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arXiv · 1601.06301

A Geometric Framework for the Inconsistency in Pairwise Comparisons

Waldemar W. Koczkodaj·Jean-Pierre Magnot
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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.

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BibTeXRIS

Waldemar W. Koczkodaj, Jean-Pierre Magnot. 2016-01-23. A Geometric Framework for the Inconsistency in Pairwise Comparisons. https://arxiv.org/abs/1601.06301

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