Additivities in fuzzy coalition games with side-payments

The fuzzy coalition game theory brings a more realistic tools for the mathe matical modelling of the negotiation process and its results. In this paper we limit our attention to the fuzzy extension of the simple model of coali tion games with side-payments, and in the frame of this model we study one of the elementary concepts of the coalition game theory, namely its "additi vities", i.e., superadditivity, subadditivity and additivity in the strict sense. In the deterministic game theory these additivites indicate the stru cture of eventual cooperation, namely the extent of finally formed coalitio ns, if the cooperation is possible. The additivities in fuzzy coalition gam es play an analogous role. But the vagueness of the input data about the ex pected coalitional incomes leads to consequently vague validity of the supe radditivity, subadditivity and additivity. In this paper we formulate the m odel of this vagueness depending on the fuzzy quantities describing the exp ected coalitional pay-offs, and we introduce some elementary results mostly determining the links between additivities in a deterministic coalition ga me and its fuzzy extensions.