Vertical Barrier Models as Unified Distortions

Vertical Barrier Models (VBM) are a family of imprecise probability models that generalise a number of well known distortion/neighbourhood models (such as the Pari-Mutuel Model, the Linear-Vacuous Model, and others) while still being relatively simple. Several of their properties were established by Pelessoni, Vicig, and Corsato. In this paper we explore, in a finite framework, further facets of these models: their interpretation as neighbourhood models, the structure of their credal set in terms of maximum number of its extreme points, the result of merging operations with VBMs, conditions for VBMs to be belief functions or possibility measures.