Other uncertainty theories based on capacities

Sébastien Destercke (1, 2) , Didier Dubois (3)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"
3 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

The two main uncertainty representations in the literature that tolerate imprecision are possibility distributions and random disjunctive sets. This chapter devotes special attention to the theories that have emerged from them. The first part of the chapter discusses epistemic logic and derives the need for capturing imprecision in information representations. It bridges the gap between uncertainty theories and epistemic logic showing that imprecise probabilities subsume modalities of possibility and necessity as much as probability. The second part presents possibility and evidence theories, their origins, assumptions and semantics, discusses the connections between them and the general framework of imprecise probability. Finally, chapter points out the remaining discrepancies between the different theories regarding various basic notions, such as conditioning, independence or information fusion and the existing bridges between them.

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

Sébastien Destercke, Didier Dubois. Other uncertainty theories based on capacities. T. Augustin; F. Coolen; G. De Cooman; M. Troffaes. Introduction to Imprecise Probabilities, Chapter 5, Wiley, pp.93-112, 2014, Wiley series in probability and statistics, 978-0-470-97381-3. ⟨10.1002/9781118763117.ch5⟩. ⟨hal-00999503⟩