Fuzzy TU Games and Their Classes

The classical theory of coalitional games with transferable utility is based on the assumption that all parameters of such games, including the expected pay-offs of coalitions, are exactly determined. In real cooperative situations, this assumption appears rather umealistic. Then the coalitional pay-offs, formally represented by the values of characteristic function of the game, cannot be represented by crisp real numbers. The fuzzy set and fuzzy quantity theory offers adequate tools for the modelling of vagueness connected with expected pay-offs. The model of TU coalitional game was investigated in numerous papers and summarized in [5J. In this paper we focuse our attention to the fact that fuzzy expected pay-offs of coalitions can be easily transformed into fuzziness connected with classes of the complete games. This transformation can be well defined and under simple assumptions also unique. This uniqueness of the relation between fuzzy pay-offs in TU games and fuzzy class of deterministic TU games generated by them is analyzed in the submitted paper.