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Chateauneuf, Alain; Jaffray, Jean-Yves

Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. (English) Zbl 0669.90003

Math. Soc. Sci. 17, No. 3, 263-283 (1989).
Monotone capacities (on finite sets) of finite or infinite order (lower probabilities) are characterized by properties of their Möbius inverses. A necessary property of probabilities dominating a given capacity is demonstrated through the use of Gale’s theorem for the transshipment problem. This property is shown to be also sufficient if and only if the capacity is monotone of infinite order. A characterization of dominating probabilities specific to capacities of order 2 is also proved.

Cited in 2 Reviews
Cited in 211 Documents

MSC:

91B06 Decision theory

Keywords:

belief functions; representation of uncertainty; Monotone capacities; lower probabilities; Möbius inverses; transshipment problem; dominating probabilities
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\textit{A. Chateauneuf} and \textit{J.-Y. Jaffray}, Math. Soc. Sci. 17, No. 3, 263--283 (1989; Zbl 0669.90003)
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References:

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