Necessity-Based Choquet Integrals for Sequential Decision Making under Uncertainty

Possibilistic decision theory is a natural one to consider when information about uncertainty cannot be quantified in probabilistic way. Different qualitative criteria based on possibility theory have been proposed, the definition of which requires a finite ordinal, non compensatory, scale for evaluating both utility and plausibility. In presence of heterogeneous information, i.e. when the knowledge about the state of the world is modeled by a possibility distribution while the utility degrees are numerical and compensatory, one should rather evaluate each decision on the basis of its Necessity-based Choquet value. In the present paper, we study the use of this criterion in the context of sequential decision trees. We show that it does not satisfy the monotonicity property on which rely the dynamic programming algorithms classically associated to decision trees. Then, we propose a Branch and Bound algorithm based on an optimistic evaluation of the Choquet value of possibilistic decision trees.