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Evidential reasoning in large partially ordered sets

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  • Thierry Denœux
  • Marie-Hélène Masson

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

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  • Thierry Denœux & Marie-Hélène Masson, 2012. "Evidential reasoning in large partially ordered sets," Annals of Operations Research, Springer, vol. 195(1), pages 135-161, May.
    • Handle: RePEc:spr:annopr:v:195:y:2012:i:1:p:135-161:10.1007/s10479-011-0887-2
    DOI: 10.1007/s10479-011-0887-2
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    References listed on IDEAS

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    1. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
    2. Patrice Perny, 1998. "Multicriteria filtering methods based onconcordance and non-discordance principles," Annals of Operations Research, Springer, vol. 80(0), pages 137-165, January.
    3. Irène Charon & Olivier Hudry, 1998. "Lamarckian genetic algorithmsapplied to the aggregation of preferences," Annals of Operations Research, Springer, vol. 80(0), pages 281-297, January.
    4. Jacinto González-Pachón & Carlos Romero, 2007. "Inferring consensus weights from pairwise comparison matrices without suitable properties," Annals of Operations Research, Springer, vol. 154(1), pages 123-132, October.
    5. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
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    Cited by:

    1. Xinyang Deng & Yong Deng & Felix Chan, 2014. "An improved operator of combination with adapted conflict," Annals of Operations Research, Springer, vol. 223(1), pages 451-459, December.
    2. Chao Fu & Min Xue & Wenjun Chang, 2022. "Multiple criteria decision making with reliability of assessment," Annals of Operations Research, Springer, vol. 312(1), pages 121-157, May.
    3. Suradej Duangpummet & Jessada Karnjana & Waree Kongprawechnon, 2021. "State-of-charge estimation based on theory of evidence and interval analysis with differential evolution optimization," Annals of Operations Research, Springer, vol. 300(2), pages 399-414, May.
    4. Lianmeng Jiao & Quan Pan & Yan Liang & Xiaoxue Feng & Feng Yang, 2016. "Combining sources of evidence with reliability and importance for decision making," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(1), pages 87-106, March.

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