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      A Geometric Framework for the Inconsistency in Pairwise Comparisons

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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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          Journal
          2016-01-23
          2016-02-06
          Article
          1601.06301
          2b7e7b3a-7fbc-471c-9fcf-04170fb6690a

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          03F25
          v2: better presentation
          math.LO cs.IT math.DG math.IT

          Numerical methods,Information systems & theory,Geometry & Topology,Logic & Foundation

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