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The consistency index in reciprocal matrices: Comparison of deterministic and statistical approaches

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  • Vargas, Luis G.

Abstract

When checking the inconsistency level of a positive reciprocal matrix Saaty uses a deterministic criterion based on two parameters, a benchmark (the average), and a consistency level, usually 10%. Using results from a simulation experiment with 100,000 positive random reciprocal matrices of size varying from 3 to 15, we developed a probabilistic criterion and compare it to Saaty's index. We found that if a positive reciprocal matrix is consistent according to the deterministic criterion is also consistent according to the probabilistic criterion only if we accept a higher than usual probability of Type I error. Reducing this error implies that the benchmark must be a small percentile of the probability distribution of the consistency index.

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  • Vargas, Luis G., 2008. "The consistency index in reciprocal matrices: Comparison of deterministic and statistical approaches," European Journal of Operational Research, Elsevier, vol. 191(2), pages 454-463, December.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:2:p:454-463
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    1. Thomas L. Saaty, 1986. "Axiomatic Foundation of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 32(7), pages 841-855, July.
    2. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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    3. Vladimír Bureš & Jiří Cabal & Pavel Čech & Karel Mls & Daniela Ponce, 2020. "The Influence of Criteria Selection Method on Consistency of Pairwise Comparison," Mathematics, MDPI, vol. 8(12), pages 1-13, December.
    4. Mohd. Sadiq & Mohd. Sadim & Azra Parveen, 2021. "Applying statistical approach to check the consistency of pairwise comparison matrices during software requirements prioritization process," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(3), pages 451-460, June.
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    6. Changsheng Lin & Gang Kou & Daji Ergu, 2013. "An improved statistical approach for consistency test in AHP," Annals of Operations Research, Springer, vol. 211(1), pages 289-299, December.
    7. Liu, Fang & Zou, Shu-Cai & Li, Qing, 2020. "Deriving priorities from pairwise comparison matrices with a novel consistency index," Applied Mathematics and Computation, Elsevier, vol. 374(C).

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