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Statistical Methods for Fuzzy Data by Reinhard Viertl

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Chapter 13

a. The classical test statistic for the hypothesis 0 : μ = μ0 is the following:

Unnumbered Display Equation

For fuzzy data x1*,…, xn*, using the extension principle the characterizing function ξt*(·) of the fuzzy value of the test statistic can be obtained. Based on the support of t* the p-value is determined.

b. In order to construct the characterizing function of the fuzzy p-value p* a suitable number of δ-values is chosen and the corresponding δ-cuts of p* are calculated.

c. This is done as described before Proposition 13.1.

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