On pairwise comparison matrices that can be made consistent by the modification of a few elements

  • Sándor Bozóki
  • János FülöpEmail author
  • Attila Poesz
Original Paper


Pairwise comparison matrices are often used in Multi-attribute Decision Making for weighting the attributes or for the evaluation of the alternatives with respect to a criteria. Matrices provided by the decision makers are rarely consistent and it is important to index the degree of inconsistency. In the paper, the minimal number of matrix elements by the modification of which the pairwise comparison matrix can be made consistent is examined. From practical point of view, the modification of 1, 2, or, for larger matrices, 3 elements seems to be relevant. These cases are characterized by using the graph representation of the matrices. Empirical examples illustrate that pairwise comparison matrices that can be made consistent by the modification of a few elements are present in the applications.


Multi-attribute decision making Consistent pairwise comparison matrix Graph representation of pairwise comparison matrices Empirical pairwise comparison matrix 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Sándor Bozóki
    • 1
    • 2
  • János Fülöp
    • 1
    Email author
  • Attila Poesz
    • 2
  1. 1.Laboratory on Engineering and Management IntelligenceResearch Group of Operations Research and Decision Systems, Computer and Automation Research Institute, Hungarian Academy of SciencesBudapestHungary
  2. 2.Department of Operations ResearchCorvinus University of BudapestBudapestHungary

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