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Statistical Methods for Fuzzy Data by Reinhard Viertl

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Chapter 8

a. Let the fuzzy values f*(x) be LR-fuzzy numbers (cf. Section 2.1). Then the δ-cuts are given by

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Therefore the upper and lower δ-level curves δ (·) and δ(·) are

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The fuzzy integral is defined by its δ-cuts which are given by .

For a fuzzy uniform density we can assume m(x) ≡ 1 ∀x ∈ [0; 1].

Now we obtain

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and

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Assuming the functions s(·) and L(·) to be integrable we obtain

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and

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