The paper presents an interesting generalisation of some results about de Finetti coherent probabilities to an assignment of indeterminate probabilities on many-valued events in an MV-algebra. After recalling the Dutch Book interpretation of probability by de Finetti and his well-known related theorem, which states that an agent's degrees of belief are coherent (i.e. they do not permit a Dutch Book) if and only if they conform to probability axioms, the author proves an analogous result for upper (and lower) probabilities defined on divisible MV-algebras. Specifically, she proves that in a divisible MV-algebra of events a book does not allow any bad bet if and only if it can be extended to an upper probability over the whole MV-algebra. The proof of this result relies on Hahn-Banach and separation theorems as well as on other tools from functional analysis.

Review of MR2731982: Fedel, Martina(I-SIN-MI) - Uncertainty, indeterminacy and fuzziness: a probabilistic approach. Probability, uncertainty and rationality, 219–242, CRM Series, 10, Ed. Norm., Pisa, 2010.

PELESSONI, RENATO
2011-01-01

Abstract

The paper presents an interesting generalisation of some results about de Finetti coherent probabilities to an assignment of indeterminate probabilities on many-valued events in an MV-algebra. After recalling the Dutch Book interpretation of probability by de Finetti and his well-known related theorem, which states that an agent's degrees of belief are coherent (i.e. they do not permit a Dutch Book) if and only if they conform to probability axioms, the author proves an analogous result for upper (and lower) probabilities defined on divisible MV-algebras. Specifically, she proves that in a divisible MV-algebra of events a book does not allow any bad bet if and only if it can be extended to an upper probability over the whole MV-algebra. The proof of this result relies on Hahn-Banach and separation theorems as well as on other tools from functional analysis.
uncertainty
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2831758
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