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

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 AHP context in the form of consistency ratio (CR), which requires estimation of the largest eigenvalue (λmax) of PCMs. Since many of these alternative 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.