On Axiomatization of Inconsistency Indicators for Pairwise Comparisons

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...

The key properties of inconsistency indicators for a triad in pairwise comparison matrices

A triad inconsistency axiomatization in pairwise comparisons was presented [2] informally. It is rectified by the use of the distance. Three key properties of the indicator are presented in this study and illustrated by several examples.

On normalization of inconsistency indicators in pairwise comparisons

In this study, we provide mathematical and practice-driven justification for using [0,1] normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization, are presented. A new type of paradox of infinity is described.

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