Abstract
We establish an equivalent representation of coherent choice functions in terms of a family of rejection sets, and investigate how each of the coherence axioms translates into this framework. In addition, we show that this family allows to simplify the verification of coherence in a number of particular cases.
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Notes
- 1.
By \({{\mathbb {R}}_{>0}}\) we mean all the (strictly) positive real numbers.
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Acknowledgements
This paper was written during a stay from Arthur van Camp at the University of Oviedo, funded by Banco Santander via Campus de Excelencia Internacional. We would like to acknowledge this funding, as well as that of project TIN2014-59543-P of the Spanish Ministerio de Economía y Competitividad. Gert de Cooman’s research was partly funded through project number 3G012512 of the Research Foundation Flanders (FWO).
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Miranda, E., Van Camp, A., de Cooman, G. (2018). Choice Functions and Rejection Sets. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_29
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DOI: https://doi.org/10.1007/978-3-319-73848-2_29
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