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Mathematical Problems in Engineering
Volume 2014, Article ID 989726, 16 pages
Research Article

Optimal Inconsistency Repairing of Pairwise Comparison Matrices Using Integrated Linear Programming and Eigenvector Methods

1DISP Laboratory, Lumière University Lyon 2, 160 boulevard de l’Université 69676, Bron Cedex, France
2Computer Science Department, Faculty of Engineering, Qatar University & ictQATAR, P.O. Box 2731, Doha, Qatar

Received 1 October 2013; Accepted 18 December 2013; Published 17 March 2014

Academic Editor: Hao-Chun Lu

Copyright © 2014 Haiqing Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Satisfying consistency requirements of pairwise comparison matrix (PCM) is a critical step in decision making methodologies. An algorithm has been proposed to find a new modified consistent PCM in which it can replace the original inconsistent PCM in analytic hierarchy process (AHP) or in fuzzy AHP. This paper defines the modified consistent PCM by the original inconsistent PCM and an adjustable consistent PCM combined. The algorithm adopts a segment tree to gradually approach the greatest lower bound of the distance with the original PCM to obtain the middle value of an adjustable PCM. It also proposes a theorem to obtain the lower value and the upper value of an adjustable PCM based on two constraints. The experiments for crisp elements show that the proposed approach can preserve more of the original information than previous works of the same consistent value. The convergence rate of our algorithm is significantly faster than previous works with respect to different parameters. The experiments for fuzzy elements show that our method could obtain suitable modified fuzzy PCMs.