Inferring efficient weights from pairwise comparison matrices

R. Blanquero (rblanquerous.es)
E. Carrizosa (ecarrizosaus.es)
E. Conde (educonus.es)

Abstract: Several Multi-Criteria-Decision-Making methodologies assume the existence of weights associated with the different criteria, reflecting their relative importance. One of the most popular ways to infer such weights is the Analytic Hierarchy Process, which constructs first a matrix of pairwise comparisons, from which weights are derived following one out of many existing procedures, such as the eigenvector method or the least (logarithmic) squares. Since different procedures yield different results (weights) we pose the problem of describing the set of weights obtained by ”sensible” methods: those which are efficient for the (vector-) optimization problem of simultaneous minimization of discrepancies. A characterization of the set of efficient solutions is given, which enables us to assert that the least-logarithmic-squares solution is always efficient, whereas the (widely used) eigenvector solution is not, in some cases, efficient, thus its use in practice may be questionable.

Keywords: Analytic Hierarchy Process, Vector Optimization, Eigenvector method, Multiobjective Fractional Programming

Category 1: Other Topics (Multi-Criteria Optimization )

Citation: Research Report 2003/25, Dept. of Statistics and Operations Research, University of Seville (Spain), December/2003

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Entry Submitted: 12/04/2003
Entry Accepted: 12/04/2003
Entry Last Modified: 12/04/2003

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