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A method to analyze the rank reversal problem in the ELECTRE II method

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  • Liu, Xianliang
  • Ma, Yonghao

Abstract

In multi-criteria decision-making (MCDM) methods, the rank reversal is a highly important problem for analyzing the reliability of MCDM methods. The main objective of this paper is to analyze and precisely predict the occurrence of rank reversal in the ELECTRE II method. First, some useful properties of the optimal alternatives are obtained in the descending and ascending distillation processes. Second, two new concepts named combination relation digraph and numerator matrix are proposed to precisely analyze and greatly simplify the rank reversal in the ELECTRE II method. Third, all the reasons for the rank reversal in the ELECTRE II method are revealed more completely. Fourth, the necessary and sufficient conditions are proposed for determining whether or not the rank reversal occurs in the ELECTRE II method. Additionally, the proposed methods in this paper are valid for analyzing the rank reversal in the ELECTRE method with discriminating thresholds. Finally, five examples are used to evaluate the correctness and effectiveness of the methods that are proposed in this paper.

Suggested Citation

  • Liu, Xianliang & Ma, Yonghao, 2021. "A method to analyze the rank reversal problem in the ELECTRE II method," Omega, Elsevier, vol. 102(C).
    • Handle: RePEc:eee:jomega:v:102:y:2021:i:c:s030504832030671x
    DOI: 10.1016/j.omega.2020.102317
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    1. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    2. Roy, B. & Figueira, J.R. & Almeida-Dias, J., 2014. "Discriminating thresholds as a tool to cope with imperfect knowledge in multiple criteria decision aiding: Theoretical results and practical issues," Omega, Elsevier, vol. 43(C), pages 9-20.
    3. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
    4. Alper, Değer & Başdar, Canan, 2017. "A Comparison of TOPSIS and ELECTRE Methods: An Application on the Factoring Industry," Business and Economics Research Journal, Uludag University, Faculty of Economics and Administrative Sciences, vol. 8(3), pages 627-646, July.
    5. Figueira, José Rui & Roy, Bernard, 2009. "A note on the paper, "Ranking irregularities when evaluating alternatives by using some ELECTRE methods", by Wang and Triantaphyllou, Omega (2008)," Omega, Elsevier, vol. 37(3), pages 731-733, June.
    6. Troutt, MD & Tadisina, SK, 1990. "Corrigendum and further results: Rank reversal and the dependence of priorities on the underlying MAV function," Omega, Elsevier, vol. 18(6), pages 655-656.
    7. Stewart, TJ, 1992. "A critical survey on the status of multiple criteria decision making theory and practice," Omega, Elsevier, vol. 20(5-6), pages 569-586.
    8. Sajjad Zahir, 2009. "Normalisation and rank reversals in the additive analytic hierarchy process: a new analysis," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 4(4), pages 446-467.
    9. James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
    10. Thomas L. Saaty, 1990. "An Exposition of the AHP in Reply to the Paper "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 259-268, March.
    11. Troutt, Marvin D, 1988. "Rank reversal and the dependence of priorities on the underlying MAV function," Omega, Elsevier, vol. 16(4), pages 365-367.
    12. Dodd, F. J. & Donegan, H. A. & McMaster, T. B. M., 1995. "Inverse inconsistency in analytic hierarchies," European Journal of Operational Research, Elsevier, vol. 80(1), pages 86-93, January.
    13. Jun, Dong & Tian-tian, Feng & Yi-sheng, Yang & Yu, Ma, 2014. "Macro-site selection of wind/solar hybrid power station based on ELECTRE-II," Renewable and Sustainable Energy Reviews, Elsevier, vol. 35(C), pages 194-204.
    14. Stam, Antonie & Duarte Silva, A. Pedro, 2003. "On multiplicative priority rating methods for the AHP," European Journal of Operational Research, Elsevier, vol. 145(1), pages 92-108, February.
    15. Shao, Meng & Han, Zhixin & Sun, Jinwei & Xiao, Chengsi & Zhang, Shulei & Zhao, Yuanxu, 2020. "A review of multi-criteria decision making applications for renewable energy site selection," Renewable Energy, Elsevier, vol. 157(C), pages 377-403.
    16. Wang, Xiaoting & Triantaphyllou, Evangelos, 2008. "Ranking irregularities when evaluating alternatives by using some ELECTRE methods," Omega, Elsevier, vol. 36(1), pages 45-63, February.
    17. Céline Verly & Yves De Smet, 2013. "Some results about rank reversal instances in the PROMETHEE methods," International Journal of Multicriteria Decision Making, Inderscience Enterprises Ltd, vol. 3(4), pages 325-345.
    18. Usha Ramanathan & Ramakrishnan Ramanathan, 2011. "An investigation into rank reversal properties of the multiplicative AHP," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 11(1), pages 54-77.
    19. Saaty, Thomas L., 1994. "Highlights and critical points in the theory and application of the Analytic Hierarchy Process," European Journal of Operational Research, Elsevier, vol. 74(3), pages 426-447, May.
    20. Doumpos, Michalis & Figueira, José Rui, 2019. "A multicriteria outranking approach for modeling corporate credit ratings: An application of the Electre Tri-nC method," Omega, Elsevier, vol. 82(C), pages 166-180.
    21. Liao, Huchang & Wu, Xingli & Mi, Xiaomei & Herrera, Francisco, 2020. "An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule," Omega, Elsevier, vol. 93(C).
    Full references (including those not matched with items on IDEAS)

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