Advertisement

Group Decision and Negotiation

, Volume 22, Issue 3, pp 429–462 | Cite as

Selection of a Representative Value Function for Robust Ordinal Regression in Group Decision Making

  • Miłosz KadzińskiEmail author
  • Salvatore Greco
  • Roman Słowiński
Open Access
Article

Abstract

In this paper, we introduce the concept of a representative value function in a group decision context. We extend recently proposed methods UTAGMS-GROUP and UTADISGMS-GROUP with selection of a compromise and collective preference model which aggregates preferences of several decision makers (DMs) and represents all instances of preference models compatible with preference information elicited from DMs. The representative value function is built on results of robust ordinal regression, so its representativeness can be interpreted in terms of robustness concern. We propose a few procedures designed for multiple criteria ranking, choice, and sorting problems. The use of these procedures is conditioned by both satisfying different degrees of consistency of the preference information provided by all DMs, as well as by some properties of particular decision making situations. The representative value function is intended to help the DMs to understand the robust results, and to provide them with a compromise result in case of conflict between the DMs.

Keywords

Group decision Robust ordinal regression Additive value function Representative value function Compromise 

Notes

Acknowledgements

The first and the third authors wish to acknowledge financial support from the Polish Ministry of Science and Higher Education, grant no. N N519 441939.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. Angilella S, Greco S, Matarazzo B (2010) Non-additive robust ordinal regression: a multiple criteria decision model based on the choquet integral. Eur J Oper Res 201(1): 277–288CrossRefGoogle Scholar
  2. Beuthe M, Scannella G (2001) Comparative analysis of UTA multicriteria methods. Eur J Oper Res 130(2): 246–262CrossRefGoogle Scholar
  3. Bous G, Fortemps P, Glineur F, Pirlot M (2010) ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements. Eur J Oper Res 206(2): 435–444CrossRefGoogle Scholar
  4. Despotis D, Yanacopoulos D, Zopounidis C (1990) A review of the UTA multucriteria method and some improvements. Found Comput Decis Sci 15(2): 63–76Google Scholar
  5. EIU: (2007) The Economist Intelligence Units index of democracy. Economist Intelligence Unit, LondonGoogle Scholar
  6. Figueira J, Greco S, Słowiński R (2008) Identifying the most representative value function among all compatible value functions in the GRIP. Proceedings of the 68th EURO Working Group on MCDA Chania, GreeceGoogle Scholar
  7. Figueira J, Greco S, Słowiński R (2009) Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method. Eur J Oper Res 195(2): 460–486CrossRefGoogle Scholar
  8. Greco S, Matarazzo B, Słowiński R (1999) Rough approximation of a preference relation by dominance relations. Eur J Oper Res 117(1): 63–83CrossRefGoogle Scholar
  9. Greco S, Mousseau V, Słowiński R (2008) Ordinal regression revisited: multiple criteria ranking using a set of additive value functions. Eur J Oper Res 191(2): 415–435CrossRefGoogle Scholar
  10. Greco S, Mousseau V, Słowiński R (2009) The possible and the necessary for multiple criteria group decision. In: Rossi F, Tsoukias A (eds) Algorithmic decision theory (ADT 2009), LNAI 5783. Springer, Berlin, pp 203–214CrossRefGoogle Scholar
  11. Greco S, Kadziński M, Słowiński R (2010a) The most representative parameter set for robust outranking approach. Presented at the 71st meeting of the European working group on multiple criteria decision aiding. Torino, ItalyGoogle Scholar
  12. Greco S, Mousseau V, Słowiński R (2010b) Multiple criteria sorting with a set of additive value functions. Eur J Oper Res 207(4): 1455–1470CrossRefGoogle Scholar
  13. Greco S, Słowiński R, Mousseau V, Figueira J (2010c) Robust ordinal regression. In: Ehrgott M, Figueira J, Greco S (eds) Trends in multiple criteria decision analysis. Springer, Berlin, pp 273–320Google Scholar
  14. Greco S, Kadziński M, Mousseau V, Słowiński R (2011a) Robust ordinal regression for multiple criteria group decision: UTAGMS-GROUP and UTADISGMS-GROUP. Deci Support Syst. doi: 10.1016/j.dss.2011.10.005
  15. Greco S, Kadziński M, Mousseau V, Słowiński R (2011b) ELECTREGKMS: Robust ordinal regression for outranking methods. Eur J Oper Res 214(1): 118–135CrossRefGoogle Scholar
  16. Greco S, Kadziński M, Słowiński R (2011c) Selection of a representative value function in robust multiple criteria sorting. Comput Oper Res 38(11): 1620–1637CrossRefGoogle Scholar
  17. Jacquet-Lagréze E, Shakun M (1984) Decision support systems for semistructured buying decisions. Eur J Oper Res 16: 48–56CrossRefGoogle Scholar
  18. Jacquet-Lagréze E, Siskos Y (1982) Assessing a set of additive utility functions for multicriteria decision making: the UTA method. Eur J Oper Res 10: 151–164CrossRefGoogle Scholar
  19. Jarke M, Jelassi M, Shakun M (1987) MEDIATOR: toward a negotiation support system. Eur J Oper Res 31(3): 314–334CrossRefGoogle Scholar
  20. Kadziński M, Greco S, Słowiński R (2012a) Extreme ranking analysis in robust ordinal regression. Omega 40(4):488–501Google Scholar
  21. Kadziński M, Greco S, Słowiński R (2012) Selection of a representative value function in robust multiple criteria ranking and choice. Eur J Oper Res 217(3): 541–553CrossRefGoogle Scholar
  22. Matsatsinis N, Samaras AP (2001) MCDA and preference disaggregation in group decision support. Eur J Oper Res 130(2): 414–429CrossRefGoogle Scholar
  23. Mousseau V, Dias L, Figueira J (2006) Dealing with inconsistent judgments in multiple criteria sorting models. 4OR 4(3): 145–158CrossRefGoogle Scholar
  24. Mousseau V, Dias L, Figueira J, Gomes C, Clímaco J (2003) Resolving inconsistencies among constraints on the parameters of an MCDA model. Eur J Oper Res 147(1): 72–93CrossRefGoogle Scholar
  25. Mousseau V, Słowiński R (1998) Inferring an ELECTRE TRI model from assignment examples. J Glob Optim 12(2): 157–174CrossRefGoogle Scholar
  26. Roy B (1985) Méthodologie Multicritére d’aide á la Décision. Economica, ParisGoogle Scholar
  27. Siskos Y, Grigoroudis E, Matsatsinis N (2005) UTA methods. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state of the art surveys. Springer, Boston, pp 297–344Google Scholar
  28. Siskos Y, Yanacopoulos D (1985) UTA STAR—an ordinal regression method for building additive value functions. Investig Oper 5: 39–53Google Scholar

Copyright information

© The Author(s) 2011

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Miłosz Kadziński
    • 1
    Email author
  • Salvatore Greco
    • 2
  • Roman Słowiński
    • 1
    • 3
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  2. 2.Faculty of EconomicsUniversity of CataniaCataniaItaly
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland

Personalised recommendations