Enumerating all spanning trees for pairwise comparisons

S. Siraj, L. Mikhailov, J. A. Keane

Research output: Contribution to journalArticlepeer-review


Determining the most suitable prioritization method for pairwise comparisons remains an open problem. This paper proposes a method based on the generation of all possible preferences from a set of judgments in pairwise comparisons. A concept of pivotal combination is introduced using a graph-theoretic approach. A set of preferences is generated by enumerating all spanning trees. The mean of these preferences is proposed as a final priority vector, and variance gives a measure of inconsistency. The proposed method provides a way of ordering objects according to a voting scheme. The proposed method is also applicable to incomplete sets of pairwise comparisons without modification, unlike other popular methods which require intermediate steps to estimate missing judgments. © 2011 Elsevier Ltd.
Original languageEnglish
Pages (from-to)191-199
Number of pages8
JournalComputers and Operations Research
Issue number2
Publication statusPublished - Feb 2012


  • Decision making
  • Graph theory
  • MCDM
  • Pairwise comparisons


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