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Statistical Methods for Fuzzy Data by Reinhard Viertl

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Chapter 16

a. In the case of precise sample the vector-characterizing function of the combined sample is the one-point indicator function ξ(.,…,.) = Therefore the membership function φ (·) of the corresponding generalized confidence set Θ1 − α* has values

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Since the indicator function () equals 1 if and only if we have φ(θ) = 1 if and only if Therefore φ(·) =

b. For precise sample the membership function ψ (·) of the generalized HPD-region ΘH, 1 − α* has values

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Now ψ (θ) is an indicator ...

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