Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Mobius Inversion

Alain Chateauneuf (1, 2) , Jean-Yves Jaffray (3)

1 CES - Centre d'économie de la Sorbonne
2 Axe Economie mathématique et jeux
3 DECISION

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.

Mots clés: Decision theory

Domaines: Economies et finances

Alain Chateauneuf, Jean-Yves Jaffray. Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Mobius Inversion. Classic Works of the Dempster-Shafer Theory of Belief Functions, 219, Springer, pp.477-498, 2008, Studies in Fuzziness and Soft Computing, ⟨10.1007/978-3-540-44792-4_19⟩. ⟨hal-00649208⟩