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Statistical Methods for Fuzzy Data by Reinhard Viertl

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4.1 Minimum of fuzzy data

Let x1*,…xn* be n fuzzy intervals whose corresponding δ-cuts are denoted by Cδ(xi*) = [δ,i,δ,i] for δ ∈ (0; 1] and i = 1(1)n. The fuzzy valued minimum min{x1*,…xn*} is a fuzzy interval xmin* whose δ-cuts Cδ(xmin*) are defined by

Unnumbered Display Equation

The characterizing function of xmin* is obtained by (the representation) Lemma 2.1.

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