A method for approximating pairwise comparison matrices by consistent matrices

Fülöp, János (2007) A method for approximating pairwise comparison matrices by consistent matrices. -. MTA SZTAKI, Budapest.

[img] Text
WP_2007_3_Fulop.pdf - Published Version
Restricted to Registered users only

Download (288kB)

Abstract

In several methods of multiattribute decision making, pairwise comparison matrices are applied to derive implicit weights for a given set of decision alternatives. A class of the approaches is based on the approximation of the pairwise comparison matrix by a consistent matrix. In the paper this approximation problem is considered in the least-squares sense. In general, the problem is nonconvex and is difficult to solve, since it may have several local optima. In the paper the classic logarithmic transformation is applied and the problem is transcribed into the form of a separable programming problem based on a univariate function with special properties. We give sufficient conditions of the convexity of the objective function over the feasible set. If such a sufficient condition holds, the global optimum of the original problem can be obtained by local search, as well. For the general case, we propose a branch-and-bound method. Computational experiments are also presented.

Item Type: Monograph (-)
Uncontrolled Keywords: pairwise comparison matrix, consistent matrix, nonconvex programming, branch-and-bound
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:30
Last Modified: 11 Dec 2012 15:30
URI: http://eprints.sztaki.hu/id/eprint/5086

Update Item Update Item