IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v195y2012i1p237-25910.1007-s10479-011-0852-0.html
   My bibliography  Save this article

Consistent union and prioritized consistent union: new operations for preference aggregation

Author

Listed:
  • Michaël Rademaker
  • Bernard De Baets

Abstract

We discuss some new approaches to preference aggregation, keeping the natural property of transitivity of strict preferences in mind. In a previous paper, we discussed various ways in which to construct and process strict partial order relations in the context of ranking objects on the basis of multiple criteria. We now broaden the scope to include more general expressions of preferences as inputs and introduce the concept of a NIP-triple, composed of a relation of necessary couples, a relation of impossible couples and a relation of possible couples. The use of NIP-triples allows for a more straightforward characterization of the consistent and prioritized consistent union as well as a smooth formulation of algorithmic implementations. We also introduce a NIP-triple closing operation, which can be combined with the consistent union operations for increased flexibility. Some properties of the proposed operations are examined. The consistent union operation is commutative, as is its composition with the closing operation. Both the consistent and prioritized consistent union are associative, but not when they are composed with the closing operation. Nevertheless, the composed operations surely have their use, which is also discussed. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Michaël Rademaker & Bernard De Baets, 2012. "Consistent union and prioritized consistent union: new operations for preference aggregation," Annals of Operations Research, Springer, vol. 195(1), pages 237-259, May.
    • Handle: RePEc:spr:annopr:v:195:y:2012:i:1:p:237-259:10.1007/s10479-011-0852-0
    DOI: 10.1007/s10479-011-0852-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0852-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0852-0?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. Bartel Van de Walle & Bernard De Baets & Etienne Kerre, 1998. "Characterizable fuzzy preference structures," Annals of Operations Research, Springer, vol. 80(0), pages 105-136, January.
    Full references (including those not matched with items on IDEAS)

    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. Haven, Emmanuel, 2002. "Fuzzy interval and semi-orders," European Journal of Operational Research, Elsevier, vol. 139(2), pages 302-316, June.
    2. Van de Walle, Bartel & Turoff, Murray, 2009. "Fuzzy relations for the analysis of traders' preferences in an information market game," European Journal of Operational Research, Elsevier, vol. 195(3), pages 905-913, June.
    3. Hanna Borzęcka, 2012. "Multi-criteria decision making using fuzzy preference relations," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(3), pages 5-21.
    4. Susana Díaz & Bernard Baets & Susana Montes, 2011. "On the Ferrers property of valued interval orders," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 421-447, December.
    5. Georgescu, Irina, 2007. "Consistency indicators for fuzzy choice functions," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 93-105, January.
    6. Doignon, Jean-Paul & Mitas, Jutta, 2000. "Dimension of valued relations," European Journal of Operational Research, Elsevier, vol. 125(3), pages 571-587, September.
    7. S. Chaudhari & S. Desai, 2014. "Transitive and acyclic rationality indicators of fuzzy choice functions on base domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 341-365, February.
    8. Bernard Baets & János Fodor, 1997. "Twenty years of fuzzy preference structures (1978–1997)," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 20(1), pages 45-66, June.
    9. repec:wut:journl:v:3:y:2012:id:1049 is not listed on IDEAS

    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:237-259:10.1007/s10479-011-0852-0. 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.