IDEAS home Printed from https://ideas.repec.org/p/ulb/ulbeco/2013-165863.html
   My bibliography  Save this paper

Minimal representation of a semiorder

Author

Listed:
  • Marc Pirlot

Abstract

In a multicriteria decision problem it may happen that the preference of the decision-maker on some criterion is modeled by means of a semiorder structure. If the available information is qualitative, one often needs a numerical representation of the semiorder. We investigate the set of representations of a semiorder and show that, once a unit has been fixed, there exists a minimal representation. This representation can be calculated by linear programming and exhibits some interesting properties: all values are integer multiples of the unit and are as scattered as possible in the sense that, in the set of all representations contained in the same bounded interval, the minimal representation is a representation for which the minimal distance between two values is maximal. The minimal representation can also be interpreted as a generalisation of the rank function associated to linear orders. © 1990 Kluwer Academic Publishers.

Suggested Citation

  • Marc Pirlot, 1990. "Minimal representation of a semiorder," ULB Institutional Repository 2013/165863, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/165863
    Note: SCOPUS: ar.j
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Denis Bouyssou & Marc Pirlot, 2021. "Unit representation of semiorders I: Countable sets," Post-Print hal-02918005, HAL.
    2. Denis Bouyssou & Marc Pirlot, 2020. "Unit representation of semiorders I: Countable sets," Working Papers hal-02918005, HAL.
    3. Denis Bouyssou & Marc Pirlot, 2021. "Unit representation of semiorders II: The general case," Post-Print hal-02918017, HAL.
    4. Candeal, Juan Carlos & Indurain, Esteban & Zudaire, Margarita, 2002. "Numerical representability of semiorders," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 61-77, January.
    5. Denis Bouyssou & Marc Pirlot, 2020. "Unit representation of semiorders II: The general case," Working Papers hal-02918017, HAL.
    6. Troxell, Denise Sakai, 1995. "On properties of unit interval graphs with a perceptual motivation," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 1-22, 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:ulb:ulbeco:2013/165863. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/ecsulbe.html .

    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.