A Geometric Framework for the Inconsistency in Pairwise Comparisons

2016/01/23 by Koczkodaj, Waldemar W., Magnot, Jean-Pierre
#03F25 #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Logic (math.LO)

paper · doi:10.48550/arxiv.1601.06301

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.

Related

• Pairwise Comparisons Matrix Decomposition into Approximation and Orthogonal Component Using Lie Theory
• On the use of group theory to generalize elements of pairwise comparisons matrix: a cautionary note
• Inconsistency indicator maps on groups for pairwise comparisons
• On random pairwise comparisons matrices and their geometry
• Pairwise Comparisons Simplified