IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00800193.html
   My bibliography  Save this paper

Finite Ordered Sets Concepts, Results and Uses

Author

Listed:
  • Nathalie Caspard

    (LACL - Laboratoire d'Algorithmique Complexité et Logique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique)

  • Bruno Leclerc

    (CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Bernard Monjardet

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. We present the first book to dealing exclusively with finite ordered sets. Five chapters are devoted to definitions of key concepts and fundamental results (ranked orders, Dilworth's and Sperner's theorem, Galois connection and residuation, duality between orders and distributive lattices, coding and dimension theory). The last - and larger - chapter presents uses of these structures in fields such as preference modelling and aggregation, operational research and management, cluster and concept analysis, and data mining. Exercises are included at the end of each chapter with helpful hints or references provided for the most difficult ones. We also point to further topics of ongoing research. At last there are appendices devoted to algorithmic complexity, documentation marks, types and numbers of ordered sets, about 500 references, a list of symbols and a (substantial) index.

Suggested Citation

  • Nathalie Caspard & Bruno Leclerc & Bernard Monjardet, 2012. "Finite Ordered Sets Concepts, Results and Uses," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00800193, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00800193
    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.

    Other versions of this item:

    Citations

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


    Cited by:

    1. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2023. "A theoretical look at Electre Tri-nB and related sorting models," 4OR, Springer, vol. 21(1), pages 1-31, March.
    2. Denis Bouyssou & Marc Pirlot, 2020. "Unit representation of semiorders I: Countable sets," Working Papers hal-02918005, HAL.
    3. repec:hal:pseose:halshs-00977005 is not listed on IDEAS
    4. 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.
    5. Ulrich Faigle & Michel Grabisch & Andres Jiménez-Losada & Manuel Ordóñez, 2014. "Games on concept lattices: Shapley value and core," Documents de travail du Centre d'Economie de la Sorbonne 14070, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Salii, Yaroslav, 2019. "Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 32-42.
    7. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02898131, HAL.
    8. repec:hal:pseose:hal-01111670 is not listed on IDEAS
    9. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02917994, HAL.
    10. Olivier Hudry, 2015. "Complexity results for extensions of median orders to different types of remoteness," Annals of Operations Research, Springer, vol. 225(1), pages 111-123, February.

    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:hal:cesptp:halshs-00800193. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.