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Robust Ordinal Regression

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Trends in Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 142))

Abstract

Within disaggregation–aggregation approach, ordinal regressionaims at inducing parameters of a preference model, for example, parameters of a value function, which represent some holistic preference comparisons of alternatives given by the Decision Maker (DM). Usually, from among many sets of parameters of a preference model representing the preference information given by the DM, only one specific set is selected and used to work out a recommendation. For example, while there exist many value functions representing the holistic preference information given by the DM, only one value function is typically used to recommend the best choice, sorting, or ranking of alternatives. Since the selection of one from among many sets of parameters compatible with the preference information given by the DM is rather arbitrary, robust ordinal regressionproposes taking into account all the sets of parameters compatible with the preference information, in order to give a recommendation in terms of necessary and possible consequences of applying all the compatible preference models on the considered set of alternatives. In this chapter, we present the basic principle of robust ordinal regression, and the main multiple criteria decision methods to which it has been applied. In particular, UTA GMSand GRIPmethods are described, dealing with choice and ranking problems, then UTADIS GMS, dealing with sorting (ordinal classification) problems. Next, we present robust ordinal regression applied to Choquet integral for choice, sorting, and ranking problems, with the aim of representing interactions between criteria. This is followed by a characterization of robust ordinal regression applied to outranking methods and to multiple criteria group decisions. Finally, we describe an interactive multiobjective optimization methodology based on robust ordinal regression, and an evolutionary multiobjective optimization method, called NEMO, which is also using the principle of robust ordinal regression.

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Author information

Authors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia 55, 95 129, Catania, Italy

    Salvatore Greco

  2. Institute of Computing Science, Poznań University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    Roman Słowiński

  3. Systems Research Institute, Polish Academy of Sciences, 00-441, Warsaw, Poland

    Roman Słowiński

  4. CEG-IST Center for Management Studies, Instituto Superior Técnico, Technical University of Lisbon and TagusPark, Av. Cavaco Silva, 2780-990, Porto Salvo, Portugal

    José Rui Figueira

  5. LAMSADE, Université Paris-Dauphine, Paris, France

    José Rui Figueira

  6. Laboratoire de Génie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92 295, Châtenay-Malabry Cedex, France

    Vincent Mousseau

Authors
  1. Salvatore Greco
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  2. Roman Słowiński
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  3. José Rui Figueira
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  4. Vincent Mousseau
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Correspondence to Salvatore Greco .

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Editors and Affiliations

  1. Dept. Engineering Science, University of Auckland, Auckland, New Zealand

    Matthias Ehrgott

  2. Depto. Engenharia e Gestao, Instituto Superior Tecnico, Av. Prof.Dr. Cavaco Silva, Porto Salvo, 2780-990, Portugal

    José Rui Figueira

  3. Faculty of Economics, University of Catania, Corso Italia 55, Catania, 95129, Italy

    Salvatore Greco

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Greco, S., Słowiński, R., Figueira, J.R., Mousseau, V. (2010). Robust Ordinal Regression. In: Ehrgott, M., Figueira, J., Greco, S. (eds) Trends in Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 142. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5904-1_9

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