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Characterization of an inconsistency ranking for pairwise comparison matrices

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Abstract

Pairwise comparisons between alternatives are a well-known method for measuring preferences of a decision-maker. Since these often do not exhibit consistency, a number of inconsistency indices has been introduced in order to measure the deviation from this ideal case. We axiomatically characterize the inconsistency ranking induced by the Koczkodaj inconsistency index: six independent properties are presented such that they determine a unique linear order on the set of all pairwise comparison matrices.

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Notes

  1.  Throughout paper, the term entity is used for the ’things’ that are compared. They are sometimes called alternatives, objects, etc.

  2.  The term ‘monotonicity’ is not used in the name of this property in order to avoid confusion with MON.

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Acknowledgements

I would like to thank to Matteo Brunelli, Michele Fedrizzi, Waldemar W. Koczkodaj and Jacek Szybowski for inspiration. I am also grateful to Matteo Brunelli, Sándor Bozóki and Miklós Pintér reading the manuscript and for useful advices. Two anonymous reviewers provided valuable comments and suggestions on earlier drafts. The research was supported by OTKA Grant K 111797 and by the MTA Premium Post Doctorate Research Program. This research was partially supported by Pallas Athene Domus Scientiae Foundation. The views expressed are those of the author’s and do not necessarily reflect the official opinion of Pallas Athene Domus Scientiae Foundation.

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Authors and Affiliations

  1. Laboratory on Engineering and Management Intelligence, Research Group of Operations Research and Decision Systems, Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Budapest, Hungary

    László Csató

  2. Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest (BCE), Budapest, Hungary

    László Csató

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  1. László Csató
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Csató, L. Characterization of an inconsistency ranking for pairwise comparison matrices. Ann Oper Res 261, 155–165 (2018). https://doi.org/10.1007/s10479-017-2627-8

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