On optimal completions of incomplete pairwise comparison matrices
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Tartalom: http://real.mtak.hu/65496/
Archívum: MTA Könyvtár
Gyűjtemény: Status = Published





Type = Article
Cím:
On optimal completions of incomplete pairwise comparison matrices
Létrehozó:
Bozóki, Sándor
Fülöp, János
RĂłnyai, Lajos
Kiadó:
Pergamon
Dátum:
2010
Téma:
HB Economic Theory / közgazdaságtudomány
HB5 Mathematical economics / matematikai közgazdaságtan
QA Mathematics / matematika
QA166-QA166.245 Graphs theory / gráfelmélet
QA72 Algebra / algebra
QA74 Analysis / analĂ­zis
Tartalmi leírás:
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 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.
Nyelv:
magyar
Típus:
Article
PeerReviewed
info:eu-repo/semantics/article
Formátum:
text
Azonosító:
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. ISSN 0895-7177
Kapcsolat:
https://doi.org/10.1016/j.mcm.2010.02.047
DOI 10.1016/j.mcm.2010.02.047