Comparative models ruled by possibility and necessity: a conditional world.

Any dynamic decision model needs to deal with conditional events and conditional uncertainty measures. Moreover, to avoid the introduction of not available information in decision processes, we should refer to domains containing only the elements of interest. According to the aforementioned guidelines we study the comparative uncertainty framework for decision models referring to possibility and necessity measures: we consider binary relations, defined on an arbitrary set of conditional events and we provide a complete characterization in terms of necessary and sufficient conditions for their representability by a conditional possibility and by a conditional necessity.