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A distance-metric methodology for the derivation of weights from a pairwise comparison matrix

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  • D F Jones

    (University of Portsmouth, Buckingham Building, Lion Terrace)

  • S J Mardle

    (University of Portsmouth, Boathouse 6)

Abstract

A variety of approaches exist for the determination of a weighting scheme from a pairwise comparison matrix describing a scale-relation between objectives or alternatives. The most common context for such an algorithm is that of the analytic hierarchy process (AHP), although uses in other areas of the field of multicriteria decision making (MCDM) can also be found. Typically, the eigenvalue method is the standard method employed in the AHP to determine weights, as in the ExpertChoice software. However, another class of techniques are the distance-metric-based approaches, which are frequently proposed as alternatives to the eigenvalue method. This paper evaluates such distance-metric-based approaches comparing their effectiveness, using the eigenvalue method as a benchmark. A common framework is introduced to establish an efficient frontier for method comparison.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:8:d:10.1057_palgrave.jors.2601745
    DOI: 10.1057/palgrave.jors.2601745
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    References listed on IDEAS

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    1. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    2. Patrick T. Harker & Luis G. Vargas, 1987. "The Theory of Ratio Scale Estimation: Saaty's Analytic Hierarchy Process," Management Science, INFORMS, vol. 33(11), pages 1383-1403, November.
    3. 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.
    4. Zahedi, Fatemeh, 1986. "A simulation study of estimation methods in the analytic hierarchy process," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 347-354.
    5. Fichtner, John, 1986. "On deriving priority vectors from matrices of pairwise comparisons," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 341-345.
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    Citations

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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. Tomasz Wachowicz & Paweł Błaszczyk, 2013. "TOPSIS Based Approach to Scoring Negotiating Offers in Negotiation Support Systems," Group Decision and Negotiation, Springer, vol. 22(6), pages 1021-1050, November.
    3. Hsu-Shih Shih, 2016. "A Mixed-Data Evaluation in Group TOPSIS with Differentiated Decision Power," Group Decision and Negotiation, Springer, vol. 25(3), pages 537-565, May.
    4. Chang-Yu Hong & Eun-Sung Chung & Heejun Chang, 2020. "The Right to Urban Streams: Quantitative Comparisons of Stakeholder Perceptions in Defining Adaptive Stream Restoration," Sustainability, MDPI, vol. 12(22), pages 1-17, November.
    5. Bozóki, Sándor & Fülöp, János, 2018. "Efficient weight vectors from pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 264(2), pages 419-427.
    6. Jacinto González-Pachón & Carlos Romero, 2007. "Inferring consensus weights from pairwise comparison matrices without suitable properties," Annals of Operations Research, Springer, vol. 154(1), pages 123-132, October.
    7. Tomashevskii, I.L., 2015. "Eigenvector ranking method as a measuring tool: Formulas for errors," European Journal of Operational Research, Elsevier, vol. 240(3), pages 774-780.

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