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Inferring Efficient Weights from Pairwise Comparison Matrices

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  • R. Blanquero
  • E. Carrizosa
  • E. Conde

Abstract

Several multi-criteria-decision-making methodologies assume the existence of weights associated with the different criteria, reflecting their relative importance.One of the most popular ways to infer such weights is the analytic hierarchy process, which constructs first a matrix of pairwise comparisons, from which weights are derived following one out of many existing procedures, such as the eigenvector method or the least (logarithmic) squares. Since different procedures yield different results (weights) we pose the problem of describing the set of weights obtained by “sensible” methods: those which are efficient for the (vector-) optimization problem of simultaneous minimization of discrepancies. A characterization of the set of efficient solutions is given, which enables us to assert that the least-logarithmic-squares solution is always efficient, whereas the (widely used) eigenvector solution is not, in some cases, efficient, thus its use in practice may be questionable. Copyright Springer-Verlag 2006

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:271-284
    DOI: 10.1007/s00186-006-0077-1
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    References listed on IDEAS

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    1. Lootsma, F. A., 1996. "A model for the relative importance of the criteria in the Multiplicative AHP and SMART," European Journal of Operational Research, Elsevier, vol. 94(3), pages 467-476, November.
    2. Saaty, Thomas L., 1990. "Eigenvector and logarithmic least squares," European Journal of Operational Research, Elsevier, vol. 48(1), pages 156-160, September.
    3. Cook, Wade D. & Kress, Moshe, 1988. "Deriving weights from pairwise comparison ratio matrices: An axiomatic approach," European Journal of Operational Research, Elsevier, vol. 37(3), pages 355-362, December.
    4. Thomas L. Saaty, 1994. "How to Make a Decision: The Analytic Hierarchy Process," Interfaces, INFORMS, vol. 24(6), pages 19-43, December.
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    Cited by:

    1. 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.
    2. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    3. Judit Oláh & József Popp & Szabolcs Duleba & Anna Kiss & Zoltán Lakner, 2021. "Positioning Bio-Based Energy Systems in a Hypercomplex Decision Space—A Case Study," Energies, MDPI, vol. 14(14), pages 1-23, July.
    4. Carrizosa, Emilio, 2012. "On approximate Monetary Unit Sampling," European Journal of Operational Research, Elsevier, vol. 217(2), pages 479-482.
    5. Csató, László & Petróczy, Dóra Gréta, 2021. "On the monotonicity of the eigenvector method," European Journal of Operational Research, Elsevier, vol. 292(1), pages 230-237.
    6. 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.
    7. 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).
    8. Conde, Eduardo & de la Paz Rivera Pérez, María, 2010. "A linear optimization problem to derive relative weights using an interval judgement matrix," European Journal of Operational Research, Elsevier, vol. 201(2), pages 537-544, March.
    9. Miguel Hervás-Peralta & Sara Poveda-Reyes & Gemma Dolores Molero & Francisco Enrique Santarremigia & Juan-Pascual Pastor-Ferrando, 2019. "Improving the Performance of Dry and Maritime Ports by Increasing Knowledge about the Most Relevant Functionalities of the Terminal Operating System (TOS)," Sustainability, MDPI, vol. 11(6), pages 1-23, March.
    10. Marcin Anholcer & János Fülöp, 2019. "Deriving priorities from inconsistent PCM using network algorithms," Annals of Operations Research, Springer, vol. 274(1), pages 57-74, March.
    11. Mariia Dushenko & Clemet Thærie Bjorbæk & Kenn Steger-Jensen, 2018. "Application of a Sustainability Model for Assessing the Relocation of a Container Terminal: A Case Study of Kristiansand Port," Sustainability, MDPI, vol. 11(1), pages 1-18, December.
    12. D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2019. "Revenue allocation in Formula One: a pairwise comparison approach," Papers 1909.12931, arXiv.org, revised Dec 2020.
    13. Bozóki, Sándor & Fülöp, János, 2018. "Efficient weight vectors from pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 264(2), pages 419-427.

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