Lexicographic refinements in the context of possibilistic decision theory

In Possibilistic Decision Theory (PDT), decisions are ranked by a pessimistic and an optimistic qualitative criteria. The preference relations in-duced by these criteria have been axiomatized by corresponding sets of rationality postulates, both a ̀ la Neumann-Morgenstern and a ̀ la Savage. In this paper we first address a particular issue re-garding the axiomatic systems of PDT a ̀ la von Neumann and Morgenstern. Namely, we show how to adapt the axiomatic systems for the pes-simistic and optimistic criteria when finiteness as-sumptions in the original model are dropped. Sec-ond, we show that a recent axiomatic approach by Giang and Shenoy using binary utilities can be captured by preference relations defined as lexi-cographic refinements of the above two criteria. We also provide an axiomatic characterization of these lexicographic refinements