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Complexity results and algorithms for possibilistic influence diagrams. (English) Zbl 1183.62133
Summary: We present the framework of Possibilistic Influence Diagrams (PID), which allows 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, the semantics however differ. Transition likelihoods are expressed as possibility distributions and rewards are considered as satisfaction degrees. The expected utility is then replaced by anyone of two possibilistic qualitative utility criteria (optimistic and pessimistic) for evaluating strategies in a PID. We then describe decision tree-based methods for evaluating PID and computing optimal strategies, and we study the computational complexity of PID optimisation problems for both cases. Finally, we propose a dedicated variable elimination algorithm that can be applied to both optimistic and pessimistic cases for solving PID.

MSC:
62L10 Sequential statistical analysis
62C99 Statistical decision theory
62-09 Graphical methods in statistics (MSC2010)
91B06 Decision theory
65C60 Computational problems in statistics (MSC2010)
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