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

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  • 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
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    References listed on IDEAS

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    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.
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    Citations

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    Cited by:

    1. Wang Feng, 2019. "Aggregation Similarity Measure Based on Hesitant Fuzzy Closeness Degree and Its Application to Clustering Analysis," Journal of Systems Science and Information, De Gruyter, vol. 7(1), pages 70-89, February.
    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. Josef Jablonský & Michal Černý & Juraj Pekár, 2022. "The last dozen of years of OR research in Czechia and Slovakia," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 435-447, June.
    4. de Hierro, A.F. Roldán López & Bustince, H. & Fernández, J. & Mesiar, R. & Roldán, C., 2018. "Two novel methodologies for considering aggregation functions by implicit equations and minimization problems," European Journal of Operational Research, Elsevier, vol. 270(2), pages 670-681.
    5. 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.
    6. 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.
    7. Kelin Luo & Yinfeng Xu & Bowen Zhang & Huili Zhang, 2018. "Creating an acceptable consensus ranking for group decision making," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 307-328, July.

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