9.1 Fuzzy random variables
Let (Ω, , P) be a classical probability space. The generalization of random variables X defined on (Ω, , P), i.e. X is a Borel-measurable function X: Ω → , to the situation of fuzzy valued quantities are fuzzy random variables, which are defined in the following way.
A fuzzy random variable X* on a probability space (Ω, , P) is a function from Ω to the set of fuzzy numbers such that
for every Borel-set B and every δ ∈[0; 1], where Xδ(ω) denotes the δ-cut of X*(ω).
If the values X*(ω) are all fuzzy intervals, then the set Xδ(ω) is a compact interval for all δ ∈ [0; 1], i.e.
Xδ is then an interval-valued function.
Let (Ω, , P) ...