Interval programming models for matrix games with interval payoffs

Abstract

The aim of this paper is to study how to solve a type of matrix game with interval payoffs. In this paper, the interval inequality relations and the concept of solutions of the matrix game with interval payoffs are defined. Based on the fuzzy ranking index defined, the solution of the matrix game with interval payoffs can be obtained through solving a pair of bi-objective linear programming models derived from the constructed auxiliary interval programming models. It is shown that the models proposed in this paper extend those of the classical matrix game. The validity and applicability of the proposed methodology are illustrated with a numerical example.

Keywords:

• interval
• matrix game
• multiobjective programming
• uncertainty mathematical theory
• optimization

AMS Subject Classifications :

• 65G30
• 91A05
• 90C29
• 68T37
• 74P99

Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and constructive suggestions. This research was sponsored by the Natural Science Foundation of China (No. 70571086, No. 70871117) and the Renwen Foundation of Dalian University of Technology (No. 2008407).