A simple method to improve the consistency ratio of the pair‐wise comparison matrix in ANP

A simple method to improve the consistency ratio of the pair‐wise comparison matrix in ANP

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Article ID: iaor20115029
Volume: 213
Issue: 1
Start Page Number: 246
End Page Number: 259
Publication Date: Aug 2011
Journal: European Journal of Operational Research
Authors: , , ,
Keywords: decision theory
Abstract:

Tests of consistency for the pair‐wise comparison matrices have been studied extensively since AHP was introduced by Saaty in 1970s. However, existing methods are either too complicated to be applied in the revising process of the inconsistent comparison matrix or are difficult to preserve most of the original comparison information due to the use of a new pair‐wise comparison matrix. Those methods might work for AHP but not for ANP as the comparison matrix of ANP needs to be strictly consistent. To improve the consistency ratio, this paper proposes a simple method, which combines the theorem of matrix multiplication, vectors dot product, and the definition of consistent pair‐wise comparison matrix, to identify the inconsistent elements. The correctness of the proposed method is proved mathematically. The experimental studies have also shown that the proposed method is accurate and efficient in decision maker’s revising process to satisfy the consistency requirements of AHP/ANP.

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