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Deriving weights from general pairwise comparison matrices

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  • Hovanov, Nikolai V.
  • Kolari, James W.
  • Sokolov, Mikhail V.

Abstract

The problem of deriving weights from pairwise comparison matrices has been treated extensively in the literature. Most of the results are devoted to the case when the matrix under consideration is reciprocally symmetric (i.e., the i, j-th element of the matrix is reciprocal to its j, i-th element for each i and j). However, there are some applications of the framework when the underlying matrices are not reciprocally symmetric. In this paper we employ both statistical and axiomatic arguments to derive weights from such matrices. Both of these approaches lead to geometric mean-type approximations. Numerical comparison of the obtained geometric mean-type solutions with Saaty's eigenvector method is provided also.

Suggested Citation

  • Hovanov, Nikolai V. & Kolari, James W. & Sokolov, Mikhail V., 2008. "Deriving weights from general pairwise comparison matrices," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 205-220, March.
    • Handle: RePEc:eee:matsoc:v:55:y:2008:i:2:p:205-220
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    Cited by:

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    3. J. Fülöp & W. Koczkodaj & S. Szarek, 2012. "On some convexity properties of the Least Squares Method for pairwise comparisons matrices without the reciprocity condition," Journal of Global Optimization, Springer, vol. 54(4), pages 689-706, December.
    4. 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.
    5. Pedro Linares & Sara Lumbreras & Alberto Santamaría & Andrea Veiga, 2016. "How relevant is the lack of reciprocity in pairwise comparisons? An experiment with AHP," Annals of Operations Research, Springer, vol. 245(1), pages 227-244, October.
    6. María Romero & María Luisa Cuadrado & Luis Romero & Carlos Romero, 2020. "Optimum acceptability of telecommunications networks: a multi-criteria approach," Operational Research, Springer, vol. 20(3), pages 1899-1911, September.
    7. Changsheng Lin & Gang Kou & Daji Ergu, 2013. "An improved statistical approach for consistency test in AHP," Annals of Operations Research, Springer, vol. 211(1), pages 289-299, December.
    8. R. Duncan McIntosh & Austin Becker, 2020. "Applying MCDA to weight indicators of seaport vulnerability to climate and extreme weather impacts for U.S. North Atlantic ports," Environment Systems and Decisions, Springer, vol. 40(3), pages 356-370, September.
    9. 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.
    10. Imad Hassan & Ibrahim Alhamrouni & Nurul Hanis Azhan, 2023. "A CRITIC–TOPSIS Multi-Criteria Decision-Making Approach for Optimum Site Selection for Solar PV Farm," Energies, MDPI, vol. 16(10), pages 1-26, May.
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    12. Alfredo Altuzarra & José María Moreno-Jiménez & Manuel Salvador, 2010. "Consensus Building in AHP-Group Decision Making: A Bayesian Approach," Operations Research, INFORMS, vol. 58(6), pages 1755-1773, December.
    13. András Farkas & Pál Rózsa, 2013. "A recursive least-squares algorithm for 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(4), pages 817-843, December.

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