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Penalty functions based upon a general class of restricted dissimilarity functions

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  • Ricci, Roberto Ghiselli

Abstract

In this paper the notion of restricted dissimilarity function is discussed and some general results are shown. The relation between the concepts of restricted dissimilarity function and penalty function is presented. A specific model of construction of penalty functions by means of a wide class of restricted dissimilarity functions based upon automorphisms of the unit interval is studied. A characterization theorem of the automorphisms which give rise to two-dimensional penalty functions is proposed. A generalization of the previous theorem to any dimension n > 2 is also provided. Finally, a not convex example of generator of penalty functions of arbitrary dimension is illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:806-814
    DOI: 10.1016/j.ejor.2014.09.004
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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. 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.
    3. Harvey J. Greenberg & William P. Pierskalla, 1971. "A Review of Quasi-Convex Functions," Operations Research, INFORMS, vol. 19(7), pages 1553-1570, December.
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