IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v325y2023i2d10.1007_s10479-022-04554-1.html
   My bibliography  Save this article

A theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes

Author

Listed:
  • Eduardo Fernández

    (Universidad Autónoma de Coahuila)

  • José Rui Figueira

    (CEG-IST, Instituto Superior Técnico, Universidade de Lisboa)

  • Jorge Navarro

    (Universidad Autónoma de Sinaloa)

Abstract

This paper addresses the general problem of designing ordinal classification methods based on comparing actions with limiting boundaries of ordered classes (categories). The fundamental requirement of the method consists of setting a relational system (D,S), where S and D are reflexive and transitive relations, respectively, S should be compatible with the order of the set of classes, and D is a subset of S. An asymmetric preference relation P is defined from S. Other requirements are imposed on the actions which compose the limiting boundaries between adjacent classes, in such a way that each class is closed below and above. The paper proposes S-based and P-based assignment procedures. Each of them is composed of two complementary assignment procedures, which correspond through the transposition operation and should be used conjointly. The methods work under several basic conditions on the set of limiting boundaries. Under other more demanding separability requirements, each procedure fulfills the set of structural properties established for other outranking-based ordinal classification methods. Our proposal avoids the conflict between the required correspondence through the transposition operation and the assignment of limiting actions to the classes to which they belong. We thus propose very diverse S and P-based ordinal classification approaches with desirable properties, which can be designed by using decision models with the capacity to build preference relations fulfilling the basic requirements to S and D.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:325:y:2023:i:2:d:10.1007_s10479-022-04554-1
    DOI: 10.1007/s10479-022-04554-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-04554-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10479-022-04554-1?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. Araz, Ceyhun & Ozkarahan, Irem, 2007. "Supplier evaluation and management system for strategic sourcing based on a new multicriteria sorting procedure," International Journal of Production Economics, Elsevier, vol. 106(2), pages 585-606, April.
    2. Patrice Perny, 1998. "Multicriteria filtering methods based onconcordance and non-discordance principles," Annals of Operations Research, Springer, vol. 80(0), pages 137-165, January.
    3. 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.
    4. Figueira, José Rui & Greco, Salvatore & Roy, Bernard, 2009. "ELECTRE methods with interaction between criteria: An extension of the concordance index," European Journal of Operational Research, Elsevier, vol. 199(2), pages 478-495, December.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Fernández, Eduardo & Figueira, José Rui & Navarro, Jorge, 2019. "An interval extension of the outranking approach and its application to multiple-criteria ordinal classification," Omega, Elsevier, vol. 84(C), pages 189-198.
    12. Koksalan, Murat & Ulu, Canan, 2003. "An interactive approach for placing alternatives in preference classes," European Journal of Operational Research, Elsevier, vol. 144(2), pages 429-439, January.
    13. Corrente, Salvatore & Greco, Salvatore & Słowiński, Roman, 2016. "Multiple Criteria Hierarchy Process for ELECTRE Tri methods," European Journal of Operational Research, Elsevier, vol. 252(1), pages 191-203.
    14. Fernández, Eduardo & Figueira, José Rui & Navarro, Jorge, 2020. "Interval-based extensions of two outranking methods for multi-criteria ordinal classification," Omega, Elsevier, vol. 95(C).
    15. Corrente, Salvatore & Greco, Salvatore & Słowiński, Roman, 2013. "Multiple Criteria Hierarchy Process with ELECTRE and PROMETHEE," Omega, Elsevier, vol. 41(5), pages 820-846.
    16. 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.
    17. 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.
    18. Denis Bouyssou & Marc Pirlot, 2015. "A note on the asymmetric part of an outranking relation," Post-Print hal-01326876, HAL.
    19. 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.
    20. Fernandez, Eduardo & Navarro, Jorge, 2011. "A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method," European Journal of Operational Research, Elsevier, vol. 213(2), pages 405-413, September.
    21. 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.
    22. Denis Bouyssou & Marc Pirlot, 2015. "A note on the asymmetric part of an outranking relation," Post-Print hal-01326876, HAL.
    23. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore & Słowiński, Roman, 2017. "A robust ranking method extending ELECTRE III to hierarchy of interacting criteria, imprecise weights and stochastic analysis," Omega, Elsevier, vol. 73(C), pages 1-17.
    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. 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.
    2. Eduardo Fernandez & Jose Rui Figueira & Jorge Navarro, 2021. "a theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes," Papers 2107.03440, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    6. Fernández, Eduardo & Navarro, Jorge & Solares, Efrain, 2022. "A hierarchical interval outranking approach with interacting criteria," European Journal of Operational Research, Elsevier, vol. 298(1), pages 293-307.
    7. 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.
    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 II: theoretical results and general issues," 4OR, Springer, vol. 21(2), pages 181-204, June.
    10. Eduardo Fernandez & Jorge Navarro & Edgar Covantes & Jorge Rodriguez, 2017. "Analysis of the effectiveness of the theseus multi-criteria sorting method: theoretical remarks and experimental evidence," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 314-339, July.
    11. Fernández, Eduardo & Figueira, José Rui & Navarro, Jorge & Solares, Efrain, 2022. "Handling imperfect information in multiple criteria decision-making through a comprehensive interval outranking approach," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    12. Dias, Luis C. & Antunes, Carlos Henggeler & Dantas, Guilherme & de Castro, Nivalde & Zamboni, Lucca, 2018. "A multi-criteria approach to sort and rank policies based on Delphi qualitative assessments and ELECTRE TRI: The case of smart grids in Brazil," Omega, Elsevier, vol. 76(C), pages 100-111.
    13. Cinelli, Marco & Kadziński, Miłosz & Miebs, Grzegorz & Gonzalez, Michael & Słowiński, Roman, 2022. "Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system," European Journal of Operational Research, Elsevier, vol. 302(2), pages 633-651.
    14. Fernández, Eduardo & Figueira, José Rui & Navarro, Jorge, 2020. "Interval-based extensions of two outranking methods for multi-criteria ordinal classification," Omega, Elsevier, vol. 95(C).
    15. Doumpos, Michalis & Figueira, José Rui, 2019. "A multicriteria outranking approach for modeling corporate credit ratings: An application of the Electre Tri-nC method," Omega, Elsevier, vol. 82(C), pages 166-180.
    16. Murat Köksalan & Vincent Mousseau & Selin Özpeynirci, 2017. "Multi-Criteria Sorting with Category Size Restrictions," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 5-23, January.
    17. 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.
    18. 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.
    19. Díaz, Raymundo & Fernández, Eduardo & Figueira, José-Rui & Navarro, Jorge & Solares, Efrain, 2023. "A new hierarchical multiple criteria ordered clustering approach as a complementary tool for sorting and ranking problems," Omega, Elsevier, vol. 117(C).
    20. Arandarenko, Mihail & Corrente, Salvatore & Jandrić, Maja & Stamenković, Mladen, 2020. "Multiple criteria decision aiding as a prediction tool for migration potential of regions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1154-1166.

    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:325:y:2023:i:2:d:10.1007_s10479-022-04554-1. 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.