A Geometric Framework for the Inconsistency in Pairwise Comparisons

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.

Article withdrawn under the request of W. Koczkodaj

Cited by in corpus (1)

• On Mathematical structures on pairwise comparisons matrices with coefficients in a group arising from quantum gravity