Bozóki, Sándor and Fülöp, János and Rónyai, Lajos (2010) On optimal completions of incomplete pairwise comparison matrices. Mathematical and Computer Modelling, 52 (12). pp. 318333. 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 multiattribute 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 Eigenvector 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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