An Axiomatic Framework for Aggregating Weights and Weight-Ratio Matrices
Jonathan Barzilai, Boaz Golany · ISAHP proceedings · 1991
In earlier work, we established an axiomatic framework for deriving consistent weight ratios from pairwise ratio matrices, using the geometric mean mapping.By adding new axioms, this framework is extended to include aggregation rules for combining weights and ratio matrices and the weighted-geometric-mean aggregation rule is shown to be consistent with this set of axioms.In addition, by defining the output of the process as weight ratios (rather than normalized absolute weights) and using multiplicative procedures (the geometric mean and the weighted-geometric-mean aggregation rule), rank reversal is avoided.