Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4728 |
| _version_ | 1827637937406214144 |
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| author | Serena Doria |
| author_facet | Serena Doria |
| author_sort | Serena Doria |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T16:07:43Z |
| format | Article |
| id | doaj.art-08ff6db814ff49cdbe57dce883de76e4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:07:43Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-08ff6db814ff49cdbe57dce883de76e42023-11-24T16:28:42ZengMDPI AGMathematics2227-73902022-12-011024472810.3390/math10244728Coherent Upper Conditional Previsions Defined through Conditional Aggregation OperatorsSerena Doria0Department of Engineering and Geology, University G. d’Annunzio, 66100 Chieti-Pescara, ItalyConditional 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.https://www.mdpi.com/2227-7390/10/24/4728conditional aggregation operatorcomposed conditional aggregation operatorcoherent upper conditional previsionsChoquet integralSugeno integralHausdorff outer measures |
| spellingShingle | Serena Doria Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators Mathematics conditional aggregation operator composed conditional aggregation operator coherent upper conditional previsions Choquet integral Sugeno integral Hausdorff outer measures |
| title | Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators |
| title_full | Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators |
| title_fullStr | Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators |
| title_full_unstemmed | Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators |
| title_short | Coherent Upper Conditional Previsions Defined through Conditional Aggregation Operators |
| title_sort | coherent upper conditional previsions defined through conditional aggregation operators |
| topic | conditional aggregation operator composed conditional aggregation operator coherent upper conditional previsions Choquet integral Sugeno integral Hausdorff outer measures |
| url | https://www.mdpi.com/2227-7390/10/24/4728 |
| work_keys_str_mv | AT serenadoria coherentupperconditionalprevisionsdefinedthroughconditionalaggregationoperators |