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A Study for Obtaining Weights in Pairwise Comparison Matrix in AHP

  • Received : 2012.02.01
  • Accepted : 2012.04.16
  • Published : 2012.06.30

Abstract

In this study, we consider various methods to estimate the weights of a pairwise comparison matrix in the Analytic Hierarchy Process widely applied in various decision-making fields. This paper uses a data dependent simulation to evaluate the statistical accuracy, minimum violation and minimum norm of the obtaining weight methods from a reciprocal symmetric matrix. No method dominates others in all criteria. Least squares methods perform best in point of mean squared errors; however, the eigenvectors method has an advantage in the minimum norm.

Keywords

References

  1. Basak, I. (1989). Estimation of the multi-criteria worths of the alternatives in a hierarchical structure of comparisons, Communication in Statistics Theory and Methods, 18, 3719-3738. https://doi.org/10.1080/03610928908830119
  2. Bernadelli, H. (1941). Population waves, Journal of the Burma Research Society, 31, 1-18.
  3. Cogger, K. O. and Yu, P. L. (1985). Eigen weight vectors and least distance approximation for revealed preference in pairwise weight ratios, Journal of Optimization Theory and Applications, 36, 483-491.
  4. Costa, C. B. and Vansnick, J. (2008). A critical analysis of the eigenvalue method used to derive priorities in AHP, European Journal of Operational Research, 187, 1422-1428. https://doi.org/10.1016/j.ejor.2006.09.022
  5. Donegan, H. A. and Dodd, F. J. (1992). A new approach to AHP decision-making, The Statistician, 41, 295-302. https://doi.org/10.2307/2348551
  6. Gass, S. I. and Rapcsak, T. (2004). Singular value decomposition in AHP, European Journal of Operational Research, 154, 573-584. https://doi.org/10.1016/S0377-2217(02)00755-5
  7. Golany, B. and Kress, M. (1993). A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices, European Journal of Operational Research, 69, 210-220. https://doi.org/10.1016/0377-2217(93)90165-J
  8. Golden, B. and Wasil, E. A. (2003). Celebrating 25 years of AHP based decision making, Computers and Operational Research, 30, 1419-1497. https://doi.org/10.1016/S0305-0548(02)00184-3
  9. Jeong, H. C. (2010). Study on AHP and non-parametric veri cation on the importance of the diagnosis indicators of personal information security level, Journal of the Korean Data Analysis Society, 12,3(B), 1499-1510.
  10. Jeong, H.C. (2011). A note for obtaining weights from pairwise comparison matrix, Preceeding of the Journal of the Korean Data Analysis Society.
  11. Johnson, C. R., Beine, W. B. and Wang, T. J. (1979). A note on right-left asymmetry in an eigenvector ranking procedure, Journal of Mathematical Psychology, 19, 61-64. https://doi.org/10.1016/0022-2496(79)90005-1
  12. Kinoshita, E. (Kang, J. K. and Min, B. C.) (2008). AHP Theory and Practice, Intervision.
  13. Kumar, N. and Ganesh, L. S. (1996). A simulation-based evaluation of the approximate and the exact eigenvector methods employed in AHP, European Journal of Operational Research, 95, 656-662. https://doi.org/10.1016/0377-2217(95)00302-9
  14. Lee, J. C. (2012). A Study on the Statistical Property of AHP, A Doctoral Dissertation, Korea University.
  15. Leslie, P. H. (1945). On the use of matrices in certain population mathematics, Biometrika, 33, 183-212. https://doi.org/10.1093/biomet/33.3.183
  16. Saaty, T. L. (1980). The Analytic Hierarchy Process, McGraw-Hill, New York.
  17. Saaty, T. L. (2003). Multicriteria Decision Making: The Analytic Hierarchy Process, McGraw-Hill, New York.
  18. Saaty, T. L. and Vargas, L. G. (1984). Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios, Mathematical Modelling, 5, 309-324. https://doi.org/10.1016/0270-0255(84)90008-3
  19. Takeda, E., Cogger, K. and Yu, P. L. (1987). Estimating criterion weights using eigenvectors: A comparative study, European Journal of Operational Research, 29, 360-369. https://doi.org/10.1016/0377-2217(87)90249-9
  20. Zahedi, F. (1986). A simulation study of estimation methods in the analytic hierarchy process, Socio-Economic Planning Sciences, 20, 347-354. https://doi.org/10.1016/0038-0121(86)90046-7

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