 
Summary: Credal Sets Approximation by Lower
Probabilities: Application to Credal Networks
Alessandro Antonuccia
and Fabio Cuzzolinb
(a) Istituto Dalle Molle di Studi sull'Intelligenza Artificiale
Galleria 2, Via Cantonale, MannoLugano (Switzerland)
alessandro@idsia.ch
(b) Department of Computing, Oxford Brookes University
Wheatley Campus, Wheatley, Oxford (United Kingdom)
fabio.cuzzolin@brookes.ac.uk
Abstract. Credal sets are closed convex sets of probability mass func
tions. The lower probabilities specified by a credal set for each element
of the power set can be used as constraints defining a second credal
set. This simple procedure produces an outer approximation, with a
bounded number of extreme points, for general credal sets. The approx
imation is optimal in the sense that no other lower probabilities can
specify smaller supersets of the original credal set. Notably, in order to
be computed, the approximation does not need the extreme points of the
credal set, but only its lower probabilities. This makes the approxima
tion particularly suited for credal networks, which are a generalization of
