Evidential reasoning in large partially ordered sets

Thierry Denœux () and Marie-Hélène Masson ()

Annals of Operations Research, 2012, vol. 195, issue 1, 135-161

Abstract: The Dempster-Shafer theory of belief functions has proved to be a powerful formalism for uncertain reasoning. However, belief functions on a finite frame of discernment Ω are usually defined in the power set 2 Ω , resulting in exponential complexity of the operations involved in this framework, such as combination rules. When Ω is linearly ordered, a usual trick is to work only with intervals, which drastically reduces the complexity of calculations. In this paper, we show that this trick can be extrapolated to frames endowed with an arbitrary lattice structure, not necessarily a linear order. This principle makes it possible to apply the Dempster-Shafer framework to very large frames such as the power set, the set of partitions, or the set of preorders of a finite set. Applications to multi-label classification, ensemble clustering and preference aggregation are demonstrated. Copyright Springer Science+Business Media, LLC 2012

Keywords: Belief functions; Dempster-Shafer theory; Evidence theory; Lattices; Lattice intervals; Classification; Clustering; Learning; Preference relation; Preorder (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10479-011-0887-2

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