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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

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.

Suggested Citation

  • Kadziński, Miłosz & Greco, Salvatore & Słowiński, Roman, 2012. "Selection of a representative value function in robust multiple criteria ranking and choice," European Journal of Operational Research, Elsevier, vol. 217(3), pages 541-553.
  • Handle: RePEc:eee:ejores:v:217:y:2012:i:3:p:541-553
    DOI: 10.1016/j.ejor.2011.09.032
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    References listed on IDEAS

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    1. Bous, Géraldine & Fortemps, Philippe & Glineur, François & Pirlot, Marc, 2010. "ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements," European Journal of Operational Research, Elsevier, vol. 206(2), pages 435-444, October.
    2. 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.
    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. Beuthe, Michel & Scannella, Giuseppe, 2001. "Comparative analysis of UTA multicriteria methods," European Journal of Operational Research, Elsevier, vol. 130(2), pages 246-262, April.
    6. 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.
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    Citations

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    Cited by:

    1. Vetschera, Rudolf, 2017. "Deriving rankings from incomplete preference information: A comparison of different approaches," European Journal of Operational Research, Elsevier, vol. 258(1), pages 244-253.
    2. 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.
    3. Beccacece, Francesca & Borgonovo, Emanuele & Buzzard, Greg & Cillo, Alessandra & Zionts, Stanley, 2015. "Elicitation of multiattribute value functions through high dimensional model representations: Monotonicity and interactions," European Journal of Operational Research, Elsevier, vol. 246(2), pages 517-527.
    4. 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.
    5. Hurson, Christian & Siskos, Yannis, 2014. "A synergy of multicriteria techniques to assess additive value models," European Journal of Operational Research, Elsevier, vol. 238(2), pages 540-551.
    6. Kadziński, Miłosz & Tervonen, Tommi & Tomczyk, Michał K. & Dekker, Rommert, 2017. "Evaluation of multi-objective optimization approaches for solving green supply chain design problems," Omega, Elsevier, vol. 68(C), pages 168-184.
    7. 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.
    8. 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.
    9. 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.
    10. Mastorakis, Kostis & Siskos, Eleftherios, 2016. "Value focused pharmaceutical strategy determination with multicriteria decision analysis techniques," Omega, Elsevier, vol. 59(PA), pages 84-96.
    11. Greco, Salvatore & Mousseau, Vincent & Słowiński, Roman, 2014. "Robust ordinal regression for value functions handling interacting criteria," European Journal of Operational Research, Elsevier, vol. 239(3), pages 711-730.
    12. repec:eee:ejores:v:264:y:2018:i:2:p:405-418 is not listed on IDEAS
    13. Reimann, Olivier & Schumacher, Christian & Vetschera, Rudolf, 2017. "How well does the OWA operator represent real preferences?," European Journal of Operational Research, Elsevier, vol. 258(3), pages 993-1003.
    14. Miłosz Kadziński & Michał K. Tomczyk, 0. "Interactive Evolutionary Multiple Objective Optimization for Group Decision Incorporating Value-based Preference Disaggregation Methods," Group Decision and Negotiation, Springer, vol. 0, pages 1-36.
    15. Ghaderi, Mohammad & Ruiz, Francisco & Agell, Núria, 2017. "A linear programming approach for learning non-monotonic additive value functions in multiple criteria decision aiding," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1073-1084.
    16. repec:spr:grdene:v:22:y:2013:i:3:d:10.1007_s10726-011-9277-z is not listed on IDEAS
    17. repec:spr:grdene:v:26:y:2017:i:4:d:10.1007_s10726-016-9506-6 is not listed on IDEAS
    18. repec:wsi:ijitdm:v:16:y:2017:i:03:n:s0219622017500122 is not listed on IDEAS
    19. 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.
    20. van Valkenhoef, Gert & Tervonen, Tommi & Postmus, Douwe, 2014. "Notes on ‘Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis’," European Journal of Operational Research, Elsevier, vol. 239(3), pages 865-867.
    21. 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.

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