IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03904412.html
   My bibliography  Save this paper

A theoretical look at Electre Tri-nB and related sorting models

Author

Listed:
  • Denis Bouyssou

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Thierry Marchant

    (UGENT - Universiteit Gent = Ghent University = Université de Gand)

  • Marc Pirlot

Abstract

Electre Tri is a set of methods designed to sort alternatives evaluated on several criteria into ordered categories. In these methods, alternatives are assigned to categories by comparing them with reference profiles that represent either the boundary or central elements of the category. The original Electre Tri-B method uses one limiting profile for separating a category from the category below. A more recent method, Electre Tri-nB, allows one to use several limiting profiles for the same purpose. We investigate the properties of Electre Tri-nB using a conjoint measurement framework. When the number of limiting profiles used to define each category is not restricted, Electre Tri-nB is easy to characterize axiomatically and is found to be equivalent to several other methods proposed in the literature. We extend this result in various directions.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2022. "A theoretical look at Electre Tri-nB and related sorting models," Post-Print hal-03904412, HAL.
    • Handle: RePEc:hal:journl:hal-03904412
    DOI: 10.1007/s10288-022-00501-9
    Note: View the original document on HAL open archive server: https://hal.science/hal-03904412v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03904412v1/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s10288-022-00501-9?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Salvatore Greco & Benedetto Matarazzo & Roman Słowiński, 2016. "Decision Rule Approach," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 497-552, Springer.
    2. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2010. "Multiple criteria sorting with a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1455-1470, December.
    3. Bouyssou, Denis & Marchant, Thierry, 2010. "Additive conjoint measurement with ordered categories," European Journal of Operational Research, Elsevier, vol. 203(1), pages 195-204, May.
    4. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    5. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    6. 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.
    7. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    8. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2012. "A multiple criteria sorting method where each category is characterized by several reference actions: The Electre Tri-nC method," European Journal of Operational Research, Elsevier, vol. 217(3), pages 567-579.
    9. Denis Bouyssou & Marc Pirlot, 2002. "Nontransitive Decomposable Conjoint Measurement," Post-Print hal-02361942, HAL.
    10. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, January.
    11. Bouyssou, Denis & Marchant, Thierry, 2015. "On the relations between ELECTRE TRI-B and ELECTRE TRI-C and on a new variant of ELECTRE TRI-B," European Journal of Operational Research, Elsevier, vol. 242(1), pages 201-211.
    12. Denis Bouyssou & Marc Pirlot, 2016. "Conjoint Measurement Tools for MCDM," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 97-151, Springer.
    13. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02917994, HAL.
    14. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    15. Bouyssou, Denis & Marchant, Thierry, 2015. "On the relations between ELECTRE TRI-B and ELECTRE TRI-C and on a new variant of ELECTRE TRI-B," European Journal of Operational Research, Elsevier, vol. 242(1), pages 201-211.
    16. 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.
    17. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "The size of the maximum antichains in products of linear orders," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 648-659, October.
    18. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    19. 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.
    20. Denis Bouyssou & Marc Pirlot, 2004. "‘Additive difference’ models without additivity and subtractivity," Post-Print hal-02361932, HAL.
    21. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 1999. "Rough approximation of a preference relation by dominance relations," European Journal of Operational Research, Elsevier, vol. 117(1), pages 63-83, August.
    22. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    23. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02898131, HAL.
    24. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2019. "The size of the largest antichains in products of linear orders," Working Papers hal-02398393, HAL.
    25. Salvatore Greco & Benedetto Matarazzo & Roman Słowinński, 2005. "Decision Rule Approach," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 507-555, Springer.
    26. Mousseau, Vincent & Dias, Luis, 2004. "Valued outranking relations in ELECTRE providing manageable disaggregation procedures," European Journal of Operational Research, Elsevier, vol. 156(2), pages 467-482, July.
    27. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2004. "Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules," European Journal of Operational Research, Elsevier, vol. 158(2), pages 271-292, October.
    28. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "The size of the maximum antichains in products of linear orders," Post-Print hal-03047087, HAL.
    29. Bouyssou, Denis & Marchant, Thierry, 2010. "Additive conjoint measurement with ordered categories," European Journal of Operational Research, Elsevier, vol. 203(1), pages 195-204, May.
    30. repec:hal:wpaper:hal-03096539 is not listed on IDEAS
    31. Raymond Bisdorff & Luis C. Dias & Patrick Meyer & Vincent Mousseau & Marc Pirlot (ed.), 2015. "Evaluation and Decision Models with Multiple Criteria," International Handbooks on Information Systems, Springer, edition 127, number 978-3-662-46816-6, November.
    32. Nathalie Caspard & Bruno Leclerc & Bernard Monjardet, 2012. "Finite Ordered Sets Concepts, Results and Uses," Post-Print halshs-00800193, HAL.
    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. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2023. "Multiple criteria sorting models and methods. Part II: theoretical results and general issues," 4OR, Springer, vol. 21(2), pages 181-204, June.
    2. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2022. "A note on ELECTRE TRI-nB with few limiting profiles," 4OR, Springer, vol. 20(3), pages 443-463, September.
    3. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "The size of the maximum antichains in products of linear orders," Post-Print hal-03047087, HAL.

    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. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02917994, HAL.
    2. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02898131, HAL.
    3. 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.
    4. Fernández, Eduardo & Figueira, José Rui & Navarro, Jorge & Solares, Efrain, 2023. "A generalized approach to ordinal classification based on the comparison of actions with either limiting or characteristic profiles," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1309-1322.
    5. 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.
    6. Eduardo Fernandez & Jorge Navarro & Rafael Olmedo, 2018. "Characterization of the Effectiveness of Several Outranking-Based Multi-Criteria Sorting Methods," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1047-1084, July.
    7. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2023. "Multiple criteria sorting models and methods. Part II: theoretical results and general issues," 4OR, Springer, vol. 21(2), pages 181-204, June.
    8. Govindan, Kannan & Jepsen, Martin Brandt, 2016. "ELECTRE: A comprehensive literature review on methodologies and applications," European Journal of Operational Research, Elsevier, vol. 250(1), pages 1-29.
    9. 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.
    10. Denis Bouyssou & Thierry Marchant, 2013. "Some remarks on ELECTRE TRI," Working Papers hal-00942310, HAL.
    11. 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.
    12. Bouyssou, Denis & Marchant, Thierry, 2015. "On the relations between ELECTRE TRI-B and ELECTRE TRI-C and on a new variant of ELECTRE TRI-B," European Journal of Operational Research, Elsevier, vol. 242(1), pages 201-211.
    13. Diaz, Raymundo & Fernández, Eduardo & Figueira, José Rui & Navarro, Jorge & Solares, Efrain, 2024. "Revisiting relational-based ordinal classification methods from a more flexible conception of characteristic profiles," Omega, Elsevier, vol. 127(C).
    14. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    15. 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.
    16. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    17. 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.
    18. Rolland, Antoine, 2013. "Reference-based preferences aggregation procedures in multi-criteria decision making," European Journal of Operational Research, Elsevier, vol. 225(3), pages 479-486.
    19. Eduardo Fernandez & Jorge Navarro & Efrain Solares, 2021. "A theoretical look at ordinal classification methods based on reference sets composed of characteristic actions," Papers 2107.04656, arXiv.org.
    20. Bouyssou, Denis & Marchant, Thierry, 2013. "Multiattribute preference models with reference points," European Journal of Operational Research, Elsevier, vol. 229(2), pages 470-481.

    More about this item

    Statistics

    Access and download statistics

    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:journl:hal-03904412. 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: 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.