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. © 2020 by the authors. Li-censee MDPI, Basel, Switzerland.

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

Serena Doria;
2021-01-01

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. © 2020 by the authors. Li-censee MDPI, Basel, Switzerland.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11564/740409
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