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

In the present study we consider a production model in which multiple decis ion makers pool resources to produce finished goods. Such a production mode l, which is assumed to be linear, can be formulated as mathematical program ming problems with fuzzy parameters from the viewpoint of experts' imprecis e or fuzzy understanding of the nature of parameters in a problem-formulati on process. It is shown that a cooperative game with values of coalitions r epresented by fuzzy numbers arises from the linear production programming p roblem with fuzzy parameters, and such a game is referred to as a fuzzy lin ear production programming game. The values of coalitions of the game can b e obtained by employing a parametric approach to solving the linear product ion programming problem with fuzzy parameters. It is proven that the alpha- core of the game is not empty, and an interval in the alpha-core is compute d by using the ideas of sensitivity analysis and the duality theory of line ar programming problems. (C) 2000 Elsevier Science B.V. All rights reserved .