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Efficient weight vectors from pairwise comparison matrices

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  • Bozóki, Sándor
  • Fülöp, János

Abstract

Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and strictly better in at least one position. A weight vector is weakly efficient if the pairwise ratios cannot be improved in all non-diagonal positions. We show that the principal eigenvector is always weakly efficient, but numerical examples show that it can be inefficient. The linear programs proposed test whether a given weight vector is (weakly) efficient, and in case of (strong) inefficiency, an efficient (strongly) dominating weight vector is calculated. The proposed algorithms are implemented in Pairwise Comparison Matrix Calculator, available at pcmc.online.

Suggested Citation

  • Bozóki, Sándor & Fülöp, János, 2018. "Efficient weight vectors from pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 264(2), pages 419-427.
  • Handle: RePEc:eee:ejores:v:264:y:2018:i:2:p:419-427
    DOI: 10.1016/j.ejor.2017.06.033
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    References listed on IDEAS

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    1. Fichtner, John, 1986. "On deriving priority vectors from matrices of pairwise comparisons," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 341-345.
    2. Lundy, Michele & Siraj, Sajid & Greco, Salvatore, 2017. "The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis," European Journal of Operational Research, Elsevier, vol. 257(1), pages 197-208.
    3. 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.
    4. Siraj, S. & Mikhailov, L. & Keane, J.A., 2012. "Preference elicitation from inconsistent judgments using multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 220(2), pages 461-471.
    5. Golany, B. & Kress, M., 1993. "A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices," European Journal of Operational Research, Elsevier, vol. 69(2), pages 210-220, September.
    6. D F Jones & S J Mardle, 2004. "A distance-metric methodology for the derivation of weights from a pairwise comparison matrix," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 869-875, August.
    7. Lin, Chang-Chun, 2007. "A revised framework for deriving preference values from pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1145-1150, January.
    8. G. Bajwa & E. U. Choo & W. C. Wedley, 2008. "Effectiveness Analysis Of Deriving Priority Vectors From Reciprocal Pairwise Comparison Matrices," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 279-299.
    9. 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.
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    Cited by:

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    2. 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.

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