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Journal of Logic and Computation Advance Access published online on July 22, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp038
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Max-based Prioritized Information Fusion without Commensurability

Salem Benferhat, Sylvain Lagrue and Julien Rossit

Univ Lille Nord de France, F-5900 Lille, France;
CRIL-CNRS UMR 8788, F-62307 Lens, France.
E-mail: benferhat{at}cril.univ-artois.fr; lagrue{at}cril.fr; rossit{at}cril.univ-artois.fr

Received 8 December 2008.

In the last decade, several approaches have been proposed for merging multiple and potentially conflicting pieces of information. Egalitarian fusion modes pick solutions that minimize the local dissatisfaction of each source (agent, expert), which is involved in the fusion process. When pieces of information to merge are prioritized, or ranked, most existing approaches assume that these priority degrees are commensurable, namely sources are assumed to share the same meaning of uncertainty scales. This article provides useful strategies for an egalitarian fusion of incommensurable ranked belief bases under constraints. In particular, it focuses on Max-based merging operators, and proposes a merging operator that allows to aggregate a set of ranked belief bases E. This operator is based on the concept of compatible scales. We provide three equivalent characterizations of this operator. The first one shows that Max-based merging of incommensurable belief bases can also be defined in terms of a Pareto-like ordering on possible worlds, denominated SMP ordering. The second one is based on the notion of compatible rankings defined on finite scales. The third one is only based on total pre-orders induced by ranked bases to merge. The last part of the article analyses rational postulates satisfied by our merging operator and compare it with some related works.

Keywords: Belief merging; ranked belief bases; incommensurability



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