Coherent numerical and ordinal probabilistic assessments

We consider a class of general decomposable measures of uncertainty, which encompasses~as its most specific elements, with respect to the properties of the rules of composition! probabilities, and~as its most general elements! belief functions. The aim, using this general context, is to introduce~in a direct way! the concept of conditional belief function as a conditional generalized decomposable measure w~{6{!, defined on a set of conditional events. Our main tool will be the following result, that we prove in the first part of the article and which is a sort of converse of a well-known result~i.e., a belief function is a lower probability!: a coherent conditional lower probability tP~{6K ! extending a coherent probability P~H i !-where the events H i s are a partition of the certain event V and K is the union of some~possibly all! of them-is a belief function.

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“…9. For the sake of brevity, we do not report here the relevant theorem: See the formulation given in Ref.…”

Section: Remarkmentioning

confidence: 97%

Toward a general theory of conditional beliefs

Coletti

Scozzafava

2006

Int. J. Intell. Syst.

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“…fundamental issue in the field of probability see Refs. 5, 6,7,8,9,13, and 16 . Our aim is to set this problem in the wider framework of Sugeno -additive Ž .…”

Section: Introductionmentioning

confidence: 99%

Consistency for uncertainty measures

Squillante

Ventre²

1998

Int. J. Intell. Syst.

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“…In [8] a characterization of coherent conditional probability, defined on a finite set of conditional events E (E does not generally coincides with B × H), is provided in terms of a class of probabilities. Moreover, in [11] it is shown that coherence, with respect to a conditional probability, can be checked by proving the coherence on any finite subset.…”

Section: Coherent Conditional Probability and Plausibility Assessmentsmentioning

confidence: 99%