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Extreme ranking analysis in robust ordinal regression

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  • Kadziński, MiŁosz
  • Greco, Salvatore
  • SŁowiński, Roman
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    Abstract

    We extend the principle of robust ordinal regression with an analysis of extreme ranking results. In our proposal, we consider the whole set of instances of a preference model that is compatible with preference information provided by the DM. We refer to both, the well-known UTAGMS method, which builds the set of general additive value functions compatible with DM's preferences, and newly introduced in this paper PROMETHEEGKS, which constructs the set of compatible outranking models via robust ordinal regression. Then, we consider all complete rankings that follow the use of the compatible preference models, and we determine the best and the worst attained ranks for each alternative. In this way, we are able to assess its position in an overall ranking, and not only in terms of pairwise comparisons, as it is the case in original robust ordinal regression methods. Additionally, we analyze the ranges of possible comprehensive scores (values or net outranking flows). We also discuss extensions of the presented approach on other multiple criteria problems than ranking. Finally, we show how the presented methodology can be applied in practical decision support, reporting results of three illustrative studies.

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    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 40 (2012)
    Issue (Month): 4 ()
    Pages: 488-501

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    Handle: RePEc:eee:jomega:v:40:y:2012:i:4:p:488-501

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    Related research

    Keywords: Multiple criteria ranking and choice; Robust ordinal regression; UTA-like method; PROMETHEE-like method;

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    Cited by:
    1. Kadziński, Miłosz & Tervonen, Tommi, 2013. "Robust multi-criteria ranking with additive value models and holistic pair-wise preference statements," European Journal of Operational Research, Elsevier, vol. 228(1), pages 169-180.
    2. Kadziński, Miłosz & Greco, Salvatore & Słowiński, Roman, 2013. "RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements," Omega, Elsevier, vol. 41(4), pages 735-751.
    3. 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.
    4. Roy, B. & Figueira, J.R. & Almeida-Dias, J., 2014. "Discriminating thresholds as a tool to cope with imperfect knowledge in multiple criteria decision aiding: Theoretical results and practical issues," Omega, Elsevier, vol. 43(C), pages 9-20.
    5. Doumpos, Michael & Zopounidis, Constantin & Galariotis, Emilios, 2014. "Inferring robust decision models in multicriteria classification problems: An experimental analysis," European Journal of Operational Research, Elsevier, vol. 236(2), pages 601-611.
    6. Montes, Ignacio & Miranda, Enrique & Montes, Susana, 2014. "Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance," European Journal of Operational Research, Elsevier, vol. 234(1), pages 209-220.
    7. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    8. Spliet, Remy & Tervonen, Tommi, 2014. "Preference inference with general additive value models and holistic pair-wise statements," European Journal of Operational Research, Elsevier, vol. 232(3), pages 607-612.
    9. Corrente, Salvatore & Greco, Salvatore & Słowiński, Roman, 2013. "Multiple Criteria Hierarchy Process with ELECTRE and PROMETHEE," Omega, Elsevier, vol. 41(5), pages 820-846.

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