IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v225y2013i3p472-478.html
   My bibliography  Save this article

Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions

Author

Listed:
  • Bustince, H.
  • Jurio, A.
  • Pradera, A.
  • Mesiar, R.
  • Beliakov, G.

Abstract

In this paper we present a generalization of the weighted voting method used in the exploitation phase of decision making problems represented by preference relations. For each row of the preference relation we take the aggregation function (from a given set) that provides the value which is the least dissimilar with all the elements in that row. Such a value is obtained by means of the selected penalty function. The relation between the concepts of penalty function and dissimilarity has prompted us to study a construction method for penalty functions from the well-known restricted dissimilarity functions. The development of this method has led us to consider under which conditions restricted dissimilarity functions are faithful. We present a characterization theorem of such functions using automorphisms. Finally, we also consider under which conditions we can build penalty functions from Kolmogoroff and Nagumo aggregation functions. In this setting, we propose a new generalization of the weighted voting method in terms of one single variable functions. We conclude with a real, illustrative medical case, conclusions and future research lines.

Suggested Citation

  • Bustince, H. & Jurio, A. & Pradera, A. & Mesiar, R. & Beliakov, G., 2013. "Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions," European Journal of Operational Research, Elsevier, vol. 225(3), pages 472-478.
  • Handle: RePEc:eee:ejores:v:225:y:2013:i:3:p:472-478
    DOI: 10.1016/j.ejor.2012.10.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712007369
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    as
    1. Mesiar, R., 2007. "Fuzzy set approach to the utility, preference relations, and aggregation operators," European Journal of Operational Research, Elsevier, vol. 176(1), pages 414-422, January.
    2. Herrera, F. & Martinez, L. & Sanchez, P. J., 2005. "Managing non-homogeneous information in group decision making," European Journal of Operational Research, Elsevier, vol. 166(1), pages 115-132, October.
    3. Dubois, Didier & Prade, Henri & Sabbadin, Regis, 2001. "Decision-theoretic foundations of qualitative possibility theory," European Journal of Operational Research, Elsevier, vol. 128(3), pages 459-478, February.
    4. Liu, Fang & Zhang, Wei-Guo & Wang, Zhong-Xing, 2012. "A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making," European Journal of Operational Research, Elsevier, vol. 218(3), pages 747-754.
    5. Doumpos, Michael & Zopounidis, Constantin, 2011. "Preference disaggregation and statistical learning for multicriteria decision support: A review," European Journal of Operational Research, Elsevier, vol. 209(3), pages 203-214, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Peláez, José Ignacio & Bernal, Rubén, 2016. "Selective majority additive ordered weighting averaging operatorAuthor-Name: Karanik, Marcelo," European Journal of Operational Research, Elsevier, vol. 250(3), pages 816-826.
    2. Ricci, Roberto Ghiselli, 2015. "Penalty functions based upon a general class of restricted dissimilarity functions," European Journal of Operational Research, Elsevier, vol. 241(3), pages 806-814.
    3. Bustince, H. & Fernandez, J. & Kolesárová, A. & Mesiar, R., 2015. "Directional monotonicity of fusion functions," European Journal of Operational Research, Elsevier, vol. 244(1), pages 300-308.

    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:eee:ejores:v:225:y:2013:i:3:p:472-478. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.