On Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons
This work addresses inconsistency measurement in decision-making for researchers and practitioners, but it is incremental as it builds on existing axioms and indices.
The paper introduces a new inconsistency measure for pairwise comparisons matrices and proposes an additional axiom, the upper boundary axiom, to the existing set of axioms. It provides proofs that selected inconsistency indices satisfy this axiom and includes a numerical comparison of these indices.
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 inconsistency index and inconsistency ratio for reciprocal pairwise comparisons matrices. This paper aims to: firstly, introduce a new measure of inconsistency of pairwise comparisons and to prove its basic properties; secondly, to postulate an additional axiom, an upper boundary axiom, to an existing set of axioms; and the last, but not least, the paper provides proofs of satisfaction of this additional axiom by selected inconsistency indices as well as it provides their numerical comparison.