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Selection of a representative value function in robust multiple criteria ranking and choice

  • Kadziński, Miłosz
  • Greco, Salvatore
  • Słowiński, Roman
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    We introduce the concept of a representative value function in robust ordinal regression applied to multiple criteria ranking and choice problems. The proposed method can be seen as a new interactive UTA-like procedure, which extends the UTAGMS and GRIP methods. The preference information supplied by the decision maker (DM) is composed of a partial preorder and intensities of preference on a subset of reference alternatives. Robust ordinal regression builds a set of general additive value functions which are compatible with the preference information, and returns two binary preference relations: necessary and possible. They identify recommendations which are compatible with all or at least one compatible value function, respectively. In this paper, we propose a general framework for selection of a representative value function from among the set of compatibles ones. There are a few targets which build on results of robust ordinal regression, and could be attained by a representative value function. In general, according to the interactively elicited preferences of the DM, the representative value function may emphasize the advantage of some alternatives over the others when all compatible value functions acknowledge this advantage, or reduce the ambiguity in the advantage of some alternatives over the others when some compatible value functions acknowledge an advantage and other ones acknowledge a disadvantage. The basic procedure is refined by few extensions. They enable emphasizing the advantage of alternatives that could be considered as potential best options, accounting for intensities of preference, or obtaining a desired type of the marginal value functions.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711008605
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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 217 (2012)
    Issue (Month): 3 ()
    Pages: 541-553

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    Handle: RePEc:eee:ejores:v:217:y:2012:i:3:p:541-553
    DOI: 10.1016/j.ejor.2011.09.032
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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    1. Figueira, José Rui & Greco, Salvatore & Slowinski, Roman, 2009. "Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method," European Journal of Operational Research, Elsevier, vol. 195(2), pages 460-486, June.
    2. BOUS, Géraldine & FORTEMPS, Philippe & GLINEUR, François & PIRLOT, Marc, . "ACUTA: a novel method for eliciting additive value functions on the basis of holistic preference statements," CORE Discussion Papers RP 2243, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
    4. Greco, Salvatore & Kadzinski, Milosz & Mousseau, Vincent & Slowinski, Roman, 2011. "ELECTREGKMS: Robust ordinal regression for outranking methods," European Journal of Operational Research, Elsevier, vol. 214(1), pages 118-135, October.
    5. Jacquet-Lagreze, E. & Siskos, J., 1982. "Assessing a set of additive utility functions for multicriteria decision-making, the UTA method," European Journal of Operational Research, Elsevier, vol. 10(2), pages 151-164, June.
    6. Beuthe, Michel & Scannella, Giuseppe, 2001. "Comparative analysis of UTA multicriteria methods," European Journal of Operational Research, Elsevier, vol. 130(2), pages 246-262, April.
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