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

and

Remark 8.3:

This concept ...

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