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Mathematical Problems in Engineering
Volume 2014, Article ID 592326, 20 pages
Research Article

A Novel Multiperson Game Approach for Linguistic Multicriteria Decision Making Problems

1Department of Industrial Education and Technology, National Changhua University of Education, 2 Shi-Da Road, Changhua County, Changhua City 500, Taiwan
2Department of Information Management, National United University, 1 Lienda Road, Miaoli County, Miaoli City 36003, Taiwan
3Institute of Mechatronoptic Systems and Department of Automation Engineering, Chienkuo Technology University, No. 1 Chiehshou North Road, Changhua City 500, Taiwan
4Department of International Business, National Chi Nan University, 1 University Road, Nantou County, Puli City 54561, Taiwan

Received 1 September 2013; Revised 2 November 2013; Accepted 24 November 2013; Published 2 February 2014

Academic Editor: Ching-Ter Chang

Copyright © 2014 Ching-San Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Game theory is considered as an efficient framework in dealing with decision making problems for two players in the competitive environment. In general, the evaluation values of payoffs matrix are expressed by crisp values in a game model. However, many uncertainties and vagueness should be considered due to the qualitative criteria and the subjective judgment of decision makers in the decision making process. The aim of this study is to develop an effective methodology for solving the payoffs matrix with linguistic variables by multiple decision makers in a game model. Based on the linguistic variables, the decision makers can easily express their opinions with respect to criteria for each alternative. By using the linear programming method, we can find the optimal solution of a game matrix in accordance with the combination of strategies of each player effectively. In addition, the expected performance value (EPV) index is defined in this paper to compare the competition ability of each player based on the optimal probability of each strategy combination. And then, numerical example will be implemented to illustrate the computation process of the proposed model. The conclusion and future research are discussed at the end of this paper.