Fonctions de croyance : décompositions canoniques et règles de combinaison. (Belief functions: canonical decompositions and combination rules)

Compare a la theorie des possibilites, le Modele des Croyances Transferables (MCT) - une interpretation non probabiliste de la theorie de Dempster-Shafer - dispose d'assez peu de choix en terme d'operateurs d'agregation pour la fusion d'informations. Dans cette these, ce probleme de manque de flexibilite pour la combinaison des fonctions de croyance - l'outil mathematique permettant la representation de l'information dans le MCT - est aborde. Notre premiere contribution est la mise a jour de familles infinies de regles de combinaison conjonctives et disjonctives, rejoignant ainsi la situation en theorie des possibilites en ce qui concerne les operateurs de fusion conjonctive et disjonctive. Notre deuxieme contribution est un ensemble de resultats rendant interessante, d'un point de vue applicatif, une famille infinie de regles de combinaison, appelee les alpha-jonctions et introduite initialement de maniere purement formelle. Tout d'abord, nous montrons que ces regles correspondent a une connaissance particuliere quant a la veracite des sources d'information. Ensuite, nous donnons plusieurs nouveaux moyens simples de calculer la combinaison par une alpha-jonction.

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