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

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  • Kadziński, Miłosz
  • Greco, Salvatore
  • Słowiński, Roman
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Multiple criteria analysis; Robust ordinal regression; UTA-like method; Post-optimality analysis; Additive value function; Representative preference model;

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    Citations

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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. Bouchery, Yann & Ghaffari, Asma & Jemai, Zied & Dallery, Yves, 2012. "Including sustainability criteria into inventory models," European Journal of Operational Research, Elsevier, vol. 222(2), pages 229-240.
    4. 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.
    5. Brito, Anderson J. & de Almeida, Adiel T., 2012. "Modeling a multi-attribute utility newsvendor with partial backlogging," European Journal of Operational Research, Elsevier, vol. 220(3), pages 820-830.
    6. Bottomley, Paul A. & Doyle, John R., 2013. "Comparing the validity of numerical judgements elicited by direct rating and point allocation: Insights from objectively verifiable perceptual tasks," European Journal of Operational Research, Elsevier, vol. 228(1), pages 148-157.
    7. 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.

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