Fuzzy cooperative games arising from linear production programming problems with fuzzy parameters

Abstract

In the present study we consider a production model in which multiple decision makers pool resources to produce finished goods. Such a production model, which is assumed to be linear, can be formulated as mathematical programming problems with fuzzy parameters from the viewpoint of experts’ imprecise or fuzzy understanding of the nature of parameters in a problem-formulation process. It is shown that a cooperative game with values of coalitions represented by fuzzy numbers arises from the linear production programming problem with fuzzy parameters, and such a game is referred to as a fuzzy linear production programming game. The values of coalitions of the game can be obtained by employing a parametric approach to solving the linear production programming problem with fuzzy parameters. It is proven that the α-core of the game is not empty, and an interval in the α-core is computed by using the ideas of sensitivity analysis and the duality theory of linear programming problems.