par Smets, Philippe
Référence Intelligent Systems for Information Processing: From Representation to Applications, Elsevier B.V., page (265-275)
Publication Publié, 2003-11
Partie d'ouvrage collectif
Résumé : This chapter highlights the fact that quantified beliefs should be represented by belief functions. The purpose of any mathematical model is for representing quantified beliefs-weighted opinions that can be supported either by defending convincing definitions with illustrative examples or by producing a set of axioms that justify it. The mathematical function that can represent quantified beliefs should be a Choquet capacity monotone of order 2. In order to show that it must be monotone of order infinite, thus a belief function, several extra rationality requirements are proposed the chapter. One of them is based on the negation of a belief function, a concept introduced by Dubois and Prade. In any model for quantified beliefs, an agent, the belief holder, and a finite frame of discernment, denoted by Ω, are considered. If revision of any measure representing quantified beliefs can be represented by a matrix multiplication of the initial beliefs, then the Mobius mass related to the measure must be non negative. This implies that any measure representing quantified beliefs is a belief function. © 2003 Elsevier B.V. All rights reserved.