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ELECTRE methods with interaction between criteria: An extension of the concordance index

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  • Figueira, José Rui
  • Greco, Salvatore
  • Roy, Bernard

Abstract

This paper presents an extension of the comprehensive (overall) concordance index of ELECTRE methods, which takes the interaction between criteria into account. In real-world decision-aiding situations, it is reasonable to consider only the interaction between a small number of criterion pairs. Three types of interaction have been considered: mutual strengthening, mutual weakening, and antagonistic. The new concordance index correctly takes into account such types of interactions, by imposing such conditions as boundary, monotonicity, and continuity. We demonstrate that the generalized index is able to take the three types of interaction, or dependencies, between criteria into account satisfactorily, first using quasi-criteria and then using pseudo-criteria. We also examine the links between the new concordance index and the Choquet integral.

Suggested Citation

  • Figueira, José Rui & Greco, Salvatore & Roy, Bernard, 2009. "ELECTRE methods with interaction between criteria: An extension of the concordance index," European Journal of Operational Research, Elsevier, vol. 199(2), pages 478-495, December.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:2:p:478-495
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    References listed on IDEAS

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    1. 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.
    2. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    3. Thomas L. Saaty, 2005. "The Analytic Hierarchy and Analytic Network Processes for the Measurement of Intangible Criteria and for Decision-Making," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 345-405, Springer.
    4. Figueira, Jose & Roy, Bernard, 2002. "Determining the weights of criteria in the ELECTRE type methods with a revised Simos' procedure," European Journal of Operational Research, Elsevier, vol. 139(2), pages 317-326, June.
    5. Roy, Bernard & Vanderpooten, Daniel, 1997. "An overview on "The European school of MCDA: Emergence, basic features and current works"," European Journal of Operational Research, Elsevier, vol. 99(1), pages 26-27, May.
    6. Roy, Bernard, 1993. "Decision science or decision-aid science?," European Journal of Operational Research, Elsevier, vol. 66(2), pages 184-203, April.
    7. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
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