Geometry of possibility measures on finite sets

The paper presents a purely geometrical characterization of the convex set of probabilities dominated by a possibility measure on a finite set. It is demonstrated that the set of dominated probabilities can be represented as a very special kind of convex polyhedral set, the so-called simple polytope, which enhances performance of computational methods. A lower bound and a new upper bound for the number of extreme points are established. It is shown that the upper bound leads in some cases to a better estimate than the exponential bound appearing in the literature.