Interpreting evidential distances by connecting them to partial orders: Application to belief function approximation

John Klein (1) , Sébastien Destercke (2, 3) , Olivier Colot (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
3 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"

The many distances defined in evidence theory provide instrumental tools to analyze and compare mass functions: they have been proposed to measure conflict, dependence or similarity in different fields (information fusion , risk analysis, machine learning). Many of their mathematical properties have been studied in the past years, yet a remaining question is to know what distance to choose in a particular problem. As a step towards answering this question, we propose to interpret distances by looking at their consistency with partial orders possessing a clear semantic. We focus on the case of in-formational partial order and on the problem of approximating initial belief functions by simpler ones. Doing so, we study which distances can be used to measure the difference of informational content between two mass functions, and which distances cannot.

Mots clés: Belief functions; distance; metric; partial order; semantics; convex optimization

Domaines: Intelligence artificielle [cs.AI]

John Klein, Sébastien Destercke, Olivier Colot. Interpreting evidential distances by connecting them to partial orders: Application to belief function approximation. International Journal of Approximate Reasoning, 2016, 71, pp.15-33. ⟨10.1016/j.ijar.2016.01.001⟩. ⟨hal-01263550⟩