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On the optimal consistent approximation to pairwise comparison matrices

โœ Scribed by Moody T. Chu

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
729 KB
Volume
272
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Consistency

retrieval from a biased relative preference table is an imperative task in decision theory. This paper considers the least squares approximation of a pairwise comparison matrix by consistent matrices.

It is observed that the highly nonlinear manifold of consistent matrices can be changed into a linear subspace by the componentwise logarithmic transformation.

A first order optimal&y condition therefore can be described in terms of coordinates in the linear subspace. This approach facilitates the otherwise much more complicated optimality condition if working with the variables in the original manifold. Fast nonlinear equation solvers can be employed to solve the problem efficiently.

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