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Sensitivity analysis of the parameters for preference functions and rank reversal analysis in the PROMETHEE II method

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  • Liu, Xianliang
  • Liu, Yunfei

Abstract

The PROMETHEE II method is a classical multiple criteria decision making method. However, it also exists the rank reversal which is a highly important problem for analyzing the reliability of a MCDM method. The main objective of this study is to analyze the sensitivity of the parameters for preference functions and the rank reversal problem in the PROMETHEE II method. By analyzing the parameters for preference functions from the standpoint of theoretics, a method is proposed to calculate the ranges of the parameters for four types of preference functions to remain the ranking of all the alternatives unchanged. Second, the sufficient and necessary condition of the rank reversal is obtained in the PROMETHEE II method when there are only three types of criteria, i.e., usual criteria, U-shape criteria and level criteria. Finally, two minor modification methods for the PROMETHEE II method itself are proposed by observing the net outranking flow formula. Numerical simulations show that the occurrence of the rank reversal is clearly reduced and the ranges of fault tolerance of the parameters for preference functions are significantly larger for each new modified PROMETHEE II method. The similarity of rankings is tested by using the similarity rank coefficient WS. This indicates the rationality of the two proposed modifications.

Suggested Citation

  • Liu, Xianliang & Liu, Yunfei, 2024. "Sensitivity analysis of the parameters for preference functions and rank reversal analysis in the PROMETHEE II method," Omega, Elsevier, vol. 128(C).
    • Handle: RePEc:eee:jomega:v:128:y:2024:i:c:s0305048324000823
    DOI: 10.1016/j.omega.2024.103116
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    1. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
    2. Gilles Dejaegere & Yves De Smet, 2022. "A new threshold for the detection of possible rank reversal occurrences in PROMETHEE II rankings," International Journal of Multicriteria Decision Making, Inderscience Enterprises Ltd, vol. 9(1), pages 1-16.
    3. De Keyser, Wim & Peeters, Peter, 1996. "A note on the use of PROMETHEE multicriteria methods," European Journal of Operational Research, Elsevier, vol. 89(3), pages 457-461, March.
    4. 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.
    5. 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.
    6. 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.
    7. Tolga Genc, 2014. "Sensitivity analysis on PROMETHEE and TOPSIS weights," International Journal of Management and Decision Making, Inderscience Enterprises Ltd, vol. 13(4), pages 403-421.
    8. Wolters, W. T. M. & Mareschal, B., 1995. "Novel types of sensitivity analysis for additive MCDM methods," European Journal of Operational Research, Elsevier, vol. 81(2), pages 281-290, March.
    9. 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.
    10. Hela Frikha & Habib Chabchoub & Jean-Marc Martel, 2010. "Inferring criteria's relative importance coefficients in PROMETHEE II," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 7(2), pages 257-275.
    11. 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.
    12. 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.
    13. 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.
    14. Edmundas Kazimieras Zavadskas & Kannan Govindan & Jurgita Antucheviciene & Zenonas Turskis, 2016. "Hybrid multiple criteria decision-making methods: a review of applications for sustainability issues," Economic Research-Ekonomska Istraživanja, Taylor & Francis Journals, vol. 29(1), pages 857-887, January.
    15. James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
    16. Liu, Xianliang & Ma, Yonghao, 2021. "A method to analyze the rank reversal problem in the ELECTRE II method," Omega, Elsevier, vol. 102(C).
    17. Troutt, Marvin D, 1988. "Rank reversal and the dependence of priorities on the underlying MAV function," Omega, Elsevier, vol. 16(4), pages 365-367.
    18. Faramondi, Luca & Oliva, Gabriele & Setola, Roberto & Bozóki, Sándor, 2023. "Robustness to rank reversal in pairwise comparison matrices based on uncertainty bounds," European Journal of Operational Research, Elsevier, vol. 304(2), pages 676-688.
    19. Wang, Xiaoting & Triantaphyllou, Evangelos, 2008. "Ranking irregularities when evaluating alternatives by using some ELECTRE methods," Omega, Elsevier, vol. 36(1), pages 45-63, February.
    20. 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.
    21. Bouyssou, D. & Perny, P., 1992. "Ranking methods for valued preference relations : A characterization of a method based on leaving and entering flows," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 186-194, August.
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