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Consistency adjustments for pairwise comparison matrices
Author(s) -
Farkas András,
Lancaster Peter,
Rózsa Pál
Publication year - 2003
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.318
Subject(s) - mathematics , consistency (knowledge bases) , rank (graph theory) , pairwise comparison , transitive relation , matrix (chemical analysis) , low rank approximation , linear least squares , least squares function approximation , mathematical optimization , linear model , combinatorics , discrete mathematics , statistics , mathematical analysis , materials science , hankel matrix , estimator , composite material
This paper is concerned with the development of a ‘best’ rank one transitive approximation to a general paired comparison matrix in a least‐squares sense. A direct attack on the non‐linear problem is frequently replaced by a sub‐optimal linear problem and, here, the best procedure of this kind is obtained. The Newton–Kantorovich method for the solution of the non‐linear problem is also studied, including the role of the best linear approximation as a starting point for this method. Numerical examples are included. Copyright © 2002 John Wiley & Sons, Ltd.