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On the extraction of weights from pairwise comparison matrices

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  • Theo Dijkstra

Abstract

We study properties of weight extraction methods for pairwise comparison matrices that minimize suitable measures of inconsistency, ‘average error gravity’ measures, including one that leads to the geometric row means. The measures share essential global properties with the AHP inconsistency measure. By embedding the geometric mean in a larger class of methods we shed light on the choice between it and its traditional AHP competitor, the principal right eigenvector. We also suggest how to assess the extent of inconsistency by developing an alternative to the Random Consistency Index, which is not based on random comparison matrices, but based on judgemental error distributions. We define and discuss natural invariance requirements and show that the minimizers of average error gravity generally satisfy them, except a requirement regarding the order in which matrices and weights are synthesized. Only the geometric row mean satisfies this requirement also. For weight extraction we recommend the geometric mean. Copyright The Author(s) 2013

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  • Theo Dijkstra, 2013. "On the extraction of weights from pairwise comparison matrices," 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(1), pages 103-123, January.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:1:p:103-123
    DOI: 10.1007/s10100-011-0212-9
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    References listed on IDEAS

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    1. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    2. Aczel, J. & Alsina, C., 1986. "On synthesis of judgements," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 333-339.
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    Cited by:

    1. 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.
    2. Alfonso Maria Ponsiglione & Francesco Amato & Santolo Cozzolino & Giuseppe Russo & Maria Romano & Giovanni Improta, 2022. "A Hybrid Analytic Hierarchy Process and Likert Scale Approach for the Quality Assessment of Medical Education Programs," Mathematics, MDPI, vol. 10(9), pages 1-20, April.
    3. Michele Fedrizzi & Nino Civolani & Andrew Critch, 2020. "Inconsistency evaluation in pairwise comparison using norm-based distances," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 657-672, December.
    4. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    5. De Marinis, Pietro & Sali, Guido, 2020. "Participatory analytic hierarchy process for resource allocation in agricultural development projects," Evaluation and Program Planning, Elsevier, vol. 80(C).
    6. László Csató, 2018. "Characterization of the Row Geometric Mean Ranking with a Group Consensus Axiom," Group Decision and Negotiation, Springer, vol. 27(6), pages 1011-1027, December.
    7. Jagroop Singh & Somesh Kumar Sharma & Rajnish Srivastava, 2019. "AHP-Entropy based priority assessment of factors to reduce aviation fuel consumption," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(2), pages 212-227, April.
    8. Jana Siebert, 2019. "Fuzzy eigenvector method for deriving normalized fuzzy priorities from fuzzy multiplicative pairwise comparison matrices," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 175-197, June.
    9. Lianmeng Jiao & Quan Pan & Yan Liang & Xiaoxue Feng & Feng Yang, 2016. "Combining sources of evidence with reliability and importance for decision making," 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. 24(1), pages 87-106, March.

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