IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v346y2025i2d10.1007_s10479-023-05278-6.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-023-05278-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-023-05278-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
    2. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Dai, Min, 2008. "A comparative study of the numerical scales and the prioritization methods in AHP," European Journal of Operational Research, Elsevier, vol. 186(1), pages 229-242, April.
    3. Aguarón, Juan & Escobar, María Teresa & Moreno-Jiménez, José María, 2021. "Reducing inconsistency measured by the geometric consistency index in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 288(2), pages 576-583.
    4. Iqbal Ali & Wade D. Cook & Moshe Kress, 1986. "On the Minimum Violations Ranking of a Tournament," Management Science, INFORMS, vol. 32(6), pages 660-672, June.
    5. Sándor Bozóki & János Fülöp & Attila Poesz, 2015. "On reducing inconsistency of pairwise comparison matrices below an acceptance threshold," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 849-866, December.
    6. Ralph L. Keeney, 1981. "Analysis of Preference Dependencies among Objectives," Operations Research, INFORMS, vol. 29(6), pages 1105-1120, December.
    7. 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.
    8. László Csató, 2019. "Axiomatizations of inconsistency indices for triads," Annals of Operations Research, Springer, vol. 280(1), pages 99-110, September.
    9. Christian Genest & Shuang-Shuang Zhang, 1996. "A Graphical Analysis of Ratio-Scaled Paired Comparison Data," Management Science, INFORMS, vol. 42(3), pages 335-349, March.
    10. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    11. Karapetrovic, Stanislav & Rosenbloom, E. S., 1999. "A quality control approach to consistency paradoxes in AHP," European Journal of Operational Research, Elsevier, vol. 119(3), pages 704-718, December.
    12. Valdecy Pereira & Helder Costa, 2015. "Nonlinear programming applied to the reduction of inconsistency in the AHP method," Annals of Operations Research, Springer, vol. 229(1), pages 635-655, June.
    13. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Influence of aggregation and measurement scale on ranking a compromise alternative in AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 700-710, April.
    14. Saaty, Thomas L & Vargas, Luis G, 1984. "The legitimacy of rank reversal," Omega, Elsevier, vol. 12(5), pages 513-516.
    15. Fichtner, John, 1986. "On deriving priority vectors from matrices of pairwise comparisons," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 341-345.
    16. Saaty, Thomas L., 2003. "Decision-making with the AHP: Why is the principal eigenvector necessary," European Journal of Operational Research, Elsevier, vol. 145(1), pages 85-91, February.
    17. Kułakowski, Konrad & Mazurek, Jiří & Ramík, Jaroslav & Soltys, Michael, 2019. "When is the condition of order preservation met?," European Journal of Operational Research, Elsevier, vol. 277(1), pages 248-254.
    18. Golany, B. & Kress, M., 1993. "A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices," European Journal of Operational Research, Elsevier, vol. 69(2), pages 210-220, September.
    19. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    20. Thomas L. Saaty, 2013. "The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach," Operations Research, INFORMS, vol. 61(5), pages 1101-1118, October.
    21. Alessio Ishizaka & Sajid Siraj, 2020. "Interactive consistency correction in the analytic hierarchy process to preserve ranks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 443-464, December.
    22. Dorit S. Hochbaum & Asaf Levin, 2006. "Methodologies and Algorithms for Group-Rankings Decision," Management Science, INFORMS, vol. 52(9), pages 1394-1408, September.
    23. Siraj, Sajid & Mikhailov, Ludmil & Keane, John, 2012. "A heuristic method to rectify intransitive judgments in pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 420-428.
    24. Schoner, Bertram & Wedley, William C. & Choo, Eng Ung, 1993. "A unified approach to AHP with linking pins," European Journal of Operational Research, Elsevier, vol. 64(3), pages 384-392, February.
    25. Siraj, S. & Mikhailov, L. & Keane, J.A., 2012. "Preference elicitation from inconsistent judgments using multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 220(2), pages 461-471.
