A gradient method for inconsistency reduction of pairwise comparisons matrices

On distance-based inconsistency reduction algorithms for pairwise comparisons

One of the major challenges for collective intelligence is inconsistency, which is unavoidable whenever subjective assessments are involved. Pairwise comparisons allow one to represent such subjective assessments and to process them by analyzing, quantifying and identifying the inconsistencies. We propose using smaller scales for pairwise comparisons and provide mathematical and practical justi...

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...

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 of a pairwise comparison matrix

A unifying functional approach for inconsistency indices of pairwise comparisons

A vast amount of indices has been proposed in the literature [1] to quantify the deviation of a pairwise comparison matrix A = (aij)n×n from the consistency property aik = aijajk ∀i, j, k. In this paper we propose a unifying approach by expressing an inconsistency index as a function of the matrix entries aij satisfying a set of suitable properties. More precisely, we first consider the ‘local’...