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Article Dans Une Revue Journal of Mathematical Psychology Année : 2015

Extreme points of the credal sets generated by comparative probabilities

Résumé

When using convex probability sets (or, equivalently, lower previsions) as uncertainty models, identifying extreme points can help simplifying various computations or the use of some algorithms. In gen-eral, sets induced by specific models such as possibility distributions, lin-ear vacuous mixtures or 2-monotone measures may have extreme points easier to compute than generic convex sets. In this paper, we study ex-treme points of another specific model: comparative probability order-ings between the singletons of a finite space. We characterise these ex-treme points by mean of a graphical representation of the comparative model, and use them to study the properties of the lower probability in-duced by this set. By doing so, we show that 2-monotone capacities are not informative enough to handle this type of comparisons without a loss of information. In addition, we connect comparative probabilities with other uncertainty models, such as imprecise probability masses.
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Dates et versions

hal-01100522 , version 1 (06-01-2015)

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Enrique Miranda, Sébastien Destercke. Extreme points of the credal sets generated by comparative probabilities. Journal of Mathematical Psychology, 2015, 64-65, pp.44 - 57. ⟨10.1016/j.jmp.2014.11.004⟩. ⟨hal-01100522⟩
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