Note on a new optimization based approach for estimating priority weights and related consistency index
The generation of priority vectors from pairwise comparison matrices is an essential part of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (REV) which was proposed by Saaty. Despite its popularity some shortcomings of the REV have been reported in literature. Among the alternative approaches one can find the statistical estimation techniques, methods founded on constrained optimization models and models based on fuzzy description of decision maker preferences. In this paper new optimization techniques for deriving priority weights are introduced. In the proposed approach, the constrained optimization models are based on the same idea which underlies the REV. The properties of the resulting prioritization techniques are studied via computer simulations. This study demonstrates that the new methods perform very well in comparison with other popular techniques known from literature. What is especially important, the new approach provides the decision maker with a meaningful index that can be used to measure consistency of his/her judgments. The new index is closely related to the well-known Saatys consistency index CI, but in difference to the latter, it can be applied to both reciprocal as well as nonreciprocal comparison matrices. Hence the new index can be considered as a natural extension of the CI to all types of matrices. Some additional advantages resulting from the new approach are discussed and illustrated by numerical examples.
consistency index priority vector eigenvalue method constrained optimization ahp