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Eliciting Electre Tri category limits for a group of decision makers

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  • Cailloux, Olivier
  • Meyer, Patrick
  • Mousseau, Vincent

Abstract

Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.

Suggested Citation

  • Cailloux, Olivier & Meyer, Patrick & Mousseau, Vincent, 2012. "Eliciting Electre Tri category limits for a group of decision makers," European Journal of Operational Research, Elsevier, vol. 223(1), pages 133-140.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:133-140
    DOI: 10.1016/j.ejor.2012.05.032
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    References listed on IDEAS

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    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, December.
    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, 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.
    4. 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.
    5. 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.
    6. Sébastien Damart & Luis Dias & Vincent Mousseau, 2007. "Supporting groups in sorting decisions: methodology and use of a multi-criteria aggregation-disaggregation DSS," Post-Print halshs-00170234, HAL.
    7. Dias, Luis & Mousseau, Vincent & Figueira, Jose & Climaco, Joao, 2002. "An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI," European Journal of Operational Research, Elsevier, vol. 138(2), pages 332-348, April.
    8. Mousseau, V. & Figueira, J. & Naux, J. -Ph., 2001. "Using assignment examples to infer weights for ELECTRE TRI method: Some experimental results," European Journal of Operational Research, Elsevier, vol. 130(2), pages 263-275, April.
    9. repec:dau:papers:123456789/2944 is not listed on IDEAS
    10. Mousseau, Vincent & Figueira, Jose & Dias, Luis & Gomes da Silva, Carlos & Climaco, Joao, 2003. "Resolving inconsistencies among constraints on the parameters of an MCDA model," European Journal of Operational Research, Elsevier, vol. 147(1), pages 72-93, May.
    11. repec:dau:papers:123456789/1482 is not listed on IDEAS
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    Cited by:

    1. 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.
    2. Liu, Jiapeng & Liao, Xiuwu & Kadziński, Miłosz & Słowiński, Roman, 2019. "Preference disaggregation within the regularization framework for sorting problems with multiple potentially non-monotonic criteria," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1071-1089.
    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. Liu, Jiapeng & Liao, Xiuwu & Huang, Wei & Yang, Jian-bo, 2018. "A new decision-making approach for multiple criteria sorting with an imbalanced set of assignment examples," European Journal of Operational Research, Elsevier, vol. 265(2), pages 598-620.
    5. Denis Bouyssou & Thierry Marchant, 2013. "Some remarks on ELECTRE TRI," Working Papers hal-00942310, HAL.
    6. 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.
    7. Kadziński, Miłosz & Ciomek, Krzysztof, 2021. "Active learning strategies for interactive elicitation of assignment examples for threshold-based multiple criteria sorting," European Journal of Operational Research, Elsevier, vol. 293(2), pages 658-680.
    8. Paulo Cesar Schotten & Leydiana Sousa Pereira & Danielle Costa Morais, 2022. "Credit granting sorting model for financial organizations," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-24, December.
    9. 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.
    10. Cailloux, Olivier & Mayag, Brice & Meyer, Patrick & Mousseau, Vincent, 2013. "Operational tools to build a multicriteria territorial risk scale with multiple stakeholders," Reliability Engineering and System Safety, Elsevier, vol. 120(C), pages 88-97.
    11. Denis Bouyssou & Marc Pirlot, 2015. "A note on the asymmetric part of an outranking relation," Post-Print hal-01326876, HAL.
    12. Miłosz Kadziński & Lucia Rocchi & Grzegorz Miebs & David Grohmann & Maria Elena Menconi & Luisa Paolotti, 2018. "Multiple Criteria Assessment of Insulating Materials with a Group Decision Framework Incorporating Outranking Preference Model and Characteristic Class Profiles," Group Decision and Negotiation, Springer, vol. 27(1), pages 33-59, February.

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