On optimal completion of incomplete pairwise comparison matrices

Sándor Bozóki, János Fülöp, Lajos Rónyai

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68 Citations (Scopus)


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. Here we study 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 examples are discussed at the end of the paper.

Original languageEnglish
Pages (from-to)318-333
Number of pages16
JournalMathematical and Computer Modelling
Issue number1-2
Publication statusPublished - Jul 1 2010



  • Convex programming
  • Incomplete pairwise comparison matrix
  • Multiple criteria analysis
  • Perron eigenvalue

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications

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