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Max-algebra and pairwise comparison matrices

✍ Scribed by L. Elsner; P. van den Driessche

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
226 KB
Volume
385
Category
Article
ISSN
0024-3795

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✦ Synopsis

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(n 3 ) procedure to calculate the maxeigenvector is detailed.

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