A geometric and game-theoretic study of the conjunction of possibility measures

Enrique Miranda (1) , Matthias C.M. Troffaes (2) , Sébastien Destercke (3, 4)

1 Universidad de Oviedo [Oviedo]
2 Department of Mathematical Sciences
3 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
4 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"

In this paper, we study the conjunction of possibility measures when they are interpreted as coherent upper probabilities, that is, as upper bounds for some set of probability measures. We identify conditions under which the minimum of two possibility measures remains a possibility measure. We provide graphical way to check these conditions, by means of a zero-sum game formulation of the problem. This also gives us a nice way to adjust the initial possibility measures so their minimum is guaranteed to be a possibility measure. Finally, we identify conditions under which the minimum of two possibility measures is a coherent upper probability, or in other words, conditions under which the minimum of two possibility measures is an exact upper bound for the intersection of the credal sets of those two possibility measures.

Mots clés: coherence; natural extension; possibility measure; conjunction; imprecise probability; game theory

Domaines: Autre [cs.OH]

Enrique Miranda, Matthias C.M. Troffaes, Sébastien Destercke. A geometric and game-theoretic study of the conjunction of possibility measures. Information Sciences, 2015, 298, pp.373 - 389. ⟨10.1016/j.ins.2014.10.067⟩. ⟨hal-01100523⟩