Possibilistic Influence Diagrams

In this article we present the framework of Possibilistic Influence Diagrams (PID), which allow to model in a compact form problems of sequential decision making under uncertainty, when only ordinal data on transitions likelihood or preferences are available. The graphical part of a PID is exactly the same as that of usual influence diagrams, however the semantics differ. Transition likelihoods are expressed as possibility distributions and rewards are here considered as satisfaction degrees. Expected utility is then replaced by anyone of two possibilistic qualitative utility criteria for evaluating strategies in a PID. We describe a decision tree-based method for evaluating PID and computing optimal strategies. We then study the computational complexity of PID-related problems (computation of the value of a policy, computation of an optimal policy).

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