Sequential Decision-Making Under Uncertainty Using Hybrid Probability-Possibility Functions

Probabilistic and possibilistic models of sequential decision problems are known to possess good behavioral and algorithmic properties. In this paper, the range of models of problems of sequential decision under uncertainty that are dynamically consistent, consequentialist and allow for tree reduction is enlarged by considering a representation of uncertainty that is both probabilistic and possibilistic. The corresponding utility functional is expected utility for highly likely states, and an optimistic or pessimistic possibility-based criterion for unlikely states.