On Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons
Jiri Mazurek

TL;DR
This paper introduces a new inconsistency measure for pairwise comparisons, proposes an additional axiom, and evaluates existing indices against this axiom to improve decision-making reliability.
Contribution
It presents a novel inconsistency measure, adds an upper boundary axiom to the set of axioms, and compares indices based on this new criterion.
Findings
The new inconsistency measure satisfies key properties.
Selected indices comply with the new upper boundary axiom.
Numerical comparison highlights differences among indices.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMulti-Criteria Decision Making · Rough Sets and Fuzzy Logic · Bayesian Modeling and Causal Inference
