On Axiomatization of Inconsistency Indicators for Pairwise Comparisons

Abstract

We examine the notion of inconsistency in pairwise comparisons and propose an axiomatization which is independent of any method of approximation or the inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It has been proven that the eigenvalue-based inconsistency (proposed as a part of AHP) is incorrect.

Enhanced text, with 21 pages and 3 figures, proves that arbitrarily inaccurate pairwise matrices are considered acceptable by theories with a inconsistency based on the principal eigenvalue (e.g., AHP). CPC (corner pairwise comparisons) matrix is the crucial part of this study as it invalidates any eigenvalue-based inconsistency. All comments are highly appreciated

References in corpus (4)

• Axiomatic properties of inconsistency indices for pairwise comparisons
• On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
• A different perspective on a scale for pairwise comparisons
• A Monte Carlo Study of Pairwise Comparisons

Cited by in corpus (20)

• On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
• Studying a set of properties of inconsistency indices for pairwise comparisons
• A characterization of the Logarithmic Least Squares Method
• New results on inconsistency indices and their relationship with the quality of priority vector estimation
• On reducing inconsistency of pairwise comparison matrices below an acceptance threshold
• Characterization of an inconsistency ranking for pairwise comparison matrices
• Inconsistency indices for incomplete pairwise comparisons matrices
• Towards quantification of incompleteness in the pairwise comparisons method
• Axiomatizations of inconsistency indices for triads
• When is the condition of order preservation met?
• On the Properties of the Priority Deriving Procedure in the Pairwise Comparisons Method
• Special cases of pairwise comparisons matrices represented by Toeplitz matrices
• Notes on the existence of solutions in the pairwise comparisons method using the Heuristic Rating Estimation approach
• A mathematical bridge between discretized gauge theories in quantum physics and approximate reasoning in pairwise comparisons
• On Mathematical structures on pairwise comparisons matrices with coefficients in a group arising from quantum gravity
• A Geometric Framework for the Inconsistency in Pairwise Comparisons
• Inconsistency indicator maps on groups for pairwise comparisons
• The key properties of inconsistency indicators for a triad in pairwise comparison matrices
• On the Convergence of the Pairwise Comparisons Inconsistency Reduction Process
• On normalization of inconsistency indicators in pairwise comparisons