Generation, combination and extension of random set approximations to coherent lower and upper probabilities

JW Hall, J Lawry

Research output: Contribution to journalArticle (Academic Journal)peer-review

57 Citations (Scopus)

Abstract

Random set theory provides a convenient mechanism for representing uncertain knowledge including probabilistic and set-based information, and extending it through a function. This paper focuses upon the situation when the available information is in terms of coherent lower and upper probabilities, which are encountered, for example, when a probability distribution is specified by interval parameters. We propose an Iterative Rescaling Method (IRM) for constructing a random set with corresponding belief and plausibility measures that are a close outer approximation to the lower and upper probabilities. The approach is compared with the discrete approximation method of Williamson and Downs (sometimes referred to as the p-box), which generates a closer approximation to lower and upper cumulative probability distributions but in most cases a less accurate approximation to the lower and upper probabilities on the remainder of the power set. Four combination methods are compared by application to example random sets generated using the IRM.
Translated title of the contributionGeneration, combination and extension of random set approximations to coherent lower and upper probabilities
Original languageEnglish
Pages (from-to)89-101
Number of pages12
JournalReliability Engineering and System Safety
Volume85
Issue number1-3
DOIs
Publication statusPublished - Jul 2004

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