Possibilistic Influence Diagrams
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Possibility theory as a basis for qualitative decision theory
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
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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.