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1 2011

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Comparison of analytic hierarchy process and some new optimization procedures for ratio scaling

Kazibudzki P.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2011

Vol. 10, nr 1

101-108

Deriving true priority vectors from intuitive pairwise comparison matrices constitutes a key part of the Analytic Hierarchy Process. The Eigenvalue Method, commonly applied in the Analytic Hierarchy Process, is the most popular concept in the process of ratio scaling. It is known that the Eigenvalue Method captures transitivity in matrices that are not consistent in a unique way. However, there are other methods such as statistical estimation techniques and methods based on constrained optimisation models that are equally interesting. This article compares two novel methods for priority vectors deriving, which combine the eigenvalue concept with a constrained optimisation based approach. Evidence is provided that contrary to the logarithmic least squares method, they coincide with the Eigenvalue Method in capturing the ratio scale rank order inherent in inconsistent pairwise comparison judgments.