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Statistical Methods for Fuzzy Data by Reinhard Viertl

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25.1 Basics

Definition 25.1:

A fuzzy random vector (also called an n-dimensional fuzzy random variable) is a mapping X from some probability space (Ω,E,) into the space ((n), h) with h(·,·) the metric defined in (23.4) if X is measurable relative to the σ-field in (n) which is generated by the open sets

Unnumbered Display Equation

with y*(n) and r > 0.

Remark 25.1:

Using ((n), h) in Definition 25.1 is important as pointed out in Körner (1997b).

Theorem 25.1:

Let X* and Y* be fuzzy random vectors, and δ ∈ (0; 1], and ...

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