Decision making over imprecise lotteries

Since von Neuman and Morgenstern's (1944) contribution to game theory, the expected utility criterion has become the standard functional to evaluate risky prospects. Risky prospects are understood to be lotteries on a set of prizes. In which case a decision maker will receive a precise prize with a given probability. A wide interest on imprecise object has been developped since Zadeh's (1978) contribution to artificial intelligence, through the use of possibility function (see Dubois Prade (1988)). In this setting a decision maker is uncertain about the precise features of the object he is dealing with. A first step has been readily made to rank imprecise objects in Rébillé (2005). Our objective is to build a decision theory which deals with imprecise lotteries i.e. lotteries on imprecise prizes, a typical situation encountered in Ellsberg's experiment (1961).