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A Geometric Framework for the Inconsistency in Pairwise Comparisons (1601.06301v3)
Published 23 Jan 2016 in math.LO, cs.IT, math.DG, and math.IT
Abstract: In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided. Basic criteria for finding a nearest consistent pairwise comparisons matrix (extended to the class of group $G$) are proposed. A geometric interpretation of pairwise comparisons matrices in terms of connections to a simplex is given. Approximate reasoning is more effective when inconsistency in data is reduced.