On the connection between probability boxes and possibility measures

Troffaes M.C.M Matthias (1) , Enrique Miranda (2) , Sébastien Destercke (3)

1 Department of Mathematical Sciences
2 Departomento de Estadistica
3 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

We explore the relationship between p-boxes on totally preordered spaces and possibility measures. We start by demonstrating that only those p-boxes who have 0-1-valued lower or upper cumulative distribution function can be possibility measures, and we derive expressions for their natural extension in this case. Next, we establish necessary and sufficient conditions for a p-box to be a possibility measure. Finally, we show that almost every possibility measure can be modelled by a p-box. Whence, any techniques for p-boxes can be readily applied to possibility measures. We demonstrate this by deriving joint possibility measures from marginals, under varying assumptions of independence, using a technique known for p-boxes.

Mots clés: Possibility measures; maxitive measures; pboxes; coherent upper previsions; natural extension

Domaines: Probabilités [math.PR]; Intelligence artificielle [cs.AI]

Troffaes M.C.M Matthias, Enrique Miranda, Sébastien Destercke. On the connection between probability boxes and possibility measures. The 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011), Jul 2011, Aix-les-Bains, France. pp.836 - 843, ⟨10.2991/eusflat.2011.150⟩. ⟨hal-00655597⟩