Abstract
In probability theory the expected value of functions of random variables plays a fundamental role in defining the basic characteristic measures of probability distributions. For example, the variance, covariance and correlation of random variables can be computed as the expected value of their appropriately chosen real-valued functions. In possibility theory we can use the principle of expected value of functions on fuzzy sets to define variance, covariance and correlation of possibility distributions. Marginal probability distributions are determined from the joint one by the principle of ‘falling integrals’ and marginal possibility distributions are determined from the joint possibility distribution by the principle of ‘falling shadows’. Probability distributions can be interpreted as carriers of incomplete information [203], and possibility distributions can be interpreted as carriers of imprecise information.
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© 2011 Springer-Verlag Berlin Heidelberg
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Carlsson, C., Fullér, R. (2011). A Normative View on Possibility Distributions. In: Possibility for Decision. Studies in Fuzziness and Soft Computing, vol 270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22642-7_3
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DOI: https://doi.org/10.1007/978-3-642-22642-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22641-0
Online ISBN: 978-3-642-22642-7
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