# On normalization of inconsistency indicators in pairwise comparisons

@article{Koczkodaj2017OnNO, title={On normalization of inconsistency indicators in pairwise comparisons}, author={Waldemar W. Koczkodaj and Jean-Pierre Magnot and Jiř{\'i} Mazurek and James F. Peters and H. Rakhshani and Michael Soltys and Dominik Strzałka and Jacek Szybowski and Arturo Tozzi}, journal={ArXiv}, year={2017}, volume={abs/1702.07205} }

## 32 Citations

### A survey of inconsistency indices for pairwise comparisons

- Computer ScienceInt. J. Gen. Syst.
- 2018

This manuscript surveys the most relevant inconsistency indices by means of a self-contained exposition and presents some conclusions and a discussion on possible directions of future research.

### Using group theory in pairwise comparisons: a brief critique

- Computer Science
- 2019

The lack of acceptable semantics for selected groups (with negative and complex numbers) and implications are analyzed and examples and mathematical reasoning indicating why inconsistency indicators for pairwise comparisons require normalization are provided.

### Some notes on the properties of inconsistency indices in pairwise comparisons

- Economics
- 2018

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies have focused on the means of expressing and…

### Consistent projections and indicators in pairwise comparisons

- MathematicsInt. J. Approx. Reason.
- 2020

### New preference violation indices for the condition of order preservation

- Computer ScienceRAIRO Oper. Res.
- 2022

The aim of this paper is to fill this gap and propose new preference violation indices for measuring violation of the condition of the order preservation, and it is shown that the proposed indices satisfy uniqueness, invariance under permutation, invariant under inversion of preferences and continuity axioms.

### Inconsistency of special cases of pairwise comparisons matrices

- Computer ScienceInt. J. Approx. Reason.
- 2018

### An Examination of Ranking Quality for Simulated Pairwise Judgments in relation to Performance of the Selected Consistency Measure

- EconomicsAdv. Oper. Res.
- 2019

The research results argue that although the performance of examined consistency measures deviates from the exemplary ones in relation to the estimation quality of decision makers preferences, solutions proposed in this paper can significantly improve that quality.

### Pairwise Comparison Matrices in Decision-Making

- Computer ScienceLecture Notes in Economics and Mathematical Systems
- 2020

Relations between transitivity and consistency of preference matrices being understood differently with respect to the type of preference matrix are investigated and the corresponding priority vectors for final ranking of alternatives are obtained.

### From pairwise comparisons to consistency with respect to a group operation and Koczkodaj's metric

- MathematicsInt. J. Approx. Reason.
- 2019

### On Mathematical structures on pairwise comparisons matrices with coefficients in a group arising from quantum gravity

- Mathematics
- 2016

We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of…

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