Abstract
Several methods for the practical representation of imprecise probabilities exist such as Ferson’s p-boxes, possibility distributions, Neumaier’s clouds, and random sets. In this paper some relationships existing between the four kinds of representations are discussed. A cloud as well as a p-box can be modelled as a pair of possibility distributions. We show that a generalized form of p-box is a special kind of belief function and also a special kind of cloud.
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References
A. Dempster. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38:325–339, 1967.
D. Dubois, L. Foulloy, G. Mauris, and H. Prade. Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliable computing, 10:273–297, 2004.
D. Dubois, P. Hajek, and H. Prade. Knowledge-driven versus data-driven logics. Journal of Logic, Language and Information, 9:65–89, 2000.
D. Dubois and H. Prade. When upper probabilities are possibility measures. Fuzzy Sets and Systems, 49:65–74, 1992.
D. Dubois and H. Prade. Interval-valued fuzzy sets, possibility theory and imprecise probability. In Proceedings of International Conference in Fuzzy Logic and Technology (EUSFLAT’05), Barcelona, September 2005.
S. Ferson, L. Ginzburg, V. Kreinovich, D. Myers, and K. Sentz. Construction probability boxes and Dempster-Shafer structures. Technical report, Sandia National Laboratories, 2003.
E. Kriegler and H. Held. Utilizing belief functions for the estimation of future climate change. International Journal of Approximate Reasoning, 39:185–209, 2005.
A. Neumaier. Clouds, fuzzy sets and probability intervals. Reliable Computing, 10:249–272, 2004.
H. Regan, S. Ferson, and D. Berleant. Equivalence of methods for uncertainty propagation of real-valued random variables. International Journal of Approximate Reasoning, 36:1–30, 2004.
G. Shafer. A mathematical Theory of Evidence. Princeton University Press, 1976.
P. Smets. Belief functions on real numbers. International Journal of Approximate Reasoning, 40:181–223, 2005.
P.Walley. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, 1991.
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Destercke, S., Dubois, D. (2006). A Unified View of Some Representations of Imprecise Probabilities. In: Lawry, J., et al. Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34777-1_30
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DOI: https://doi.org/10.1007/3-540-34777-1_30
Publisher Name: Springer, Berlin, Heidelberg
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