Enumerating all spanning trees for pairwise comparisons

Sajid Siraj, L. Mikhailov, John 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 judgements 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 judgements.
Original languageEnglish
Pages (from-to)191-199
Number of pages9
JournalComputers & Operations Research
Issue number2
Publication statusPublished - Feb 2012


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