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A Graphical Analysis of Ratio-Scaled Paired Comparison Data

Author

Listed:
  • Christian Genest

    (Département de mathématiques et de statistique, Université Laval, Québec, Canada G1K 7P4)

  • Shuang-Shuang Zhang

    (Département de mathématiques et de statistique, Université Laval, Québec, Canada G1K 7P4)

Abstract

One of the building blocks of the Analytic Hierarchy Process (Saaty [Saaty, T. L. 1977. A scaling method for priorities in hierarchical structures. Math. Psych. 15 234--281.]) is the ratio-scaled assessment of an agent's preferences between pairs of alternatives. This article shows how it is possible to visualize such data and to detect cardinal and ordinal inconsistencies in the respondent's judgments. The graphical method used to display preferences is not new in itself: it dates back at least to the work of Gower (Gower, J. C. 1977. The analysis of asymmetry and orthogonality. J.-R. Barra, F. Brodeau, G. Romier, B. Van Cutsem, eds. Recent Developments in Statistics. North-Holland, Amsterdam, 109--123.), and many variants of his technique can be found in the literature. But Gower plots provide an especially valuable diagnostic tool in the context of AHP, as discussed and abundantly illustrated herein.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:3:p:335-349
    DOI: 10.1287/mnsc.42.3.335
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    Citations

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    Cited by:

    1. Easley, Robert F. & Valacich, Joseph S. & Venkataramanan, M. A., 2000. "Capturing group preferences in a multicriteria decision," European Journal of Operational Research, Elsevier, vol. 125(1), pages 73-83, August.
    2. 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.
    3. Zhibin Wu & Rong Yuan & Jiancheng Tu, 2021. "Group Decision Making with Transitive Preferences Under Ordinal and Cardinal Consistencies: An Optimization Approach," Group Decision and Negotiation, Springer, vol. 30(1), pages 221-250, February.
    4. Li-Ching Ma, 2018. "Discovering Consensus Preferences Visually Based on Gower Plots," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 741-761, May.
    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. Seeve, Teemu & Vilkkumaa, Eeva, 2022. "Identifying and visualizing a diverse set of plausible scenarios for strategic planning," European Journal of Operational Research, Elsevier, vol. 298(2), pages 596-610.

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