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A general formulation for some inconsistency indices of pairwise comparisons

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Abstract

We propose a unifying approach to the problem of measuring the inconsistency of judgments. More precisely, we define a general framework to allow several well-known inconsistency indices to be expressed as special cases of this new formulation. We consider inconsistency indices as aggregations of ‘local’, i.e. triple-based, inconsistencies. We show that few reasonable assumptions guarantee a set of good properties for the obtained general inconsistency index. Under this representation, we prove a property of Pareto efficiency and show that OWA functions and t-conorms are suitable aggregation functions of local inconsistencies. We argue that the flexibility of this proposal allows tuning of the index. For example, by using different types of OWA functions, the analyst can obtain the desired balance between an averaging behavior and a ‘largest inconsistency-focused’ behavior.

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Notes

  1. A similar property, called locality, was formulated in “W.W. Koczkodaj and J. Szybowski, Axiomatization of inconsistency indicators for pairwise comparisons matrices revisited, arXiv:1509.03781v1”.

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Acknowledgements

The authors acknowledge the anonymous reviewers for their constructive comments which helped improve the original version of this manuscript.

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  1. Department of Industrial Engineering, University of Trento, Trento, Italy

    Matteo Brunelli & Michele Fedrizzi

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  1. Matteo Brunelli
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  2. Michele Fedrizzi
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Correspondence to Matteo Brunelli.

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Brunelli, M., Fedrizzi, M. A general formulation for some inconsistency indices of pairwise comparisons. Ann Oper Res 274, 155–169 (2019). https://doi.org/10.1007/s10479-018-2936-6

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