 Extreme probability distributions of random sets, fuzzy sets and p-boxesA. Bernardini and F. Tonon International Journal of Reliability and Safety, 2009, vol. 3, issue 1/2/3, 57-78 Abstract: The uncertain information given by a random set on a finite space of singletons determines a set of probability distributions defined by the convex hull of a finite set of extreme distributions. After placing random sets in the context of the theory of imprecise probabilities, algorithms are given to calculate these extreme distributions, and hence exact upper/lower bounds on the expectation of functions of the uncertain variable. Detailed applications are given to consonant random sets (or their equivalent fuzzy sets) and to p-boxes (non-consonant random sets). A procedure is presented to calculate the random set equivalent to a p-box and hence to derive extreme distributions from a p-box. A hierarchy of non-consonant (and eventually consonant) random sets ordered by the inclusion of the corresponding sets of probability distributions can yield the same upper and lower cumulative distribution functions of the p-box. Simple numerical examples illustrate the presented concepts and algorithms. Keywords: random sets; fuzzy sets; p-boxes; extreme probability distributions; imprecise probabilities; uncertainty. (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ids:ijrsaf:v:3:y:2009:i:1/2/3:p:57-78 Access Statistics for this article More articles in International Journal of Reliability and Safety from Inderscience Enterprises Ltd |
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