Coherent lower previsions and Choquet integrals

✍ Scribed by Volker Krätschmer

• Book ID: 104291526
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 287 KB
• Volume: 138
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(02)00545-6

✦ Synopsis

Walley (Statistical Reasoning with Imprecise Probabilities, Chapman & Hall, London, 1991) has given a helpful general framework of uncertain reasoning which is grounded on a behavioural foundation, and extends de Finetti's work. For some important applications like the expected utility theory it might be a tool, alternatively to the techniques of Choquet integration. Therefore, this paper tries to clarify the relation between Walley's central concept of coherent lower prevision and the Choquet integration theory. In one direction we deal with the problem to represent coherent lower previsions by Choquet integrals, and obtain general results using Greco's representation theorem. Another aspect of investigation is to compare Walley's concept to deÿne integrals of coherent fuzzy measures, the so-called natural extensions, with Choquet integrals. We succeed in exploring completely the relationship.