ON THE OPTIMAL CONSISTENT APPROXIMATION TO PAIRWISE COMPARISON MATRICES

Consistency retrieval from a biased relative preference table is an im perative task in decision theory. This paper considers the least squar es approximation of a pairwise comparison matrix by consistent matrice s. It is observed that the highly nonlinear manifold of consistent mat rices can be changed into a linear subspace by the componentwise logar ithmic transformation. A first order optimality condition therefore ca n be described in terms of coordinates in the linear subspace. This ap proach facilitates the otherwise much more complicated optimality cond ition if working with the variables in the original manifold. Fast non linear equation solvers can be employed to solve the problem efficient ly. (C) 1998 Elsevier Science Inc.