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Data Perturbations of Matrices of Pairwise Comparisons

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  • András Farkas
  • Pál Rózsa

Abstract

This paper deals with data perturbations of pairwise comparison matrices (PCM). Transitive and symmetrically reciprocal (SR) matrices are defined. Characteristic polynomials and spectral properties of certain SR perturbations of transitive matrices are presented. The principal eigenvector components of some of these PCMs are given in explicit form. Results are applied to PCMs occurring in various fields of interest, such as in the analytic hierarchy process (AHP) to the paired comparison matrix entries of which are positive numbers, in the dynamic input–output analysis to the matrix of economic growth elements of which might become both positive and negative and in vehicle system dynamics to the input spectral density matrix whose entries are complex numbers. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • András Farkas & Pál Rózsa, 2001. "Data Perturbations of Matrices of Pairwise Comparisons," Annals of Operations Research, Springer, vol. 101(1), pages 401-425, January.
    • Handle: RePEc:spr:annopr:v:101:y:2001:i:1:p:401-425:10.1023/a:1010986321720
    DOI: 10.1023/A:1010986321720
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    Cited by:

    1. Dong-Ling Xu, 2012. "An introduction and survey of the evidential reasoning approach for multiple criteria decision analysis," Annals of Operations Research, Springer, vol. 195(1), pages 163-187, May.
    2. Kun Chen & Gang Kou & J. Michael Tarn & Yan Song, 2015. "Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices," Annals of Operations Research, Springer, vol. 235(1), pages 155-175, December.
    3. Wen-Hsien Tsai & Pei-Ling Lee & Yu-Shan Shen & Elliott Hwang, 2014. "A combined evaluation model for encouraging entrepreneurship policies," Annals of Operations Research, Springer, vol. 221(1), pages 449-468, October.

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