Decision-making with the analytic hierarchy process: Why is the principal eigenvector necessary?

Decision-making with the analytic hierarchy process: Why is the principal eigenvector necessary?

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Article ID: iaor20042765
Country: Netherlands
Volume: 145
Issue: 1
Start Page Number: 85
End Page Number: 91
Publication Date: Feb 2003
Journal: European Journal of Operational Research
Authors:
Keywords: analytic hierarchy process
Abstract:

In this paper it is shown that the principal eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix A=(aij) when A is a small perturbation of a consistent matrix. When providing numerical judgments, an individual attempts to estimate sequentially an underlying ratio scale and its equivalent consistent matrix of ratios. Near consistent matrices are essential because when dealing with intangibles, human judgment is of necessity inconsistent, and if with new information one is able to improve inconsistency to near consistency, then that could improve the validity of the priorities of a decision. In addition, judgment is much more sensitive and responsive to large rather than to small perturbations, and hence once near consistency is attained, it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one. If such perturbations were forced, they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision.

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