A Geometric Framework for the Inconsistency in Pairwise Comparisons

@article{Koczkodaj2016AGF,
  title={A Geometric Framework for the Inconsistency in Pairwise Comparisons},
  author={Waldemar W. Koczkodaj and Jean-Pierre Magnot},
  journal={ArXiv},
  year={2016},
  volume={abs/1601.06301}
}
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… CONTINUE READING
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