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Analytic hierarchy process rank reversals: causes and solutions

Author

Listed:
  • Jiancheng Tu

    (Sichuan University)

  • Zhibin Wu

    (Sichuan University)

Abstract

The analytic hierarchy process (AHP) has been widely used. However, since the early 1980 s, the rank reversals resulting from the addition or deletion of alternatives have attracted criticism. Therefore, this study seeks to determine the causes and solutions to AHP rank reversals. First, we find that the intransitive preference and the prioritization methods cause rank reversals in single pairwise comparison matrices, and we present an optimization model for obtaining the priority vector with minimal rank violations and logarithmic square errors. The applicability and shortcomings of existing revised AHP models are then analyzed to determine the causes of rank reversal in distributive AHP, ideal AHP, and multiplicative AHP, which are respectively found to be inconsistency, the prioritization methods, and the aggregation rules. Finally, when the collective pairwise comparison matrix is intransitive, a modification suggestion is generated using an optimization model based on minimizing the number of reversed preferences and the amount of change in preferences.

Suggested Citation

  • Jiancheng Tu & Zhibin Wu, 2025. "Analytic hierarchy process rank reversals: causes and solutions," Annals of Operations Research, Springer, vol. 346(2), pages 1785-1809, March.
    • Handle: RePEc:spr:annopr:v:346:y:2025:i:2:d:10.1007_s10479-023-05278-6
    DOI: 10.1007/s10479-023-05278-6
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