Normal cones corresponding to credal sets of lower probabilities
| Autor: | Damjan Škulj |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
convex polyhedron
normal cone credal set convex polyhedron extreme point imprecise probability coherent lower probability Applied Mathematics Probability (math.PR) extreme point udc:519.2 Matematični modeli credal set matematični modeli Theoretical Computer Science 60A86 52B11 imprecise probability verjetnosti Verjetnosti Artificial Intelligence Optimization and Control (math.OC) normal cone FOS: Mathematics coherent lower probability Mathematics - Optimization and Control Software Mathematics - Probability |
| Zdroj: | International journal of approximate reasoning, str. 35-54 : Ilustr., Vol. 150, Nov. 2022 COBISS-ID: 14231301 International journal of approximate reasoning, vol. 150, pp. 35-54, 2022. |
| ISSN: | 0888-613X |
| Popis: | 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. Bibliografija: str. 53-54. Abstract. |
| Databáze: | OpenAIRE |
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