IDEAS home Printed from https://ideas.repec.org/h/spr/lnechp/978-3-319-08323-0_2.html
   My bibliography  Save this book chapter

Pairwise Comparison Matrices in Decision Making

In: Decision Making and Optimization

Author

Listed:
  • Martin Gavalec

    (University of Hradec Kralove)

  • Jaroslav Ramík

    (Silesian University in Opava)

  • Karel Zimmermann

    (Charles University in Prague)

Abstract

In multicriteria decision making context, a pairwise comparison matrix is a helpful tool to determine the weighted ranking of alternatives or criteria. The entry of the matrix can assume different meanings: it can be a preference ratio (multiplicative case) or a preference difference (additive case), or, it belongs to the unit interval and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). When comparing two elements, the decision maker assigns the value from a scale to any pair of alternatives representing the element of the pairwise preference matrix. Here, we investigate particularly relations between transitivity and consistency of preference matrices being understood differently with respect to the type of preference matrix. By various methods for deriving priorities from various types of preference matrices we obtain the corresponding priority vectors for final ranking of alternatives. The obtained results are also applied to situations where some elements of the fuzzy preference matrix are missing. Finally, a unified framework for pairwise comparison matrices based on abelian linearly ordered groups is presented. Illustrative numerical examples are supplemented.

Suggested Citation

  • Martin Gavalec & Jaroslav Ramík & Karel Zimmermann, 2015. "Pairwise Comparison Matrices in Decision Making," Lecture Notes in Economics and Mathematical Systems, in: Decision Making and Optimization, edition 127, chapter 0, pages 29-90, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-08323-0_2
    DOI: 10.1007/978-3-319-08323-0_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Kułakowski, Konrad & Mazurek, Jiří & Ramík, Jaroslav & Soltys, Michael, 2019. "When is the condition of order preservation met?," European Journal of Operational Research, Elsevier, vol. 277(1), pages 248-254.

    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:spr:lnechp:978-3-319-08323-0_2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.