IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v198y2009i2p626-636.html
   My bibliography  Save this article

Rough set approach to multiple criteria classification with imprecise evaluations and assignments

Author

Listed:
  • Dembczynski, Krzysztof
  • Greco, Salvatore
  • Slowinski, Roman

Abstract

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.

Suggested Citation

  • Dembczynski, Krzysztof & Greco, Salvatore & Slowinski, Roman, 2009. "Rough set approach to multiple criteria classification with imprecise evaluations and assignments," European Journal of Operational Research, Elsevier, vol. 198(2), pages 626-636, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:2:p:626-636
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00802-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. 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, July-Dece.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2002. "Rough sets methodology for sorting problems in presence of multiple attributes and criteria," European Journal of Operational Research, Elsevier, vol. 138(2), pages 247-259, April.
    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. 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.
    2. Doumpos, Michael & Zopounidis, Constantin, 2011. "Preference disaggregation and statistical learning for multicriteria decision support: A review," European Journal of Operational Research, Elsevier, vol. 209(3), pages 203-214, March.
    3. 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.
    4. 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.
    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. Fan, Tuan-Fang & Liu, Duen-Ren & Tzeng, Gwo-Hshiung, 2007. "Rough set-based logics for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 182(1), pages 340-355, October.
    7. Ravi Kumar, P. & Ravi, V., 2007. "Bankruptcy prediction in banks and firms via statistical and intelligent techniques - A review," European Journal of Operational Research, Elsevier, vol. 180(1), pages 1-28, July.
    8. Salvatore Greco & Benedetto Matarazzo & Roman Slowinski & Stelios Zanakis, 2011. "Global investing risk: a case study of knowledge assessment via rough sets," Annals of Operations Research, Springer, vol. 185(1), pages 105-138, May.
    9. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02917994, HAL.
    10. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02898131, HAL.
    11. Blaszczynski, Jerzy & Greco, Salvatore & Slowinski, Roman, 2007. "Multi-criteria classification - A new scheme for application of dominance-based decision rules," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1030-1044, September.
    12. Fernandez, Eduardo & Navarro, Jorge & Bernal, Sergio, 2010. "Handling multicriteria preferences in cluster analysis," European Journal of Operational Research, Elsevier, vol. 202(3), pages 819-827, May.
    13. Pawel Lezanski & Maria Pilacinska, 2018. "The dominance-based rough set approach to cylindrical plunge grinding process diagnosis," Journal of Intelligent Manufacturing, Springer, vol. 29(5), pages 989-1004, June.
    14. García Cáceres, Rafael Guillermo & Aráoz Durand, Julián Arturo & Gómez, Fernando Palacios, 2009. "Integral analysis method - IAM," European Journal of Operational Research, Elsevier, vol. 192(3), pages 891-903, February.
    15. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
    16. Du, Wen Sheng & Hu, Bao Qing, 2018. "A fast heuristic attribute reduction approach to ordered decision systems," European Journal of Operational Research, Elsevier, vol. 264(2), pages 440-452.
    17. 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.
    18. Salvatore Corrente & Michael Doumpos & Salvatore Greco & Roman Słowiński & Constantin Zopounidis, 2017. "Multiple criteria hierarchy process for sorting problems based on ordinal regression with additive value functions," Annals of Operations Research, Springer, vol. 251(1), pages 117-139, April.
    19. Sarah Ben Amor & Fateh Belaid & Ramzi Benkraiem & Boumediene Ramdani & Khaled Guesmi, 2023. "Multi-criteria classification, sorting, and clustering: a bibliometric review and research agenda," Annals of Operations Research, Springer, vol. 325(2), pages 771-793, June.
    20. Du, Wen Sheng & Hu, Bao Qing, 2017. "Dominance-based rough fuzzy set approach and its application to rule induction," European Journal of Operational Research, Elsevier, vol. 261(2), pages 690-703.

    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:eee:ejores:v:198:y:2009:i:2:p:626-636. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.