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On optimal completions of incomplete pairwise comparison matrices

Bozóki, Sándor and Fülöp, János and Rónyai, Lajos (2010) On optimal completions of incomplete pairwise comparison matrices. Mathematical and Computer Modelling, 52 (1-2). pp. 318-333. DOI 10.1016/j.mcm.2010.02.047

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Official URL: http://www.sciencedirect.com/science/article/pii/S0895717710001159


Abstract

An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uniqueness problem of the best completion for two weighting methods, the Eigen-vector Method and the Logarithmic Least Squares Method. In both settings we obtain the same simple graph theoretic characterization of the uniqueness. The optimal completion will be unique if and only if the graph associated with the partially defined matrix is connected. Some numerical experiences are discussed at the end of the paper.

Item Type:Article
Uncontrolled Keywords:Multiple criteria analysis, Incomplete pairwise comparison matrix, Perron eigenvalue, Convex programming
Subjects:Mathematics, Econometrics
Computer science
DOI:10.1016/j.mcm.2010.02.047
ID Code:729
Deposited By: Ádám Hoffmann
Deposited On:03 Jul 2012 11:30
Last Modified:09 Aug 2012 10:57

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