Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix

Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix

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Article ID: iaor2014737
Volume: 161
Issue: 3
Start Page Number: 980
End Page Number: 993
Publication Date: Jun 2014
Journal: Journal of Optimization Theory and Applications
Authors: , , ,
Keywords: matrices, networks
Abstract:

The inconsistency issue of pairwise comparison matrices has been an important subject in the study of the analytical network process. Most inconsistent elements can efficiently be identified by inducing a bias matrix only based on the original matrix. This paper further discusses the induced bias matrix and integrates all related theorems and corollaries into the induced bias matrix model. The theorem of inconsistency identification is proved mathematically using the maximum eigenvalue method and the contradiction method. In addition, a fast inconsistency identification method for one pair of inconsistent elements is proposed and proved mathematically. Two examples are used to illustrate the proposed fast identification method. The results show that the proposed new method is easier and faster than the existing method for the special case with only one pair of inconsistent elements in the original comparison matrix.

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