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Statistical Methods for Fuzzy Data by Reinhard Viertl

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8.3 General fuzzy probability distributions

In abstraction of fuzzy histograms and generalizing fuzzy probability distributions generated by fuzzy probability densities, and also to include fuzzy discrete probabilities, the following definition is appropriate.

Definition 8.3:

Let (M, ) be a measurable space and be the set of all fuzzy intervals whose support is contained in [0, ∞). Then a fuzzy probability distribution P* on (M, ) is a function P* : obeying the following:

1. P*() = 0.

2. P*(M) = 1.

3. For all δ ∈ (0; 1] and pairwise disjoint events A1,…, An in

Unnumbered Display Equation

and

Unnumbered Display Equation

Remark 8.3:

This concept ...

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