A New Approach to Improve Inconsistency in the Analytical Hierarchy Process

作者: Hamidreza Navidi , Morteza Rahmami

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摘要: In this paper, a new approach based on the generalized Purcell method for solving system of homogenous linear equations is applied to improve near consistent judgment matrices. The proposed relies altering components pairwise comparison matrix in such way that resulting sequences improved matrices matrix. complexity method, together with examples, shows less cost and better results computation than methods practice.

参考文章(13)
Thomas L. Saaty, Luis G. Vargas, Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios Mathematical Modelling. ,vol. 5, pp. 309- 324 ,(1984) , 10.1016/0270-0255(84)90008-3
Bernard Aupetit, Christian Genest, On some useful properties of the Perron eigenvalue of a positive reciprocal matrix in the context of the analytic hierarchy process European Journal of Operational Research. ,vol. 70, pp. 263- 268 ,(1993) , 10.1016/0377-2217(93)90044-N
T.L. Saaty, G. Hu, Ranking by eigenvector versus other methods in the analytic hierarchy process Applied Mathematics Letters. ,vol. 11, pp. 121- 125 ,(1998) , 10.1016/S0893-9659(98)00068-8
Thomas L Saaty, A Scaling Method for Priorities in Hierarchical Structures Journal of Mathematical Psychology. ,vol. 15, pp. 234- 281 ,(1977) , 10.1016/0022-2496(77)90033-5
Thomas L. Saaty, Decision-making with the AHP: Why is the principal eigenvector necessary European Journal of Operational Research. ,vol. 145, pp. 85- 91 ,(2003) , 10.1016/S0377-2217(02)00227-8
Geir Dahl, A method for approximating symmetrically reciprocal matrices by transitive matrices Linear Algebra and its Applications. ,vol. 403, pp. 207- 215 ,(2005) , 10.1016/J.LAA.2005.02.002
Christian Genest, Shuang-Shuang Zhang, A graphical analysis of ratio-scaled paired comparison data Management Science. ,vol. 42, pp. 335- 349 ,(1996) , 10.1287/MNSC.42.3.335
S.I. Gass, T. Rapcsák, Singular value decomposition in AHP European Journal of Operational Research. ,vol. 154, pp. 573- 584 ,(2004) , 10.1016/S0377-2217(02)00755-5
András Farkas, Peter Lancaster, Pál Rózsa, Consistency adjustments for pairwise comparison matrices Numerical Linear Algebra With Applications. ,vol. 10, pp. 689- 700 ,(2003) , 10.1002/NLA.318