Inner approximations of coherent lower probabilities and their application to decision making problems.
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| Title: | Inner approximations of coherent lower probabilities and their application to decision making problems. |
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| Authors: | Miranda, Enrique1 (AUTHOR) mirandaenrique@uniovi.es, Montes, Ignacio1 (AUTHOR) imontes@uniovi.es, Presa, Andrés2 (AUTHOR) presa@strw.leidenuniv.nl |
| Source: | Annals of Operations Research. Dec2025, Vol. 355 Issue 3, p2777-2815. 39p. |
| Subjects: | Decision making, Probability measures, Quadratic programming, Approximation error, Uncertainty (Information theory) |
| Abstract: | We consider a decision making problem under imprecision, where the probabilistic information is given in terms of a set of probability measures, and where finding the optimal alternative(s) may be difficult. To ease the computation, we propose to transform the initial model into another one that (1) belongs to some subclass with better mathematical properties, such as supermodularity or complete monotonicity; (2) is at least as informative as the original model, while being as close as possible to it. We show that the problem can be approached in terms of linear or quadratic programming and that it can be connected with the one of determining the incenter of a credal set. Finally, we compare the solutions of a decision making problem with the initial and the transformed models and illustrate how our approach can be applied in a decision making problem under severe uncertainty. [ABSTRACT FROM AUTHOR] |
| Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 190357768 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Inner approximations of coherent lower probabilities and their application to decision making problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Miranda%2C+Enrique%22">Miranda, Enrique</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mirandaenrique@uniovi.es</i><br /><searchLink fieldCode="AR" term="%22Montes%2C+Ignacio%22">Montes, Ignacio</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> imontes@uniovi.es</i><br /><searchLink fieldCode="AR" term="%22Presa%2C+Andrés%22">Presa, Andrés</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> presa@strw.leidenuniv.nl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Annals+of+Operations+Research%22">Annals of Operations Research</searchLink>. Dec2025, Vol. 355 Issue 3, p2777-2815. 39p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Decision+making%22">Decision making</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+measures%22">Probability measures</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+programming%22">Quadratic programming</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty+%28Information+theory%29%22">Uncertainty (Information theory)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider a decision making problem under imprecision, where the probabilistic information is given in terms of a set of probability measures, and where finding the optimal alternative(s) may be difficult. To ease the computation, we propose to transform the initial model into another one that (1) belongs to some subclass with better mathematical properties, such as supermodularity or complete monotonicity; (2) is at least as informative as the original model, while being as close as possible to it. We show that the problem can be approached in terms of linear or quadratic programming and that it can be connected with the one of determining the incenter of a credal set. Finally, we compare the solutions of a decision making problem with the initial and the transformed models and illustrate how our approach can be applied in a decision making problem under severe uncertainty. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10479-023-05577-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 39 StartPage: 2777 Subjects: – SubjectFull: Decision making Type: general – SubjectFull: Probability measures Type: general – SubjectFull: Quadratic programming Type: general – SubjectFull: Approximation error Type: general – SubjectFull: Uncertainty (Information theory) Type: general Titles: – TitleFull: Inner approximations of coherent lower probabilities and their application to decision making problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Miranda, Enrique – PersonEntity: Name: NameFull: Montes, Ignacio – PersonEntity: Name: NameFull: Presa, Andrés IsPartOfRelationships: – BibEntity: Dates: – D: 21 M: 12 Text: Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02545330 Numbering: – Type: volume Value: 355 – Type: issue Value: 3 Titles: – TitleFull: Annals of Operations Research Type: main |
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