Enumerating all spanning trees for pairwise comparisons

• Published in: Computers & operations research Vol. 39; no. 2; pp. 191 - 199
• Main Authors: Siraj, S., Mikhailov, L., Keane, J.A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-02-2012; Elsevier; Pergamon Press Inc
• Subjects: Applied sciences; Decision analysis; Decision making; Decision theory. Utility theory; Estimates; Exact sciences and technology; Flows in networks. Combinatorial problems; Graph theory; Judgment; Judgments; Mathematical analysis; MCDM; Operational research and scientific management; Operational research. Management science; Operations research; Pairwise comparisons; Preferences; Studies; Trees; Vectors (mathematics); Voting; Graph theory; Pairwise comparisons; MCDM; Decision making; Paired comparison; Decision support system; Multicriteria analysis; Hierarchical classification; Priority; Voting; Preference; Spanning tree; Open systems; Ordering; Judgment
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2011.03.010

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.