Coherence in the aggregate: A betting method for belief functions on many-valued events

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Abstract

Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an (operational) interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework generalises the classical Dutch Book method.

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Flaminio, T., Godo, L., & Hosni, H. (2015). Coherence in the aggregate: A betting method for belief functions on many-valued events. International Journal of Approximate Reasoning, 58, 71–86. https://doi.org/10.1016/j.ijar.2015.01.001

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