Two axiomatic approaches to decision making using possibility theory

This paper proposes a utility theory for decision making under uncertainty that is described by possibility theory. We show that our approach is a natural generalization of the two axiomatic systems that correspond to pessimistic and optimistic decision criteria proposed by Dubois et al. The generalization is achieved by removing axioms that are supposed to reflect attitudes toward uncertainty, namely, pessimism and optimism. In their place we adopt an axiom that imposes an order on a class of canonical lotteries that realize either in the best or in the worst prize. We prove an expected utility theorem for the generalized axiomatic system based on the newly introduced concept of binary utility.