A Study for Obtaining Weights in Pairwise Comparison Matrix in AHP Jeong, Hyeong-Chul; Lee, Jong-Chan; Jhun, Myoung-Shic;
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.
AHP;Pairwise comparison matrix;Eigenvector method;Distance least squares;minimum norm;
A Statistical Testing of the Consistency Index in Analytic Hierarchy Process, Korean Journal of Applied Statistics, 2014, 27, 1, 103
Decision methodology for nitrogen removal process in the LNG plant using analytic hierarchy process, Journal of Industrial and Engineering Chemistry, 2016, 37, 75
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.
Bernadelli, H. (1941). Population waves, Journal of the Burma Research Society, 31, 1-18.
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.
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.
Donegan, H. A. and Dodd, F. J. (1992). A new approach to AHP decision-making, The Statistician, 41, 295-302.
Gass, S. I. and Rapcsak, T. (2004). Singular value decomposition in AHP, European Journal of Operational Research, 154, 573-584.
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.
Golden, B. and Wasil, E. A. (2003). Celebrating 25 years of AHP based decision making, Computers and Operational Research, 30, 1419-1497.
Jeong, H. C. (2010). Study on AHP and non-parametric verication on the importance of the diagnosis indicators of personal information security level, Journal of the Korean Data Analysis Society, 12,3(B), 1499-1510.
Jeong, H.C. (2011). A note for obtaining weights from pairwise comparison matrix, Preceeding of the Journal of the Korean Data Analysis Society.
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.
Kinoshita, E. (Kang, J. K. and Min, B. C.) (2008). AHP Theory and Practice, Intervision.
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.
Lee, J. C. (2012). A Study on the Statistical Property of AHP, A Doctoral Dissertation, Korea University.
Leslie, P. H. (1945). On the use of matrices in certain population mathematics, Biometrika, 33, 183-212.
Saaty, T. L. (1980). The Analytic Hierarchy Process, McGraw-Hill, New York.
Saaty, T. L. (2003). Multicriteria Decision Making: The Analytic Hierarchy Process, McGraw-Hill, New York.
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.
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.
Zahedi, F. (1986). A simulation study of estimation methods in the analytic hierarchy process, Socio-Economic Planning Sciences, 20, 347-354.