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An exact algorithm for the multicriteria ordered clustering problem

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  • De Smet, Yves
  • Nemery, Philippe
  • Selvaraj, Ramkumar

Abstract

In the context of multicriteria decision aid, we address the problem of regrouping alternatives into completely ordered categories based on valued preference degrees. We assume that the number of groups is fixed a priori. This will be referred to as the multicriteria ordered clustering problem. The model is based on the definition of an inconsistency matrix and only uses the ordinal properties of the pairwise preference relations. An exact algorithm is proposed to find the ordered partition and is applied as illustration to the Human Development Index.

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  • De Smet, Yves & Nemery, Philippe & Selvaraj, Ramkumar, 2012. "An exact algorithm for the multicriteria ordered clustering problem," Omega, Elsevier, vol. 40(6), pages 861-869.
  • Handle: RePEc:eee:jomega:v:40:y:2012:i:6:p:861-869
    DOI: 10.1016/j.omega.2012.01.007
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    1. Jiménez, Antonio & Mateos, Alfonso & Ríos-Insua, Sixto, 2009. "Missing consequences in multiattribute utility theory," Omega, Elsevier, vol. 37(2), pages 395-410, April.
    2. Oral, Muhittin & Kettani, Ossama & Cosset, Jean-Claude & Daouas, Mohamed, 1992. "An estimation model for country risk rating," International Journal of Forecasting, Elsevier, vol. 8(4), pages 583-593, December.
    3. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    4. Saini, Krishan G. & Bates, Philip S., 1984. "A survey of the quantitative approaches to country risk analysis," Journal of Banking & Finance, Elsevier, vol. 8(2), pages 341-356, June.
    5. Jean-Claude Cosset & Jean Roy, 1991. "The Determinants of Country Risk Ratings," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 22(1), pages 135-142, March.
    6. Belacel, Nabil, 2000. "Multicriteria assignment method PROAFTN: Methodology and medical application," European Journal of Operational Research, Elsevier, vol. 125(1), pages 175-183, August.
    7. Kadziński, MiŁosz & Greco, Salvatore & SŁowiński, Roman, 2012. "Extreme ranking analysis in robust ordinal regression," Omega, Elsevier, vol. 40(4), pages 488-501.
    8. Dias, Luis & Mousseau, Vincent & Figueira, Jose & Climaco, Joao, 2002. "An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI," European Journal of Operational Research, Elsevier, vol. 138(2), pages 332-348, April.
    9. Doumpos, Michael & Zopounidis, Constantin, 2001. "Assessing financial risks using a multicriteria sorting procedure: the case of country risk assessment," Omega, Elsevier, vol. 29(1), pages 97-109, February.
    10. Peng, Yi & Kou, Gang & Wang, Guoxun & Shi, Yong, 2011. "FAMCDM: A fusion approach of MCDM methods to rank multiclass classification algorithms," Omega, Elsevier, vol. 39(6), pages 677-689, December.
    11. Tang, J. C. S. & Espinal, C. G., 1989. "A model to assess country risk," Omega, Elsevier, vol. 17(4), pages 363-367.
    12. Dias, Luis C. & Lamboray, Claude, 2010. "Extensions of the prudence principle to exploit a valued outranking relation," European Journal of Operational Research, Elsevier, vol. 201(3), pages 828-837, March.
    13. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834.
    14. Koksalan, Murat & Ulu, Canan, 2003. "An interactive approach for placing alternatives in preference classes," European Journal of Operational Research, Elsevier, vol. 144(2), pages 429-439, January.
    15. Farhad Noorbakhsh, 1998. "The human development index: some technical issues and alternative indices," Journal of International Development, John Wiley & Sons, Ltd., vol. 10(5), pages 589-605.
    16. Bertrand Mareschal & Jean Pierre Brans & Philippe Vincke, 1986. "How to select and how to rank projects: the Prométhée method," ULB Institutional Repository 2013/9307, ULB -- Universite Libre de Bruxelles.
    17. Brans, J. P. & Vincke, Ph. & Mareschal, B., 1986. "How to select and how to rank projects: The method," European Journal of Operational Research, Elsevier, vol. 24(2), pages 228-238, February.
    18. Tervonen, Tommi & Figueira, José Rui & Lahdelma, Risto & Dias, Juscelino Almeida & Salminen, Pekka, 2009. "A stochastic method for robustness analysis in sorting problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 236-242, January.
    19. Cosset, Jean-Claude & Siskos, Yannis & Zopounidis, Constantin, 1992. "Evaluating country risk: A decision support approach," Global Finance Journal, Elsevier, vol. 3(1), pages 79-95.
    20. Frank, Charles Jr. & Cline, William R., 1971. "Measurement of debt servicing capacity: An application of discriminant analysis," Journal of International Economics, Elsevier, vol. 1(3), pages 327-344, August.
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    6. Raquel Lourenço Carvalhal Monteiro & Valdecy Pereira & Helder Gomes Costa, 2018. "A Multicriteria Approach to the Human Development Index Classification," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(2), pages 417-438, April.
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    17. Pereira, Javier & Contreras, Pedro & Morais, Danielle C. & Arroyo-López, Pilar, 2022. "Multi-criteria ordered clustering of countries in the Global Health Security Index," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).

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