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Statistical Methods for Fuzzy Data by Reinhard Viertl

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9.2 Fuzzy probability distributions induced by fuzzy random variables

Every fuzzy random variable naturally induces a fuzzy probability distribution. Let X* be a fuzzy random variable defined on a probability space (Ω, , P). Defining the following functions and on the Borel σ -field :

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and

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a fuzzy probability distribution P* on the system of Borel-sets is defined in the following way:

For B the fuzzy interval P*(B) is defined using the functions and . The characterizing function ξ(·) of the ...

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