Normal cones corresponding to credal sets of lower probabilities

Škulj, Damjan (author)

Credal sets are one of the most important models for describing probabilistic uncertainty. They usually arise as convex sets of probabilistic models compatible with judgments provided in terms of coherent lower previsions or more specific models such as coherent lower probabilities or probability intervals. In finite spaces, credal sets usually take the form of convex polytopes. Many properties of convex polytopes can be derived from their normal cones, which form polyhedral complexes called normal fans. We analyze the properties of normal cones corresponding to credal sets of coherent lower probabilities. For two important classes of coherent lower probabilities, 2-monotone lower probabilities and probability intervals, we provide a detailed description of the normal fan structure. These structures are related to the structure of the extreme points of the credal sets. To arrive at our main results, we provide some general results on triangulated normal fans of convex polyhedra and their adjacency structure.

• Language: English
• Keywords: normal cone, credal set, convex polyhedron, extreme point, imprecise probability, coherent lower probability
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FDV - Faculty of Social Sciences
• Publication status: Published
• Publication version: Version of Record
• Year: 2022
• Number of pages: Str. 35-54
• Numbering: Vol. 150
• PID: 20.500.12556/RUL-138898
• UDC: 519.2
• ISSN on article: 0888-613X
• DOI: 10.1016/j.ijar.2022.08.006
• COBISS.SI-ID: 119057667
• Publication date in RUL: 24.08.2022

Record is a part of a journal

• Title: International journal of approximate reasoning
• Shortened title: Int. j. approx. reason.
• Publisher: Elsevier
• ISSN: 0888-613X
• COBISS.SI-ID: 14231301

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: verjetnosti, matematični modeli

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P5-0168
• Name: Družboslovna metodologija, statistika in informatika