Linear coalitional games and their fuzzy extensions

The paper deals with fuzzifications of the coalitional game models in which the expected pay-offs of players and coalitions are known only vaguely. Th ere exists a class of games, here we call them linear coalitional games, wh ich can be modelled as games with, as well as without, side payments. In th e deterministic case both types of models of a linear coalitional game lead to the same results. As the fuzzification of games with side-payments is b ased on other principles than the fuzzification of more general games witho ut side-payments, the linear coalitional games offer situations in which bo th approaches to the fuzzification of coalitional game models can be compar ed and their differences can be clearly illustrated. In this paper the atte ntion is focused to the analysis of concepts of superadditivity and core of coalitional games.