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}
}
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32 Citations
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9
Methods Citations
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32 Citations

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References

SHOWING 1-10 OF 22 REFERENCES

Inconsistency indicator maps on groups for pairwise comparisons

Pairwise Comparisons Rating Scale Paradox

This study demonstrates that incorrect data are entered into a pairwise comparisons matrix for processing into weights for the data collected by a rating scale, and proposes a solution, based on normalization, to solve the paradox.

A new definition of consistency of pairwise comparisons

A Scaling Method for Priorities in Hierarchical Structures

Pairwise comparisons simplified

A general unified framework for pairwise comparison matrices in multicriterial methods

By introducing a more general notion of metric, this work provides a consistency index that has a natural meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix.

Inconsistencies in a schedule of paired comparisons

1. THE METHOD, AND THE HYPOTHESES CONCERNING IT The method of paired comparison has had a long and honourable history in psychological experiments, beginning with the researches of Witmer and Cohn,…

The Sources of Kolmogorov’s Grundbegriffe

Andrei Kolmogorov's Grundbegriffe der Wahrscheinlichkeits-rechnung put probability's modern mathematical formalism in place. It also provided a philosophy of probability--an explanation of how the…

Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability

We shall distinguish two aspects of the problems of estimation . (i) the practical and (ii) the theoretical. The practical aspect may be described as follows: (i a ) The statistician is concerned…

The origins and legacy of Kolmogorov's Grundbegriffe

April 25, 2003, marked the 100th anniversary of the birth of Andrei Nikolaevich Kolmogorov, the twentieth century's foremost contributor to the mathematical and philosophical foundations of…