Alfa-cut based linear programming methodology for constrained matrix games with payoffs of trapezoidal fuzzy numbers

作者：Li, Deng-Feng^*; Hong, Fang-Xuan

来源：Fuzzy Optimization and Decision Making, 2013, 12(2): 191-213.

DOI：10.1007/s10700-012-9148-3

• Fuzzy game theory
• Group decision making
• Interval computation
• Linear programming
• Algorithm

The purpose of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of trapezoidal fuzzy numbers (TrFNs), which are a type of two-person non-cooperative games with payoffs expressed by TrFNs and players' strategies being constrained. In this methodology, it is proven that any Alfa-constrained matrix game has an interval-type value and hereby any constrained matrix game with payoffs of TrFNs has a TrFN-type value. The auxiliary linear programming models are derived to compute the interval-type value of any Alfa-constrained matrix game and players' optimal strategies. Thereby the TrFN-type value of any constrained matrix game with payoffs of TrFNs can be directly obtained through solving the derived four linear programming models with data taken from only 1-cut and 0-cut of TrFN-type payoffs. Validity and applicability of the models and method proposed in this paper are demonstrated with a numerical example of the market share game problem.

• 出版日期2013-6
• 单位福州大学