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Coherent restrictions of vague conditional lower-upper probability extensions
In this paper we propose a way to restrict extension bounds
induced by coherent conditional lower-upper probability assessments.
Such shrinkage turns out to be helpful whenever the natural bounds
are too vague to be used. Since coherence of a conditional lower-upper
probability assessment can be characterized through a class of conditional probability distributions, the idea is to take the intersection of the extension bounds induced by each single element of the class instead of
the convex combination, as it is usually done. Coherence of such method
is proved for extensions performed on both conditional events logical dependent and not-dependent on the initial domain