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Lexicographic combinations of preference relations in the context of Possibilistic Decision Theory

Other TitlesCombinaciones lexicográficas de relaciones de preferencia en el contexto de la Teoría de la Decisión Posibilista
AuthorsGodo, Lluis ; Zapico, Adriana
KeywordsAxiomatic systems
Possibilistic decision theory
Lexicographic refinements
Issue Date2006
PublisherUniversidad Politécnica de Cataluña
CitationMathware and Soft Computing, 2006, 13 (3): 157-171.
AbstractIn Possibilistic Decision Theory (PDT), decisions are ranked by a pressimistic or by an optimistic qualitative criteria. The preference relations induced by these criteria have been axiomatized by corresponding sets of rationality postulates, both à la von Neumann and Morgenstern and à la Savage. In this paper we first address a particular issue regarding the axiomatic systems of PDT à la von Neumann and Morgenstern. Namely, we show how to adapt the axiomatic systems for the pessimistic and optimistic criteria when some finiteness assumptions in the original model are dropped. Second, we show that a recent axiomatic approach by Giang and Shenoy using binary utilities can be captured by preference relations defined as lexicographic refinements of the above two criteria. We also provide an axiomatic characterization of these lexicographic refinements.
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