FOURTH INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS
Carnegie Mellon University
Pittsburgh, PA, USA
July 20-23 2005

ISIPTA'05 ELECTRONIC PROCEEDINGS

Gert De Cooman, Matthias Troffaes, Enrique Miranda

n-Monotone lower previsions and lower integrals

Abstract

We study n-monotone lower previsions, which constitute a generalisation of n-monotone lower probabilities. We investigate their relation to the concepts of coherence and natural extension in the behavioural theory of imprecise probabilities, and improve along the way upon a number of results from the literature. Finally, we indicate how many approaches to integration in the literature fall nicely within the framework of the present study of coherent n-monotone lower previsions. This discussion allows us to characterise which types of integrals can be used to calculate the natural extension of a probability charge.

Keywords. n-monotonicity, coherence, natural extension, Choquet integral, comonotone additivity, lower prevision, lower integral

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Authors addresses:

Gert De Cooman
Technologiepark - Zwijnaarde 914
9052 Zwijnaarde

Matthias Troffaes
Technologiepark Zwijnaarde 914
9052 Zwijnaarde

Enrique Miranda
Dpto. de Inform�tica, Estad�stica y Telem�tica
Univ. Rey Juan Carlos
C-Tulip�n, s/n
M�stoles (Madrid)
SPAIN

E-mail addresses:

Gert De Cooman gert.decooman@ugent.be
Matthias Troffaes matthias.troffaes@gmail.com
Enrique Miranda enrique.miranda@urjc.es


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