Possibilistic previsions

The paper deals with a possibilistic imprecise second-order probability model. It is argued that such models appear naturally in a number of situations. They lead to the introduction of a new type of previsions, called possibilistic previsions, which formally generalise coherent upper and lower previsions. The converse problem is also looked at: given a possibilistic prevision, under what conditions can it be generated by a second-order possibility distribution? This leads to the definition of normality, representability and natural extension of possibilistic previsions. Finally, some attention is paid to the special class of full possibilistic previsions, which can be formally related to Zadeh’s fuzzy probabilities. The results have immediate applicability in decision making and statistical reasoning.