Extreme points of the credal sets generated by elementary comparative probabilities

Authors:
Enrique Miranda;Sébastien Destercke
Affiliations:
Dept. of Statistics and O.R., University of Oviedo, Oviedo, Spain;CNRS, HEUDIASYC Joint Research Unit, France
Venue:
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2013

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Abstract

When using convex probability sets (or, equivalently, lower previsions) as models of uncertainty, identifying extreme points can be useful to perform various computations or to use some algorithms. In general, sets induced by specific models such as possibility distributions, linear vacuous mixtures or 2-monotone measures may have extreme points easier to compute than generic convex sets. In this paper, we study extreme points of another specific model: comparative probability orderings between the elements of a finite space. We use these extreme points to study the properties of the lower probability induced by this set, and connect comparative probabilities with other uncertainty models.