Decision under Uncertainty

By Philippe Smets. arXiv.org, 2013

433 citations recorded by the source corpus.

We derive axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.

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Possibility theory and statistical reasoning (2006, neutral): “Another view, whose main proponent is Smets [100], contends that one should distinguish between a credal level whereby an agent entertains beliefs and incomplete information is explicitly accounted for (in terms of belief functions according to Smets, but it could be imprecise probabilities likewise”
Handling uncertainty in the hydroinformatic process (2003, neutral): “This deliberative level of communication and negotiation, that characterises most complex decision-making process, is referred to by Smets (1990) as the credal level.”
Decision making in the TBM: the necessity of the pignistic transformation (2005, methodology): “The intuitive justification based on the previous scenario was presented in ( Smets, 1990, 1993; Smets & Kennes, 1994).”
Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities (2004, positive): “Therefore p¢(x) = p¢(g(x))g¢(x) because p(x) = p(g(x)) , and thus Therefore, ∫ (x m , +∞] p ( y ) d y = -∫ (–∞, x m ] p(x)g¢(x)dx and the function p so defined satisfies the normalization condition: When p is a continuous unimodal probability distribution, applying successively (3) and (4) retrieves”