a. Let the fuzzy values f*(x) be LR-fuzzy numbers (cf. Section 2.1). Then the δ-cuts are given by
Therefore the upper and lower δ-level curves δ (·) and δ(·) are
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
Assuming the functions s(·) and L(·) to be integrable we obtain