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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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    References listed on IDEAS

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    1. Szádoczki, Zsombor & Bozóki, Sándor & Tekile, Hailemariam Abebe, 2022. "Filling in pattern designs for incomplete pairwise comparison matrices: (Quasi-)regular graphs with minimal diameter," Omega, Elsevier, vol. 107(C).
    2. Chao, Xiangrui & Kou, Gang & Li, Tie & Peng, Yi, 2018. "Jie Ke versus AlphaGo: A ranking approach using decision making method for large-scale data with incomplete information," European Journal of Operational Research, Elsevier, vol. 265(1), pages 239-247.
    3. Bice Cavallo, 2020. "Functional relations and Spearman correlation between consistency indices," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(2), pages 301-311, February.
    4. László Csató, 2013. "Ranking by pairwise comparisons for Swiss-system tournaments," 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. 21(4), pages 783-803, December.
    5. Konrad Kułakowski & Jiri Mazurek & Michał Strada, 2022. "On the similarity between ranking vectors in the pairwise comparison method," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 73(9), pages 2080-2089, October.
    6. Bozóki, Sándor & Csató, László & Temesi, József, 2016. "An application of incomplete pairwise comparison matrices for ranking top tennis players," European Journal of Operational Research, Elsevier, vol. 248(1), pages 211-218.
    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. Kwiesielewicz, M., 1996. "The logarithmic least squares and the generalized pseudoinverse in estimating ratios," European Journal of Operational Research, Elsevier, vol. 93(3), pages 611-619, September.
    9. Takeda, Eiji & Yu, Po-Lung, 1995. "Assessing priority weights from subsets of pairwise comparisons in multiple criteria optimization problems," European Journal of Operational Research, Elsevier, vol. 86(2), pages 315-331, October.
    10. Tekile, Hailemariam Abebe & Brunelli, Matteo & Fedrizzi, Michele, 2023. "A numerical comparative study of completion methods for pairwise comparison matrices," Operations Research Perspectives, Elsevier, vol. 10(C).
    11. R. Blanquero & E. Carrizosa & E. Conde, 2006. "Inferring Efficient Weights from Pairwise Comparison Matrices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 271-284, October.
    12. Alessio Ishizaka & Markus Lusti, 2006. "How to derive priorities in AHP: a comparative study," 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. 14(4), pages 387-400, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    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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