IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v213y2011i2p405-413.html
   My bibliography  Save this article

A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method

Author

Listed:
  • Fernandez, Eduardo
  • Navarro, Jorge

Abstract

In this paper, we propose the THESEUS method, a new approach based on fuzzy outranking relations to multi-criteria sorting problems. Compared with other outranking-based methods, THESEUS is inspired by another view of multi-criteria classification problems. It utilizes a new way of evaluating the assignment of an object to an element of the set of ordered categories that were previously defined. This way is based on comparing every possible assignment with the information from various preference relations that are derived from a fuzzy outranking relation defined on the universe of objects. The appropriate assignment is determined by solving a simple selection problem. The capacity of a reference set for making appropriate assignments is related to a good characterization of the categories. A single reference action characterizing a category may be insufficient to achieve well-determined assignments. In this paper, the reference set capacity to perform appropriate assignments is characterized by some new concepts. This capacity may be increased when more objects are added to the reference set. THESEUS is a method for handling the preference information contained in such larger reference sets.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:213:y:2011:i:2:p:405-413
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711002736
    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. 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.
    2. 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.
    3. Doumpos, Michael & Zopounidis, Constantin, 2004. "A multicriteria classification approach based on pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 158(2), pages 378-389, October.
    4. Belacel, Nabil, 2000. "Multicriteria assignment method PROAFTN: Methodology and medical application," European Journal of Operational Research, Elsevier, vol. 125(1), pages 175-183, August.
    5. Patrice Perny, 1998. "Multicriteria filtering methods based onconcordance and non-discordance principles," Annals of Operations Research, Springer, vol. 80(0), pages 137-165, January.
    6. Fortemps, Philippe & Greco, Salvatore & Slowinski, Roman, 2008. "Multicriteria decision support using rules that represent rough-graded preference relations," European Journal of Operational Research, Elsevier, vol. 188(1), pages 206-223, July.
    7. Siskos, Yannis & Grigoroudis, Evangelos & Krassadaki, Evangelia & Matsatsinis, Nikolaos, 2007. "A multicriteria accreditation system for information technology skills and qualifications," European Journal of Operational Research, Elsevier, vol. 182(2), pages 867-885, October.
    8. 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.
    9. 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.
    10. Georgopoulou, E. & Sarafidis, Y. & Mirasgedis, S. & Zaimi, S. & Lalas, D. P., 2003. "A multiple criteria decision-aid approach in defining national priorities for greenhouse gases emissions reduction in the energy sector," European Journal of Operational Research, Elsevier, vol. 146(1), pages 199-215, April.
    11. Arondel, Cecile & Girardin, Philippe, 2000. "Sorting cropping systems on the basis of their impact on groundwater quality," European Journal of Operational Research, Elsevier, vol. 127(3), pages 467-482, December.
    12. 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.
    13. 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.
    14. 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.
    15. Tervonen, Tommi & Figueira, José Rui & Lahdelma, Risto & Dias, Juscelino Almeida & Salminen, Pekka, 2009. "A stochastic method for robustness analysis in sorting problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 236-242, January.
    16. Brito, Anderson J. & de Almeida, Adiel Teixeira & Mota, Caroline M.M., 2010. "A multicriteria model for risk sorting of natural gas pipelines based on ELECTRE TRI integrating Utility Theory," European Journal of Operational Research, Elsevier, vol. 200(3), pages 812-821, February.
    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. Fernandez, Eduardo & Navarro, Jorge & Duarte, Alfonso, 2008. "Multicriteria sorting using a valued preference closeness relation," European Journal of Operational Research, Elsevier, vol. 185(2), pages 673-686, March.
    19. K. Raju & Lucien Duckstein & Cecile Arondel, 2000. "Multicriterion Analysis for Sustainable Water Resources Planning: A Case Study in Spain," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 14(6), pages 435-456, December.
    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. 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.
    2. 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.
    3. Bernard Roy & Roman Slowinski, 2013. "Questions guiding the choice of a multicriteria decision aiding method," Post-Print hal-00874292, HAL.
    4. 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.
    5. Kadziński, Miłosz & Tervonen, Tommi & Rui Figueira, José, 2015. "Robust multi-criteria sorting with the outranking preference model and characteristic profiles," Omega, Elsevier, vol. 55(C), pages 126-140.
    6. Chen, Ting-Yu & Chang, Chien-Hung & Rachel Lu, Jui-fen, 2013. "The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making," European Journal of Operational Research, Elsevier, vol. 226(3), pages 615-625.
    7. Alessio Ishizaka & Maynard Gordon, 2017. "MACBETHSort: a multiple criteria decision aid procedure for sorting strategic products," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 53-61, January.
    8. 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).
    9. 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.
    10. 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).
    11. 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.
    12. Oussama Raboun & Eric Chojnacki & Alexis Tsoukiàs, 2023. "Dynamic-R: a “challenge-free” method for rating problem statements," Annals of Operations Research, Springer, vol. 325(2), pages 845-873, June.
    13. Ishizaka, Alessio & Lokman, Banu & Tasiou, Menelaos, 2021. "A Stochastic Multi-criteria divisive hierarchical clustering algorithm," Omega, Elsevier, vol. 103(C).
    14. 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.
    15. Bruno Brentan & Silvia Carpitella & Daniel Barros & Gustavo Meirelles & Antonella Certa & Joaquín Izquierdo, 2021. "Water Quality Sensor Placement: A Multi-Objective and Multi-Criteria Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(1), pages 225-241, January.
    16. repec:hal:wpaper:hal-00874292 is not listed on IDEAS
    17. Ishizaka, Alessio & Nemery, Philippe, 2014. "Assigning machines to incomparable maintenance strategies with ELECTRE-SORT," Omega, Elsevier, vol. 47(C), pages 45-59.
    18. Hong-gang Peng & Jian-qiang Wang, 2020. "Multi-criteria sorting decision making based on dominance and opposition relations with probabilistic linguistic information," Fuzzy Optimization and Decision Making, Springer, vol. 19(4), pages 435-470, December.
    19. 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).
    20. 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.
    21. 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.
    22. Wang, Liang & Zhang, Zi-Xin & Ishizaka, Alessio & Wang, Ying-Ming & Martínez, Luis, 2023. "TODIMSort: A TODIM based method for sorting problems," Omega, Elsevier, vol. 115(C).
    23. Miłosz Kadziński & Roman Słowiński, 2013. "DIS-CARD: a new method of multiple criteria sorting to classes with desired cardinality," Journal of Global Optimization, Springer, vol. 56(3), pages 1143-1166, July.
    24. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Fu-Ling Cai & Xiuwu Liao & Kan-Liang Wang, 2012. "An interactive sorting approach based on the assignment examples of multiple decision makers with different priorities," Annals of Operations Research, Springer, vol. 197(1), pages 87-108, August.
    7. 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.
    8. 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).
    9. 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.
    10. 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.
    11. 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.
    12. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    13. 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.
    14. 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.
    15. 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.
    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. 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.
    19. Liu, Jiapeng & Kadziński, Miłosz & Liao, Xiuwu & Mao, Xiaoxin & Wang, Yao, 2020. "A preference learning framework for multiple criteria sorting with diverse additive value models and valued assignment examples," European Journal of Operational Research, Elsevier, vol. 286(3), pages 963-985.
    20. Miłosz Kadziński & Magdalena Martyn, 2021. "Enriched preference modeling and robustness analysis for the ELECTRE Tri-B method," Annals of Operations Research, Springer, vol. 306(1), pages 173-207, November.

    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:213:y:2011:i:2:p:405-413. 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.