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 |