Enumerating all spanning trees for pairwise comparisons

Authors:
S. Siraj;L. Mikhailov;J. A. Keane
Affiliations:
Department of Electrical Engineering, COMSATS Institute of Information Technology, Wah Cantonment, Pakistan and School of Computer Science, The University of Manchester, M13 9PL, United Kingdom;Manchester Business School, Booth Street West, The University of Manchester, M15 6PB, United Kingdom;School of Computer Science, The University of Manchester, M13 9PL, United Kingdom
Venue:
Computers and Operations Research
Year:
2012

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Abstract

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.