On Eigenvalues and Eigenvectors of Perturbed Pairwise Comparison Matrices

Authors

  • Pudji Astuti 1Algebra Research Group, FMIPA ITB, Indonesia
  • Agah D. Garnadi 2Scientific Computing Research Group, Dept. Mathematics, FMIPA IPB, Indonesia

DOI:

https://doi.org/10.5614/itbj.sci.2009.41.2.1

Abstract

This work studied eigenvalues and eigenvectors of a class of perturbed pairwise comparison matrices (PCMs). This type of matrices arises from Analytical Hierarchical Process with inconsistency comparison. By employing some nice structures of the PCMs, we show that the object dimension of size n 3 can be reduced into a case of size 3, hence simplify the studies.

References

Saaty, T.L., The Analytical Hierarchy Process, McGraw-Hill, New York, 1980.

Horn, R.A. & Johnson, C.R., Matrix Analysis, Cambridge University Press, Cambridge, 1985.

Gass, S.I. & Rapcsak, T., Singular Value Decomposition in AHP, European Journal of Operational Research, 154, 573-584, 2004.

Chu, M.T., On the Optimal Consistent Approximation to Pairwise Comparison Matrices, Linear Algebra and Its Applications, 272, 155-168, 1998.

Farkas, Andras, The Analysis of The Principal Eigenvector of Pairwise Comparison Matrices, Acta Polytechnica Hungarica, 4(2), 2007.

Ding, Jiu & Pye, Wallace C., On The Spectrum And Pseudoinverse of A Special Bordered Matrix, Linear Algebra and Its Applications, 331, 11 - 20, 2001.

Laub, A.J., Matrix Analysis for Scientist & Engineers, SIAM, USA, 2005.

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How to Cite

Astuti, P., & Garnadi, A. D. (2013). On Eigenvalues and Eigenvectors of Perturbed Pairwise Comparison Matrices. Journal of Mathematical and Fundamental Sciences, 41(2), 69-77. https://doi.org/10.5614/itbj.sci.2009.41.2.1

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