Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators

Abstract

Conditional aggregation operators are introduced, and coherent upper conditional previsions are constructed by sub-additive, positively homogenous, and shift-invariant conditional aggregation operators. Composed operators defined by positively homogenous conditional aggregation operators are proven to be conditional aggregation operators and they are involved in the construction of coherent upper conditional previsions. The given results show that the composed conditional aggregation operator obtained as the supremum of the class of the Choquet integrals with respect to Hausdorff outer measures defined by bi-Lipschitz equivalent metrics is a coherent upper conditional prevision.

Keywords

• conditional aggregation operator
• composed conditional aggregation operator
• coherent upper conditional previsions
• Choquet integral
• Sugeno integral
• Hausdorff outer measures