    26. Ho, William & Ma, Xin, 2018. "The state-of-the-art integrations and applications of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 267(2), pages 399-414.
    27. Grošelj, Petra & Zadnik Stirn, Lidija, 2012. "Acceptable consistency of aggregated comparison matrices in analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 223(2), pages 417-420.
    28. James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
    29. Millet, Ido & Saaty, Thomas L., 2000. "On the relativity of relative measures - accommodating both rank preservation and rank reversals in the AHP," European Journal of Operational Research, Elsevier, vol. 121(1), pages 205-212, February.
    30. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alessio Ishizaka & Sajid Siraj, 2020. "Interactive consistency correction in the analytic hierarchy process to preserve ranks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 443-464, December.
    2. Dong, Yucheng & Hong, Wei-Chiang & Xu, Yinfeng & Yu, Shui, 2013. "Numerical scales generated individually for analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 229(3), pages 654-662.
    3. Ardalan Bafahm & Minghe Sun, 2019. "Some Conflicting Results in the Analytic Hierarchy Process," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 465-486, March.
    4. Liu, Qizhi, 2022. "Identifying and correcting the defects of the Saaty analytic hierarchy/network process: A comparative study of the Saaty analytic hierarchy/network process and the Markov chain-based analytic network ," Operations Research Perspectives, Elsevier, vol. 9(C).
    5. Kou, Gang & Ergu, Daji & Shang, Jennifer, 2014. "Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction," European Journal of Operational Research, Elsevier, vol. 236(1), pages 261-271.
    6. Cooper, Orrin & Yavuz, Idil, 2016. "Linking validation: A search for coherency within the Supermatrix," European Journal of Operational Research, Elsevier, vol. 252(1), pages 232-245.
    7. Fernandes, Rosário & Furtado, Susana, 2022. "Efficiency of the principal eigenvector of some triple perturbed consistent matrices," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1007-1015.
    8. Tomashevskii, I.L., 2015. "Eigenvector ranking method as a measuring tool: Formulas for errors," European Journal of Operational Research, Elsevier, vol. 240(3), pages 774-780.
    9. József Temesi, 2019. "An interactive approach to determine the elements of a pairwise comparison matrix," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 533-549, June.
    10. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Does AHP help us make a choice? An experimental evaluation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1801-1812, October.
    11. Li, Kevin W. & Wang, Zhou-Jing & Tong, Xiayu, 2016. "Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices," European Journal of Operational Research, Elsevier, vol. 250(2), pages 628-638.
    12. Ho, William & Ma, Xin, 2018. "The state-of-the-art integrations and applications of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 267(2), pages 399-414.
    13. Bice Cavallo, 2019. "Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem," Journal of Global Optimization, Springer, vol. 75(1), pages 143-161, September.
    14. Siraj, S. & Mikhailov, L. & Keane, J.A., 2012. "Preference elicitation from inconsistent judgments using multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 220(2), pages 461-471.
    15. József Temesi, 2011. "Pairwise comparison matrices and the error-free property of the decision maker," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(2), pages 239-249, June.
    16. Abel, Edward & Mikhailov, Ludmil & Keane, John, 2018. "Inconsistency reduction in decision making via multi-objective optimisation," European Journal of Operational Research, Elsevier, vol. 267(1), pages 212-226.
    17. Fujun Hou, 2016. "Market Competitiveness Evaluation of Mechanical Equipment with a Pairwise Comparisons Hierarchical Model," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-18, January.
    18. Susana Furtado & Charles R. Johnson, 2024. "Efficient vectors in priority setting methodology," Annals of Operations Research, Springer, vol. 332(1), pages 743-764, January.
    19. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez & Alberto Turón, 2020. "The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    20. Alessio Ishizaka, 2014. "Comparison of fuzzy logic, AHP, FAHP and hybrid fuzzy AHP for new supplier selection and its performance analysis," International Journal of Integrated Supply Management, Inderscience Enterprises Ltd, vol. 9(1/2), pages 1-22.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:346:y:2025:i:2:d:10.1007_s10479-023-05278-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.