###
3rd International Symposium
on

Imprecise
Probabilities and Their Applications

ISIPTA '03

#####
University of Lugano

Lugano, Switzerland

14-17 July 2003

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ELECTRONIC PROCEEDINGS

# Geometry of upper probabilities

### Abstract

In this paper we adopt the geometric approach to the theory of evidence to study the geometric counterparts of the
plausibility functions, or upper probabilities. The computation of the coordinate change between the two natural
reference frames in the belief space allows us to introduce the dual notion of basic plausibility assignment and
understand its relation with the classical basic probability assignment. The convex shape of the plausibility space
$\Pi$ is recovered in analogy to what done for the belief space, and the pointwise geometric relation between a belief
function and the corresponding plausibility vector is discussed. The orthogonal projection of an arbitrary belief
function $s$ onto the probabilistic subspace is computed and compared with other significant entities, such as the relative plausibility
and mean probability vectors.

** Keywords. ** Theory of evidence, belief space, basic plausibility assignment, plausibility space, orthogonal projection

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** Authors addresses: **

Dipartimento di Ingegneria dell'Informazione

Via Gradenigo 6/A

35131 Padova

Italy

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