期刊
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
卷 223, 期 2, 页码 421-429出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.ejor.2012.06.020
关键词
I. Game theory; S. Fuzzy sets; S. Group decisions and negotiations; I. Linear programming; P. Uncertainty modeling
资金
- Ministry of Education of China [NCET-10-0020]
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20113514110009]
- National Natural Science Foundation of China [71171055, 70871117, 71101033, 70902041, 70901021, 71001015]
The aim of this paper is to develop an effective method for solving matrix games with payoffs of triangular fuzzy numbers (TFNs) which are arbitrary. In this method, it always assures that players' gain-floor and loss-ceiling have a common TFN-type fuzzy value and hereby any matrix game with payoffs of TFNs has a TFN-type fuzzy value. Based on duality theorem of linear programming (LP) and the representation theorem for fuzzy sets, the mean and the lower and upper limits of the TFN-type fuzzy value are easily computed through solving the derived LP models with data taken from 1-cut set and 0-cut set of fuzzy payoffs. Hereby the TFN-type fuzzy value of any matrix game with payoffs of TFNs can be explicitly obtained. Moreover, we can easily compute the upper and lower bounds of any Alfa-cut set of the TFN-type fuzzy value for any matrix game with payoffs of TFNs and players' optimal mixed strategies through solving the derived LP models at any specified confidence level Alfa. The proposed method in this paper is demonstrated with a numerical example and compared with other methods to show the validity, applicability and superiority. (C) 2012 Elsevier B.V. All rights reserved.
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