Simulation Experiments for Improving the Consistency Ratio of Reciprocal Matrices

Daji Ergu, Gang Kou, Yi Peng, Xinfeng Yang


The consistency issue is one of the hot research topics in the analytic
hierarchy process (AHP) and analytic network process (ANP). To identify the most
inconsistent elements for improving the consistency ratio of a reciprocal pairwise
comparison matrix (PCM), a bias matrix can be induced to efficiently identify the
most inconsistent elements, which is only based on the original PCM. The goal of this
paper is to conduct simulation experiments by randomly generating millions numbers
of reciprocal matrices with different orders in order to validate the effectiveness of
the induced bias matrix model. The experimental results show that the consistency
ratios of most of the random inconsistent matrices can be improved by the induced
bias matrix model, few random inconsistent matrices with high orders failed the
consistency adjustment.


Reciprocal random matrix, Consistency ratio, induced bias matrix, simulation experiment; analytic hierarchy process (AHP)/analytic network process (ANP)

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