Idempotent Conjunctive Combination of Belief Functions by Distance Minimization

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"

When combining multiple belief functions, designing a combination rule that selects the least informative belief function among those more informative than each of the combined ones is a difficult task. Such rules, commonly depicted as " cautious " , are typically required to be idempotent, since when one is cautious, combining identical information should not lead to the reinforcement of some hypothesis. However, applying the least commitment principle using partial orders is in general not straightforward, mainly due to the non-uniqueness of solutions. Building upon previous work, this paper investigates the use of distances compatible with such partial orders to determine a unique solution to the combination problem. The obtained operators are conjunctive, idempo-tent and commutative, but lack associativity. They are, however, quasi-associative allowing sequential combinations at no extra complexity.

Mots clés: distance; optimization; belief function; idempotence; conjunctive combination

Domaines: Autre [cs.OH]

John Klein, Sébastien Destercke, Olivier Colot. Idempotent Conjunctive Combination of Belief Functions by Distance Minimization. 4th International Conference on Belief Functions : Theory and Applications (BELIEF 2016), Sep 2016, Pragua, Czech Republic. pp.156-163, ⟨10.1007/978-3-319-45559-4_16⟩. ⟨hal-01396205⟩