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

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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. 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.
    12. Ishizaka, Alessio & Lokman, Banu & Tasiou, Menelaos, 2021. "A Stochastic Multi-criteria divisive hierarchical clustering algorithm," Omega, Elsevier, vol. 103(C).
    13. 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.
    14. 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.
    15. repec:hal:wpaper:hal-00874292 is not listed on IDEAS
    16. Ishizaka, Alessio & Nemery, Philippe, 2014. "Assigning machines to incomparable maintenance strategies with ELECTRE-SORT," Omega, Elsevier, vol. 47(C), pages 45-59.
    17. 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.
    18. 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).
    19. 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.
    20. 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.
    21. 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).
    22. 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.
    23. 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.

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