Article: A heuristics approach for computing the largest eigenvalue of a pairwise comparison matrix Journal: International Journal of Operational Research (IJOR) 2019 Vol.34 No.4 pp.524 - 541 Abstract: Pairwise comparison matrices (PCMs) are widely used to capture subjective human judgements, especially in the context of the analytic hierarchy process (AHP). Consistency of judgements is normally computed in the AHP context in the form of consistency ratio (CR), which requires estimation of the largest eigenvalue (λmax) of PCMs. Since many of these alternatives methods do not require calculation of eigenvector, λmax and hence the CR of a PCM cannot be easily estimated. We propose in this paper a simple heuristics for calculating λmax without any need to use eigenvector method (EM). We illustrated the proposed procedure with larger size matrices. Simulation is used to compare the accuracy of the proposed heuristics procedure with actual λmax for PCMs of various sizes. It has been found that the proposed heuristics is highly accurate, with errors less than 1%. The proposed procedure would avoid biases and help managers to make better decisions. The advantage of the proposed heuristics is that it can be easily calculated with simple calculations without any need for specialised mathematical procedures or software and is independent of the method used to derive priorities from PCMs. Inderscience Publishers - linking academia, business and industry through research

Title: A heuristics approach for computing the largest eigenvalue of a pairwise comparison matrix

Authors: Nachiappan Subramanian; Ramakrishnan Ramanathan

Addresses: Nottingham University Business School China, The University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo 315-100, China ' Business and Management Research Institute, University of Bedfordshire, Putteridge Bury, Luton LU2 8LE, UK

Abstract: Pairwise comparison matrices (PCMs) are widely used to capture subjective human judgements, especially in the context of the analytic hierarchy process (AHP). Consistency of judgements is normally computed in the AHP context in the form of consistency ratio (CR), which requires estimation of the largest eigenvalue (λ_max) of PCMs. Since many of these alternatives methods do not require calculation of eigenvector, λ_max and hence the CR of a PCM cannot be easily estimated. We propose in this paper a simple heuristics for calculating λ_max without any need to use eigenvector method (EM). We illustrated the proposed procedure with larger size matrices. Simulation is used to compare the accuracy of the proposed heuristics procedure with actual λ_max for PCMs of various sizes. It has been found that the proposed heuristics is highly accurate, with errors less than 1%. The proposed procedure would avoid biases and help managers to make better decisions. The advantage of the proposed heuristics is that it can be easily calculated with simple calculations without any need for specialised mathematical procedures or software and is independent of the method used to derive priorities from PCMs.

Keywords: multiple criteria analysis; pairwise comparison matrix; PCM; eigenvector method; the largest eigenvalue; consistency index.

DOI: 10.1504/IJOR.2019.099107

International Journal of Operational Research, 2019 Vol.34 No.4, pp.524 - 541

Received: 14 Oct 2015
Accepted: 06 May 2016
Published online: 16 Apr 2019 *

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Title: A heuristics approach for computing the largest eigenvalue of a pairwise comparison matrix

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