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Directional Shift-Stable Functions

Author

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  • Radko Mesiar

    (Faculty of Civil Engineering, Slovakia University of Technology in Bratislava, Radlinského 11, 810 05 Bratislava, Slovakia
    Department of Algebra and Geometry, Faculty of Science, Palacky University Olomouc, 17 Listopadu 12, 771 46 Olomouc, Czech Republic
    Both authors contributed equally to this work.)

  • Andrea Stupňanová

    (Faculty of Civil Engineering, Slovakia University of Technology in Bratislava, Radlinského 11, 810 05 Bratislava, Slovakia
    Both authors contributed equally to this work.)

Abstract

Recently, some new types of monotonicity—in particular, weak monotonicity and directional monotonicity of an n -ary real function—were introduced and successfully applied. Inspired by these generalizations of monotonicity, we introduce a new notion for n-ary functions acting on [ 0 , 1 ] n , namely, the directional shift stability. This new property extends the standard shift invariantness (difference scale invariantness), which can be seen as a particular directional shift stability. The newly proposed property can also be seen as a particular kind of local linearity. Several examples and a complete characterization for the case of n = 2 of directionally shift-stable aggregation and pre-aggregation functions are also given.

Suggested Citation

  • Radko Mesiar & Andrea Stupňanová, 2021. "Directional Shift-Stable Functions," Mathematics, MDPI, vol. 9(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1077-:d:552016
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    References listed on IDEAS

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    1. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    2. 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.
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