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Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions

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Listed:
  • Serena Doria

    (Department of Engineering and Geology, University G. d’Annunzio, 66100 Chieti-Pescara, Italy)

  • Radko Mesiar

    (Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia)

  • Adam Šeliga

    (Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia)

Abstract

In this paper, we explore the use of aggregation functions in the construction of coherent upper previsions. Sub-additivity is one of the defining properties of a coherent upper prevision defined on a linear space of random variables and thus we introduce a new sub-additive transformation of aggregation functions, called a revenue transformation, whose output is a sub-additive aggregation function bounded below by the transformed aggregation function, if it exists. Method of constructing coherent upper previsions by means of shift-invariant, positively homogeneous and sub-additive aggregation functions is given and a full characterization of shift-invariant, positively homogeneous and idempotent aggregation functions on [ 0 , ∞ [ n is presented. Lastly, some concluding remarks are added.

Suggested Citation

  • Serena Doria & Radko Mesiar & Adam Šeliga, 2020. "Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions," Mathematics, MDPI, vol. 9(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:2-:d:466142
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    References listed on IDEAS

    as
    1. Serena Doria, 2012. "Characterization of a coherent upper conditional prevision as the Choquet integral with respect to its associated Hausdorff outer measure," Annals of Operations Research, Springer, vol. 195(1), pages 33-48, May.
    2. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    3. Serena Doria, 2019. "Preference orderings represented by coherent upper and lower conditional previsions," Theory and Decision, Springer, vol. 87(2), pages 233-252, September.
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