A generalized notion of lottery is considered, where the uncertainty is expressed by a belief function. Given a partial preference relation on an arbitrary set of generalized lotteries all on the same finite totally ordered set of prizes, conditions for the representability, either by a linear utility or a Choquet expected utility are provided. Both the cases of a finite and an infinite set of generalized lotteries are investigated.
Axioms are given for positive comparative probabilities and plausibilities defined either on Boolean algebras or on arbitrary sets of events. These axioms allow to characterize binary relations representable by either standard or nonstandard measures (i. e. taking values either on the real field or on a hyperreal field). We also study relations between conditional events induced by preferences on conditional acts.