Probabilistic Merging Operators

Adamcik, Martin and Wilmers, George (2013) Probabilistic Merging Operators. Logique et Analyse. (Submitted)

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The present work presents a general theoretical framework for the study of operators which merge partial probabilistic evidence from different sources which are individually coherent, but may be collectively incoherent. We consider a number of principles for such an operator to satisfy including a set of principles derived from those of Konieczny and Pino Perez which were formulated for the different context of propositional merging. Finally we investigate two specific such merging operators derived from the Kullback-Leibler notion of informational distance: the social entropy operator, and its dual, the linear entropy operator. The first of these is strongly related to both the multi-agent normalised geometric mean pooling operator and the single agent maximum entropy inference process, ME. By contrast the linear entropy operator is similarly related to both the arithmetic mean pooling operator and the limit centre of mass inference process, CM^infinity.

Item Type: Article
Uncontrolled Keywords: uncertain reasoning, probability function, merging of evidence, Kullback-Leibler, divergence, probabilistic merging, merging operator, Konieczny and Pino Perez, social entropy process, inference process, aggregation of probabilities, pooling operator, probabilistic inference, maximum entropy
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
MSC 2010, the AMS's Mathematics Subject Classification > 52 Convex and discrete geometry
MSC 2010, the AMS's Mathematics Subject Classification > 91 Game theory, economics, social and behavioral sciences
Depositing User: Mr Martin Adamcik
Date Deposited: 23 Jul 2013
Last Modified: 20 Oct 2017 14:13

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