Annals of Operations Research

, Volume 251, Issue 1–2, pp 117–139 | Cite as

Multiple criteria hierarchy process for sorting problems based on ordinal regression with additive value functions

  • Salvatore Corrente
  • Michael Doumpos
  • Salvatore Greco
  • Roman Słowiński
  • Constantin Zopounidis
Article

Abstract

A hierarchical decomposition is a common approach for coping with complex decision problems involving multiple dimensions. Recently, the multiple criteria hierarchy process (MCHP) has been introduced as a new general framework for dealing with multiple criteria decision aiding in case of a hierarchical structure of the family of evaluation criteria. This study applies the MCHP framework to multiple criteria sorting problems and extends existing disaggregation and robust ordinal regression techniques that induce decision models from data. The new methodology allows the handling of preference information and the formulation of recommendations at the comprehensive level, as well as at all intermediate levels of the hierarchy of criteria. A case study on bank performance rating is used to illustrate the proposed methodology.

Keywords

Multiple criteria decision aiding Multiple criteria hierarchy process Sorting problems Robust ordinal regression Bank rating 

References

  1. Angilella, S., Corrente, S., Greco, S., & Słowiński, R. (2013). Multiple criteria hierarchy process for the Choquet integral. In R. C. Purshouse, P. J. Fleming, C. M. Fonseca, S. Greco, & J. Shaw, (Eds.), Evolutionary multi-criterion optimization, volume 7811 of lecture notes in computer science (pp. 475–489). Berlin: Springer.Google Scholar
  2. Bana e Costa, C. A., & Jean-Claude Vansnick,. (2008). A critical analysis of the eigenvalue method used to derive priorities in AHP. European Journal of Operational Research, 187(3), 1422–1428.Google Scholar
  3. Bouyssou, D., & Marchant, T. (2010). Additive conjoint measurement with ordered categories. European Journal of Operational Research, 203(1), 195–204.CrossRefGoogle Scholar
  4. Comptroller of the Currency Administrator of National Banks. Bank supervision process. Available at: http://www.occ.gov/publications/publications-by-type/comptrollers-handbook/banksupervisionprocess.html, 2007
  5. Corrente, S., Greco, S., Kadziński, M., & Słowiński, R. (2014). Robust ordinal regression. Wiley Encyclopedia of Operations Research and Management Science (pp. 1–10).Google Scholar
  6. Corrente, S., Figueira, J. R., & Greco, S. (2014). Dealing with interaction between bipolar multiple criteria preferences in PROMETHEE methods. Annals of Operations Research, 217, 137–164.CrossRefGoogle Scholar
  7. Corrente, S., Greco, S., Kadziński, M., & Słowiński, R. (2013). Robust ordinal regression in preference learning and ranking. Machine Learning, 93, 381–422.CrossRefGoogle Scholar
  8. Corrente, S., Greco, S., & Słowiński, R. (2012). Multiple criteria hierarchy process in robust ordinal regression. Decision Support Systems, 53(3), 660–674.CrossRefGoogle Scholar
  9. Corrente, S., Greco, S., & Słowiński, R. (2013). Multiple criteria hierarchy process with ELECTRE and PROMETHEE. Omega, 41, 820–846.CrossRefGoogle Scholar
  10. Devaud, J. M., Groussaud, G., & Jacquet-Lagréze, E. (1980). Une méthode de construction de fonctions d’utilité additives rendant compte de judgments globaux. In Proceedings of EURO Working Group Meeting on Multicriteria Decision Aiding, Bochum.Google Scholar
  11. Doumpos, M., & Zopounidis, C. (2002). Multicriteria decision aid classification methods. New York: Springer.Google Scholar
  12. Doumpos, M., & Zopounidis, C. (2010). A multicriteria decision support system for bank rating. Decision Support Systems, 50(1), 55–63.CrossRefGoogle Scholar
  13. Doumpos, M., Zopounidis, C., & Galariotis, E. (2014). Inferring robust decision models in multicriteria classification problems: An experimental analysis. European Journal of Operational Research, 236, 601–611.CrossRefGoogle Scholar
  14. Grabisch, M., & Labreuche, C. (2010). A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals of Operations Research, 1(175), 247–286.CrossRefGoogle Scholar
  15. Greco, S., Kadziński, M., & Słowiński, R. (2011). Selection of a representative value function in robust multiple criteria sorting. Computers & Operations Research, 38, 1620–1637.CrossRefGoogle Scholar
