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

TL;DR

This paper analyzes the fundamental properties of inconsistency indicators for triads in pairwise comparison matrices, providing axiomatization, theoretical proofs, and illustrative examples to clarify their key characteristics.

Contribution

It rectifies an informal axiomatization of triad inconsistency indicators using distance measures and formal proofs, clarifying their core properties.

Findings

Three key properties of inconsistency indicators are identified.

The properties are supported by theoretical proofs.

Illustrative examples demonstrate the properties.

Abstract

Processing information, acquired by subjective assessments, involves inconsistency analysis in most (if not all) applications of which some are of considerable importance at a national level (see, Koczkodaj/Kulakowski/Ligenza, Scientometrics, 99(3): 911-926, 2014)A triad inconsistency axiomatization in pairwise comparisons was informally proposed in Koczkodaj/Szwarc, FUNDAMENTA INFORMATICAE, 132(4): 485-500, 2014. This study, rectifies it by the use of the distance and theoretical proofs. Three key properties of the indicator are presented in this study and illustrated by several examples.