IDEAS home Printed from https://ideas.repec.org/a/taf/tjorxx/v69y2018i7p1125-1134.html
   My bibliography  Save this article

A chi-square-based inconsistency index for pairwise comparison matrices

Author

Listed:
  • Michele Fedrizzi
  • Fabio Ferrari

Abstract

In this paper, we introduce a new method for evaluating the inconsistency level of a pairwise comparison matrix. The classical Chi-square index suggests an interesting formal similarity for a consistent pairwise comparison matrix and, as a consequence, a method for measuring the relative deviation of the elicited preferences from a set of consistent preferences defined on the basis of the similarity mentioned above. Contrary to some previously introduced Chi-square-based approaches, no optimisation problems are involved. We verify that the new index satisfies some recently introduced characterising properties of inconsistency indices. Then, by means of numerical simulations, we compare our index with some other well-known inconsistency indices and we focus, in particular, on the comparison with Saaty’s consistency index. We discuss some numerical results showing that the new index is closely related with Saaty’s one but it is more stable with respect to the number of alternatives.

Suggested Citation

  • Michele Fedrizzi & Fabio Ferrari, 2018. "A chi-square-based inconsistency index for pairwise comparison matrices," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(7), pages 1125-1134, July.
    • Handle: RePEc:taf:tjorxx:v:69:y:2018:i:7:p:1125-1134
    DOI: 10.1080/01605682.2017.1390523
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01605682.2017.1390523
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01605682.2017.1390523?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuji Sato & Kim Hua Tan, 2023. "Inconsistency indices in pairwise comparisons: an improvement of the Consistency Index," Annals of Operations Research, Springer, vol. 326(2), pages 809-830, July.
    2. László Csató, 2019. "Axiomatizations of inconsistency indices for triads," Annals of Operations Research, Springer, vol. 280(1), pages 99-110, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:tjorxx:v:69:y:2018:i:7:p:1125-1134. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/tjor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.