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Statistical Methods for Fuzzy Data by Reinhard Viertl

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9.5 Problems

a. Let ψ(·) be the membership function of a normalized fuzzy subset of with bounded support. Find the convex hull of ψ(·). This is the characterizing function ξ(·) of the fuzzy number, such that ψ(x) ≤ ξ(x) ∀x, and there is no characterizing function between ψ(·) and ξ(·).

b. Prove the following: For every δ-cut of the characterizing function of a fuzzy number x* the following is true:

Unnumbered Display Equation

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