi.org/10.1007/s10700-012-9148-3
Liu, F.; Qu, Y.; Wang,Y. (2012). A linear programming approximation for network capacity control problem with customer choice, Journal of System and Management Sciences, 2(3), 1-8, 2012.
Mousavi, M.; Yap, H. J.; Musa, S. N.; Dawal, S. Z. M.(2017). A fuzzy hybrid GA-PSO algorithm for multi-objective AGV scheduling in FMS, International Journal of Simulation Modelling, 16(1), 58-71, 2017. https://doi.org/10.2507/IJSIMM16(1)5.368
Nan, J. X.; Li, D. F. (2013). Linear programming approach to matrix games with intuitionistic fuzzy goals, International Journal of Computational Intelligence Systems, 6 (1), 186-197, 2013. https://doi.org/10.1080/18756891.2013.761781
Nan, J. X.; Li, D. F.; Zhang, M. J. (2010). A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers, International Journal of Computational Intelligence Systems, 3(3), 280-289, 2010. https://doi.org/10.1080/18756891.2010.9727699
Quang, H. N.; Huu, T. D. (2017). A fuzzy ANP model for assessing the construction risk of a public construction project in Vietnam, Journal of System and Management Sciences, 7(3), 79-96, 2017.
Torra, V. (2010). Hesitant fuzzy sets, International Journal of Intelligent Systems, 25(6), 529-539, 2010. https://doi.org/10.1002/int.20418
Vijay, V.; Mehra, A.; Chandra, S.; Bector, C. (2007). Fuzzy matrix games via a fuzzy relation approach, Fuzzy Optimization and DecisionMaking, 6(4), 299-314, 2007. https://doi.org/10.1007/s10700-007-9015-9
Wang, J. F.; Fei, Z. C.; Chang, Q.; Fu, Y.; Li, S. Q. (2019). Energy-saving operation of multistage stochastic manufacturing systems based on fuzzy logic, International Journal of Simulation Modelling, 18(1), 138-149, 2019. https://doi.org/10.2507/IJSIMM18(1)CO1
Wu, H. C. (2019). Cores and dominance cores of cooperative games endowed with fuzzy payoffs, Fuzzy Optimization and DecisionMaking, 18(2), 219-257, 2019. https://doi.org/10.1007/s10700-018-9294-3
Xu, W.; Liu, L.; Zhang, Q.; Liu, P. (2018). Location decision-making of equipment manufacturing enterprise under dual channel purchase and sale mode, Complexity, 2018. https://doi.org/10.1155/2018/3797131
Xu, W.; Yin, Y. (2018). Functional objectives decision-making of discrete manufacturing system based on integrated ant colony optimization and particle swarm optimization approach, Advances in Production Engineering Management, 13(4), 389-404, 2018. https://doi.org/10.14743/apem2018.4.298
Yang, J.; Fei, W.; Li, D. F. (2016). Non-linear programming approach to solve bimatrix games with payoffs represented by i-fuzzy numbers, International Journal of Fuzzy Systems, 18(3), 492- 503, 2016. https://doi.org/10.1007/s40815-015-0052-1
Yu, X.; Zhang, Q.; Zhou, Z. (2018). Linear fuzzy game with coalition interaction and its coincident solutions, Fuzzy Sets and Systems, 349, 1-22, 2018. https://doi.org/10.1016/j.fss.2018.03.005
Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8(3), 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhu, B.; Xu, Z.; Xia, M. (2012). Dual hesitant fuzzy sets, Journal of Applied Mathematics, 13 pages, 2012. https://doi.org/10.1155/2012/879629
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