Generalization of the RCGM and LSLRpairwise comparison methods

Pairwise comparison methods are convenient procedures for predicting a sound weight vector from a set of relative comparisons between elements to be weighted. Several pairwise comparison methods exist. After a brief presentation of the least squares logarithmic regression (LSLR) method of de Graan [1] and Lootsma [2] and the recent row and column geometric mean (RCGM) of Koczkodaj and Orlowski [3], this paper proposes a common mathematical formulation for these two approaches. This common formulation leads to two generalized methods. The GLSLR is now able to process nonreciprocal comparison matrices, and the GRCGM is extended to several decision makers expressing different opinions per pairwise comparison. It also results in an explicit formulation of the weights that generalizes Koczkodaj and Orlowskiʹs formulation of the closest consistent comparison matrix