Max-algebra and pairwise comparison matrices Original Research Article

The max-eigenvector of a symmetrically reciprocal matrix A can be used to construct a transitive matrix that is closest to A in a relative error measure. As an alternative to the Perron eigenvector, the max-eigenvector can be used successfully for ranking in the analytical hierarchy process. When either one measurement is corrected or a new alternative is added, the max-eigenvector gives more consistent rankings. Some properties of the max-eigenvector that are important in this process are discussed, and an O(n3) procedure to calculate the max-eigenvector is detailed.