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Directional monotonicity of fusion functions

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  • Bustince, H.
  • Fernandez, J.
  • Kolesárová, A.
  • Mesiar, R.

Abstract

In this paper we deal with fusion functions, i.e., mappings from [0, 1]n into [0, 1]. As a generalization of the standard monotonicity and recently introduced weak monotonicity, we introduce and study the directional monotonicity of fusion functions. For distinguished fusion functions the sets of all directions in which they are increasing are determined. Moreover, in the paper the directional monotonicity of piecewise linear fusion functions is completely characterized. These results cover, among others, weighted arithmetic means, OWA operators, the Choquet, Sugeno and Shilkret integrals.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:1:p:300-308
    DOI: 10.1016/j.ejor.2015.01.018
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    References listed on IDEAS

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    1. 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.
    2. Llamazares, Bonifacio, 2004. "Simple and absolute special majorities generated by OWA operators," European Journal of Operational Research, Elsevier, vol. 158(3), pages 707-720, November.
    3. Pedrycz, W., 2009. "Statistically grounded logic operators in fuzzy sets," European Journal of Operational Research, Elsevier, vol. 193(2), pages 520-529, March.
    4. Angilella, Silvia & Greco, Salvatore & Matarazzo, Benedetto, 2010. "Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral," European Journal of Operational Research, Elsevier, vol. 201(1), pages 277-288, February.
    5. Marichal, Jean-Luc, 2007. "k-intolerant capacities and Choquet integrals," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1453-1468, March.
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    Cited by:

    1. Boczek, Michał & Hovana, Anton & Hutník, Ondrej & Kaluszka, Marek, 2021. "New monotone measure-based integrals inspired by scientific impact problem," European Journal of Operational Research, Elsevier, vol. 290(1), pages 346-357.
    2. 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.
    3. Mesiar, R. & Kolesárová, A. & Bustince, H. & Dimuro, G.P. & Bedregal, B.C., 2016. "Fusion functions based discrete Choquet-like integrals," European Journal of Operational Research, Elsevier, vol. 252(2), pages 601-609.
    4. Radko Mesiar & Andrea Stupňanová, 2021. "Directional Shift-Stable Functions," Mathematics, MDPI, vol. 9(10), pages 1-12, May.

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