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An interval extension of the outranking approach and its application to multiple-criteria ordinal classification
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An interval extension of the outranking approach and its application to multiple-criteria ordinal classification

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  • Fernández, Eduardo
  • Figueira, José Rui
  • Navarro, Jorge

Abstract

This paper presents a new outranking method whose main feature is its capacity to handle imperfect knowledge. This research is interested in two important sources of imperfect knowledge: 1) poorly known model parameters, and 2) imperfectly known (even missing) criterion values characterizing the actions. The use of interval numbers to model imperfect knowledge is suggested, and a new interval-based outranking method is proposed as an extension of the outranking approach to the interval framework. This method handles different sources of imperfect knowledge coming from model parameters (weights, veto thresholds, majority threshold) and from ill-determined, imprecise, uncertain, arbitrary (even missing) criterion values. The index of likelihood of the interval outranking is interpreted from a logical perspective, and could be used for choice, ranking and ordinal classification. Specifically, this paper proposes the method INTERCLASS for ordinal classification, which is inspired by ELECTRE TRI-B. Their assignment rules and structural properties are similar, but INTERCLASS is able to handle imprecisions in weights, veto thresholds, cutting level, and even in criteria defining limiting profiles.

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  • 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.
    • Handle: RePEc:eee:jomega:v:84:y:2019:i:c:p:189-198
    DOI: 10.1016/j.omega.2018.05.003
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    1. 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).
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    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. 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).
    8. Balderas, Fausto & Fernández, Eduardo & Cruz-Reyes, Laura & Gómez-Santillán, Claudia & Rangel-Valdez, Nelson, 2022. "Solving group multi-objective optimization problems by optimizing consensus through multi-criteria ordinal classification," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1014-1029.
    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. 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.
    11. 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.
    12. Fausto Balderas & Eduardo Fernandez & Claudia Gomez-Santillan & Nelson Rangel-Valdez & Laura Cruz, 2019. "An Interval-Based Approach for Evolutionary Multi-Objective Optimization of Project Portfolios," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1317-1358, July.
    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. Jindong Qin & Yingying Liang & Luis Martinez & Alessio Ishizaka & Witold Pedrycz, 2023. "ORESTE-SORT: a novel multiple criteria sorting method for sorting port group competitiveness," Annals of Operations Research, Springer, vol. 325(2), pages 875-909, June.

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