# 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.
pp. 318-333.

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## 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 A 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: | ISI Article |
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Uncontrolled Keywords: | Multiple criteria analysis, Incomplete pairwise comparison matrix, Perron eigenvalue, Convex programming |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Divisions: | Research Laboratory on Engineering & Management Intelligence Informatics Laboratory |

Depositing User: | Eszter Nagy |

Date Deposited: | 11 Dec 2012 15:31 |

Last Modified: | 26 Nov 2016 16:18 |

URI: | https://eprints.sztaki.hu/id/eprint/5293 |

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