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Deriving weights from general pairwise comparison matrices


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


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.

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  • 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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    References listed on IDEAS

    1. J. Ramsay, 1977. "Maximum likelihood estimation in multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 241-266, June.
    2. Giora Slutzki & Oscar Volij, 2006. "Scoring of web pages and tournaments—axiomatizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 75-92, January.
    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. Aczel, Janos & Roberts, Fred S., 1989. "On the possible merging functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 205-243, June.
    5. Hovanov, Nikolai V. & Kolari, James W. & Sokolov, Mikhail V., 2004. "Computing currency invariant indices with an application to minimum variance currency baskets," Journal of Economic Dynamics and Control, Elsevier, vol. 28(8), pages 1481-1504, June.
    6. Aczel, Janos & Moszner, Zenon, 1994. "New results on 'scale' and 'size' arguments justifying invariance properties of empirical indices and laws," Mathematical Social Sciences, Elsevier, vol. 28(1), pages 3-33, August.
    7. Hartvigsen, David, 2005. "Representing the strengths and directions of pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 163(2), pages 357-369, June.
    8. 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.
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    Cited by:

    1. repec:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-016-2131-6 is not listed on IDEAS
    2. repec:spr:annopr:v:245:y:2016:i:1:d:10.1007_s10479-014-1767-3 is not listed on IDEAS
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. repec:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2888-x is not listed on IDEAS
    8. 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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