IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i7p952-d1362471.html
   My bibliography  Save this article

Traces of Ternary Relations Based on Bandler–Kohout Compositions

Author

Listed:
  • Lemnaouar Zedam

    (KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, Belgium
    Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of M’sila, M’sila 28000, Algeria)

  • Hamza Boughambouz

    (KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, Belgium
    Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of M’sila, M’sila 28000, Algeria)

  • Bernard De Baets

    (KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, Belgium)

Abstract

Recently, we have introduced and studied all possible four-point compositions (one degree of freedom) and five-point compositions (two degrees of freedom) of ternary relations in analogy with the usual composition of binary relations. In this paper, we introduce and study new types of compositions of ternary relations inspired by the compositions of binary relations introduced by Bandler and Kohout (BK-compositions, for short). Moreover, we pay particular attention to the link between BK-compositions and the traces of binary relations and use it as source of inspiration to introduce traces of ternary relations. Moreover, we show that these new notions of BK-compositions and traces are useful tools to solve some relational equations in an unknown ternary relation.

Suggested Citation

  • Lemnaouar Zedam & Hamza Boughambouz & Bernard De Baets, 2024. "Traces of Ternary Relations Based on Bandler–Kohout Compositions," Mathematics, MDPI, vol. 12(7), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:952-:d:1362471
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/7/952/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/7/952/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bouyssou, Denis & Pirlot, Marc, 2005. "Following the traces:: An introduction to conjoint measurement without transitivity and additivity," European Journal of Operational Research, Elsevier, vol. 163(2), pages 287-337, June.
    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. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    2. Bouyssou, Denis & Pirlot, Marc, 2009. "An axiomatic analysis of concordance-discordance relations," European Journal of Operational Research, Elsevier, vol. 199(2), pages 468-477, December.
    3. Simone Cerreia-Vioglio & Alfio Giarlotta & Salvatore Greco & Fabio Maccheroni & Massimo Marinacci, 2020. "Rational preference and rationalizable choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 61-105, February.
    4. Nobuo Koida, 2021. "Intransitive indifference with direction-dependent sensitivity," KIER Working Papers 1061, Kyoto University, Institute of Economic Research.
    5. Denis Bouyssou & Marc Pirlot, 2015. "A consolidated approach to the axiomatization of outranking relations: a survey and new results," Annals of Operations Research, Springer, vol. 229(1), pages 159-212, June.
    6. Bouyssou, Denis & Marchant, Thierry, 2013. "Multiattribute preference models with reference points," European Journal of Operational Research, Elsevier, vol. 229(2), pages 470-481.

    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:gam:jmathe:v:12:y:2024:i:7:p:952-:d:1362471. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.