Abstract
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.
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Notes
- 1.
Given from a possibility distribution \(\pi \) over a set S, the possibility and the necessity of any event \(A \subseteq S\) are defined by \(\varPi (A) = \max _{s \in A} \pi (s), N(A) = 1 - \varPi (\bar{A}) = 1 - \max _{s \notin A} \pi (s)\).
- 2.
A t-conorm is a non-decreasing semi-group operation on [0, 1] with identity 0 and absorbing element 1. A t-norm is a non-decreasing semi-group operation on [0, 1] with identity 1 and absorbing element 0. T-norms and t-conorms are gradual models of conjunction and disjunction. See [9] for more details.
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Dubois, D., Fargier, H., Guillaume, R., Rico, A. (2021). Sequential Decision-Making Under Uncertainty Using Hybrid Probability-Possibility Functions. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2021. Lecture Notes in Computer Science(), vol 12898. Springer, Cham. https://doi.org/10.1007/978-3-030-85529-1_5
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