New light on the theorem of Perron.
We prove that the principal eigenvector of a positive matrix represents the relative dominance of its rows or ranking of alternatives in a decision represented by the rows of a pairwise comparison matrix.
Relative Measurement and Its Generalization in Decision Making. Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors. The Analytic Hierarchy/Network Process.
According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value...
Basic theory of the analytic hierarchy process: How to make a Decision.
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