A Note on the Multiplicative AHP

The paper concerns the pairwise comparison method used to rank a finite, usually small number of alternatives, in the Analytic Hierarchy Process (AHP), which belongs to a certain class of multiple attribute decision making methods. Ranking of alternatives is calculated based on expert judgments expressing relative importance for each pair of alternatives. From mathematical point of view calculation of weights associated with alternatives leads to approximation of a judgement matrix created based on expert opinions, by a matrix of weights ratios. There are two main approximation techniques: the maximal eigenvalue method and logarithmic least squares one. The study focuses on the former one showing its multiplicative properties. An illustrative numerical example is included. Key-Words: Pairwise Comparisons, Relative Weights, Logarithmic Regression, Maximal Eigenvalue Method, Multiple Attribute Decision Making, Analytic Hierarchy Process, Rank Preservation