Abstract
There are always uncertainty, incompleteness and imprecision existing in decision making information. These are why fuzzy set theory is commonly used in decision making. Vague set can indicate the decision makers’ preference information in terms of favor against and neutral. When dealing with uncertain information, vague set indicates information more abundant than fuzzy set. According to the theories of multiobjective decision making and fuzzy game, the multiobjective two-person zero-sum matrix game, whose payoff values are vague values is researched. Firstly, the concept of vague set and the order function is introduced. Then the model of multiobjective two-person zero-sum matrix game based on vague set is described. Thirdly, two solutions of vague multiobjective two-person zero-sum matrix game are discussed: one is making the vague multiobjective game problem crisp through the order function of vague values, then turning it into single objective game; the other method is turning vague multiobjective game problem into vague single objective game problem first, then making it crisp through the order function of vague values. Finally, numerical examples are given to apply the proposed methods.
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References
Campos, L.: Fuzzy linear programming models to solve fuzzy matrix games. Fuzzy Sets and Systems 32, 275–289 (1989)
Nishizaki, I., Sakawa, M.: Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals. Fuzzy Sets and Systems 111, 99–116 (2000)
Maeda, T.: On characterization of equilibrium strategy of two-person zero-sum games with fuzzy payoffs. Fuzzy Sets and Systems 139, 283–296 (2003)
Vijay, V., Chandra, S., Bector, C.R.: Matrix games with fuzzy goals and fuzzy payoffs. The international Journal of Management Science 33, 425–429 (2005)
Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Transactions on Systems, Man, and Cybernetics 23(2), 610–614 (1993)
Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 79, 403–405 (1996)
Zhou, X.G., Zhang, Q.: Comparison and improvement on similarity measures between vague sets and between elements (in Chinese). Journal of Systems Engineering 20(6), 613–619 (2005)
Zhou, X.G., Zhang, Q.: Aggregation vague opinions under group decision making. In: Proceeding of the 4th Wuhan International Conference on E-business, vol. 6, Wuhan, pp. 1736–1742 (2005)
Liu, H.W.: Vague set methods of multicriteria fuzzy decision making (in Chinese). System Engineering Theory and Practice 5, 103–109 (2004)
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© 2007 Springer-Verlag Berlin Heidelberg
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Zhou, X., Song, Y., Zhang, Q., Gao, X. (2007). Multiobjective Matrix Game with Vague Payoffs. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_59
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DOI: https://doi.org/10.1007/978-3-540-71441-5_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71440-8
Online ISBN: 978-3-540-71441-5
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