Title: An approach to solve fuzzy interval valued matrix game

Authors: Sankar Kumar Roy; Shakti Nath Mondal

Addresses: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India

Abstract: The conventional game theory is based on known payoffs. In the real situations, usually the payoffs are not known and have to be approximated. The aim of this paper is to develop a simple and an effective fuzzy multi-objective linear programming method for solving matrix game in which the payoffs are expressed with fuzzy intervals. Since, the payoffs of the matrix game are fuzzy intervals, the value of the matrix game is also fuzzy interval. Using upper and lower bounds of the payoffs, we obtain upper and lower bounds of the value of the matrix game by fuzzy multi-objective linear programming method. Lastly, a numerical example is given to illustrate the method.

Keywords: matrix games; fuzzy interval numbers; fuzzy multi-objective linear programming; interval arithmetic; game theory; fuzzy intervals.

DOI: 10.1504/IJOR.2016.076880

International Journal of Operational Research, 2016 Vol.26 No.3, pp.253 - 267

Received: 23 Sep 2013
Accepted: 01 May 2014
Published online: 06 Jun 2016 *

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