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On the coincidence of optimal completions for small pairwise comparison matrices with missing entries

Author

Listed:
  • László Csató

    (HUN-REN Institute for Computer Science and Control (HUN-REN SZTAKI)
    Corvinus University of Budapest)

  • Kolos Csaba Ágoston

    (Corvinus University of Budapest)

  • Sándor Bozóki

    (HUN-REN Institute for Computer Science and Control (HUN-REN SZTAKI)
    Corvinus University of Budapest)

Abstract

Incomplete pairwise comparison matrices contain some missing judgements. A natural approach to estimate these values is provided by minimising a reasonable measure of inconsistency after unknown entries are replaced by variables. Two widely used inconsistency indices for this purpose are Saaty’s inconsistency index and the geometric inconsistency index, which are closely related to the eigenvector and the logarithmic least squares priority deriving methods, respectively. The two measures are proven to imply the same optimal filling for incomplete pairwise comparison matrices up to order four but not necessarily for order at least five.

Suggested Citation

  • László Csató & Kolos Csaba Ágoston & Sándor Bozóki, 2024. "On the coincidence of optimal completions for small pairwise comparison matrices with missing entries," Annals of Operations Research, Springer, vol. 333(1), pages 239-247, February.
    • Handle: RePEc:spr:annopr:v:333:y:2024:i:1:d:10.1007_s10479-023-05586-x
    DOI: 10.1007/s10479-023-05586-x
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    Keywords

    Analytic Hierarchy Process (AHP); Decision analysis; Eigenvalue method; Incomplete pairwise comparisons; Logarithmic least squares method;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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