  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.
