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

H. Bustince, A. Jurio, A. Pradera, R. Mesiar and G. Beliakov

European Journal of Operational Research, 2013, vol. 225, issue 3, pages 472-478

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.

Keywords: Restricted dissimilarity function; Penalty function; Selection process; Weighted voting method (search for similar items in EconPapers)
Date: 2013
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European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

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