## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

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.

Definition 9.1:

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).

Remark 9.1:

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.

Lemma 9.1:

Let (Ω, , P) ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required