Inconsistency of special cases of pairwise comparisons matrices

Axiomatization of inconsistency indicators for pairwise comparisons

This study proposes axioms for inconsistency indicators in pairwise comparisons. The new observation (by Szybowski), that “no PC submatrix may have a worse inconsistency indicator than the given PC matrix” is an essential simplification of the axiomatization. The goal of formulating axioms for all future definitions of new inconsistency indicators is difficult and as illusive as the inconsisten...

On Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several inconsistency indices were proposed as an alternative to Saaty’s inconsistency index and inconsistency ratio for reciprocal pairwise comparisons matrices. This paper aim...

On inconsistency of a pairwise comparison matrix

Fast Convergence of Distance-based Inconsistency in Pairwise Comparisons

This study presents theoretical proof and empirical evidence of the reduction algorithm convergence for the distance-based inconsistency in pairwise comparisons. Our empirical research shows that the convergence very quick. It usually takes less than 10 reductions to bring the inconsistency of the pairwise comparisons matrix below the assumed threshold of 1/3 (sufficient for most applications)....

On the Convergence of the Pairwise Comparisons Inconsistency Reduction Process

This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into a consistent PC matrix which is generated by the geometric means of rows of a given inconsistent PC matrix. The distance-based inconsistency indicator was de...