IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v195y2012i1p135-16110.1007-s10479-011-0887-2.html
   My bibliography  Save this article

Evidential reasoning in large partially ordered sets

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0887-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0887-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fu-Ling Cai & Xiuwu Liao & Kan-Liang Wang, 2012. "An interactive sorting approach based on the assignment examples of multiple decision makers with different priorities," Annals of Operations Research, Springer, vol. 197(1), pages 87-108, August.
    2. Eduardo Fernández & José Rui Figueira & Jorge Navarro, 2023. "A theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes," Annals of Operations Research, Springer, vol. 325(2), pages 819-843, June.
    3. Doumpos, M. & Marinakis, Y. & Marinaki, M. & Zopounidis, C., 2009. "An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method," European Journal of Operational Research, Elsevier, vol. 199(2), pages 496-505, December.
    4. Fernandez, Eduardo & Navarro, Jorge & Bernal, Sergio, 2010. "Handling multicriteria preferences in cluster analysis," European Journal of Operational Research, Elsevier, vol. 202(3), pages 819-827, May.
    5. Roy, Bernard & Slowinski, Roman, 2008. "Handling effects of reinforced preference and counter-veto in credibility of outranking," European Journal of Operational Research, Elsevier, vol. 188(1), pages 185-190, July.
    6. Ana Sara Costa & Isabella M. Lami & Salvatore Greco & José Rui Figueira & José Borbinha, 2021. "Assigning a house for refugees: an application of a multiple criteria nominal classification method," Operational Research, Springer, vol. 21(4), pages 2651-2687, December.
    7. Zopounidis, Constantin & Doumpos, Michael, 2002. "Multicriteria classification and sorting methods: A literature review," European Journal of Operational Research, Elsevier, vol. 138(2), pages 229-246, April.
    8. Mosmans, Alain & Praet, Jean-Claude & Dumont, Christophe, 2002. "A decision support system for the budgeting of the Belgian health care system," European Journal of Operational Research, Elsevier, vol. 139(2), pages 449-460, June.
    9. John Martin, 2014. "Spatial processes and Galois/concept lattices," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(2), pages 961-981, March.
    10. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2023. "Multiple criteria sorting models and methods—Part I: survey of the literature," 4OR, Springer, vol. 21(1), pages 1-46, March.
    11. Tlili, Ali & Belahcène, Khaled & Khaled, Oumaima & Mousseau, Vincent & Ouerdane, Wassila, 2022. "Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations," European Journal of Operational Research, Elsevier, vol. 298(3), pages 979-1006.
    12. Michel Grabisch & Agnieszka Rusinowska, 2015. "Lattices in Social Networks with Influence," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-18.
    13. Jean-Paul Doignon & Kota Saito, 2022. "Adjacencies on random ordering polytopes and flow polytopes," Papers 2207.06925, arXiv.org.
    14. Fernandez, Eduardo & Navarro, Jorge & Bernal, Sergio, 2009. "Multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm," European Journal of Operational Research, Elsevier, vol. 198(2), pages 602-609, October.
    15. Bernard Monjardet, 2007. "Some Order Dualities In Logic, Games And Choices," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 1-12.
    16. Yuan Li & Xiuwu Liao & Wenhong Zhao, 2009. "A rough set approach to knowledge discovery in analyzing competitive advantages of firms," Annals of Operations Research, Springer, vol. 168(1), pages 205-223, April.
    17. Doumpos, Michael & Zopounidis, Constantin, 2004. "Developing sorting models using preference disaggregation analysis: An experimental investigation," European Journal of Operational Research, Elsevier, vol. 154(3), pages 585-598, May.
    18. Murat Köksalan & Vincent Mousseau & Özgür Özpeynirci & Selin Bilgin Özpeynirci, 2009. "A new outranking‐based approach for assigning alternatives to ordered classes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(1), pages 74-85, February.
    19. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    20. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2010. "Electre Tri-C: A multiple criteria sorting method based on characteristic reference actions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 565-580, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:195:y:2012:i:1:p:135-161:10.1007/s10479-011-0887-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.