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Construction method of coherent lower and upper previsions based on collection integrals

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Abstract

Given a finite non-empty set \(\varOmega \) a new type of integral, named super-additive integral, is proposed to define coherent lower previsions on the class of all bounded functions. It is the extension to the class of all bounded random variables of a shift-invariant collection integral with respect to a collection \({\mathcal {D}}\) and a capacity \(\mu \). Related coherent upper previsions are also considered.

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Acknowledgements

The second and the third author were supported by the Slovak Research and Development Agency under the Contracts Nos. APVV-17-0066 and APVV-18-0052. Also the support of the Grant VEGA 1/0006/19 is kindly announced.

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Authors and Affiliations

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

    Serena Doria

  2. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05, Bratislava, Slovakia

    Radko Mesiar & Adam Seliga

Authors
  1. Serena Doria
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  2. Radko Mesiar
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  3. Adam Seliga
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Correspondence to Serena Doria.

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Dedicated to Professor Domenico Candeloro

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Doria, S., Mesiar, R. & Seliga, A. Construction method of coherent lower and upper previsions based on collection integrals. Boll Unione Mat Ital 13, 469–476 (2020). https://doi.org/10.1007/s40574-020-00220-1

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  • DOI: https://doi.org/10.1007/s40574-020-00220-1

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