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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Decision Support Sys...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Decision Support Systems
Article . 2008 . Peer-reviewed
License: Elsevier TDM
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Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach

Authors: D. Cao; L.C. Leung; J.S. Law;

Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach

Abstract

Test of consistency is a critical step in the AHP methodology. When a pairwise comparison matrix fails to satisfy the consistency requirement, a decision maker needs to make revisions. To aid the decision maker's revising process, several approaches identify changes to the consistency requirement with respect to changes to a single entry in the original inconsistent matrix [P.T. Harker, Derivatives of the Perron root of a positive reciprocal matrix: with application to the analytic hierarchy process, Applied Mathematics and Computation, 22, 217-232 (1987); T.L. Saaty, Decision-making with the AHP: Why is the principal eigenvector necessary, European Journal of Operational Research, 145, 85-91 (2003)]. Instead of revising single entries, Xu and Wei [Z. Xu and C. Wei, A consistency improving method in the analytic hierarchy process, European Journal of Operational Research, V.116, 443-449 (1999)] derived a consistent matrix by an auto-adaptive process based on the original inconsistent matrix. In this paper, we develop a heuristic approach that auto-generates a consistent matrix based on the original inconsistent matrix. Expressing the inconsistent matrix in terms of a deviation matrix, an iterative process adjusts the deviation matrix to improve the consistency ratio, while preserving most of the original comparison information. We show that the proposed method is able to preserve more original comparison information than Xu and Wei [Z. Xu and C. Wei, A consistency improving method in the analytic hierarchy process, European Journal of Operational Research, V.116, 443-449 (1999)]. It is also shown that the heuristic approach can be used to examine the effects of revising a sub-bloc as well as revising a single entry of the original matrix.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
165
Top 1%
Top 1%
Top 10%
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