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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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    2. 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.
    3. 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.
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    5. Hartvigsen, David, 2005. "Representing the strengths and directions of pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 163(2), pages 357-369, June.
    6. J. Ramsay, 1977. "Maximum likelihood estimation in multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 241-266, June.
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    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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    1. repec:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-016-2131-6 is not listed on IDEAS
    2. 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.
    3. repec:spr:annopr:v:245:y:2016:i:1:d:10.1007_s10479-014-1767-3 is not listed on IDEAS
    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. 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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