Imprecise probabilistic models based on hierarchical intervals

Abstract

This paper proposes a generalization of the imprecise probability model given by probability intervals on singleton sets. This enables us not only to represent probability intervals in a hierarchy of sets with a tree structure but also to represent other models such as possibility measures and generalized p-boxes. The paper also shows how the resulting model is always an order-2 capacity and that the basic operations of checking coherence, computing the natural extension or conditioning can be performed in an extremely efficient way.