  16. Greco, S., Matarazzo, B., & Słowiński, R. (1999). The use of rough sets and fuzzy sets in MCDM. In T. Gal, T. Stewart, & T. Hanne, (Eds.), Advances in multiple criteria decision making, chapter 14 (pp. 14.1–14.59). Dordrecht: Kluwer Academic.Google Scholar
  17. Greco, S., Matarazzo, B., & Słowiński, R. (2001). Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 129(1), 1–47.CrossRefGoogle Scholar
  18. Greco, S., Matarazzo, B., & Słowiński, R. (2002). Rough sets methodology for sorting problems in presence of multiple attributes and criteria. European Journal of Operational Research, 138(2), 247–259.CrossRefGoogle Scholar
  19. Greco, S., Matarazzo, B., & Słowiński, R. (2010). Dominance-based rough set approach to decision under uncertainty and time preference. Annals of Operations Research, 176(1), 41–75.CrossRefGoogle Scholar
  20. Greco, S., Mousseau, V., & Słowiński, R. (2008). Ordinal regression revisited: multiple criteria ranking using a set of additive value functions. European Journal of Operational Research, 191(2), 416–436.CrossRefGoogle Scholar
  21. Greco, S., Mousseau, V., & Słowiński, R. (2010). Multiple criteria sorting with a set of additive value functions. European Journal of Operational Research, 207(3), 1455–1470.CrossRefGoogle Scholar
  22. Jacquet-Lagrèze, E., & Siskos, Y. (2001). Preference disaggregation: 20 years of MCDA experience. European Journal of Operational Research, 130(2), 233–245.CrossRefGoogle Scholar
  23. Kadziński, M., & Tervonen, T. (2013). Stochastic ordinal regression for multiple criteria sorting problems. Decision Support Systems, 55(11), 55–66.CrossRefGoogle Scholar
  24. Keeney, R. L., & Raiffa, H. (1993). Decisions with multiple objectives: Preferences and value tradeoffs. New York: Wiley.CrossRefGoogle Scholar
  25. Saaty, T. L. (2005). The analytic hierarchy and analytic network processes for the measurement of intangible criteria and for decision-making. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multiple criteria decision analysis: State of the art surveys (pp. 345–382). Berlin: Springer.CrossRefGoogle Scholar
  26. Sahajwala, R., & Van den Bergh, P. (December 2000). Supervisory risk assessment and early warning systems. Technical Report 4, Bank of International Settlements, Basel.Google Scholar
  27. Słowiński, R., Greco, S., & Matarazzo, B. (2002). Rough set analysis of preference-ordered data. In J. J Alpigini, J. F. Peters, A. Skowron, & N. Zhong, (Eds.), Rough sets and current trends in computing, volume 2475 of lecture notes in artificial intelligence (pp. 44–59). Berlin: Springer.Google Scholar
  28. Słowiński, R., Stefanowski, J., Greco, S., & Matarazzo, B. (2000). Rough set based processing of inconsistent information in decision analysis. Control and Cybernetics, 29, 379–404.Google Scholar
  29. van Greuning, H., & Brajovic Bratanovic, S. (2009). Analyzing banking risk—a framework for assessing corporate governance and risk management (3rd ed.). Washington, DC: The World Bank.CrossRefGoogle Scholar
  30. Wakker, P. P. (1989). Additive representations of preferences: A new foundation of decision analysis, volume 4 of Theory and Decision Library C. Berlin: Springer.CrossRefGoogle Scholar
  31. Yu, W. (1992). Aide multicritère à la décision dans le cadre de la problématique du tri: méthodes et applications. Ph.D. thesis, LAMSADE, Université Paris Dauphine, Paris.Google Scholar
  32. Zopounidis, C., & Doumpos, M. (1999). A multicriteria decision aid methodology for sorting decision problems: The case of financial distress. Computational Economics, 14, 197–218.CrossRefGoogle Scholar
  33. Zopounidis, C., & Doumpos, M. (2002). Multicriteria classification and sorting methods: A literature review. European Journal of Operational Research, 138, 229–246.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Salvatore Corrente
    • 1
  • Michael Doumpos
    • 2
  • Salvatore Greco
    • 1
    • 3
  • Roman Słowiński
    • 4
    • 5
  • Constantin Zopounidis
    • 2
    • 6
  1. 1.Department of Economics and BusinessUniversity of CataniaCataniaItaly
  2. 2.School of Production Engineering and Management, Financial Engineering LaboratoryTechnical University of CreteChaniaGreece
  3. 3.Portsmouth Business School, Centre of Operations Research and Logistics (CORL)University of PortsmouthPortsmouthUK
  4. 4.Institute of Computing SciencePoznań University of TechnologyPoznanPoland
  5. 5.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  6. 6.Audencia Nantes School of ManagementNantesFrance

Personalised recommendations