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 :
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 ...