The α-core of fuzzy linear production games

In this paper 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 a 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