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Testing fuzzy hypotheses with crisp data. (English) Zbl 0940.62015
Summary: An approach is presented how statistical tests originally constructed to examine crisp hypotheses can also be applied to fuzzily formulated hypotheses. In particular, criterions \(\alpha\) and \(\beta\) are proposed generalizing the probabilities of the errors of type I and type II, respectively. The general approach is applied to one- and two-sided Gauß tests. Here, diagrams are given to determine the critical values in the most popular cases of \(\alpha=0.01\) and \(\alpha=0.05\). If, in addition, the value of \(\beta\) is fixed in advance the sample size of a one- or two-sided Gauß test can be obtained using supplementary graphs.

62F03 Parametric hypothesis testing
62F99 Parametric inference
Full Text: DOI
[1] Bandemer, H.; Gottwald, S., Einführung in fuzzy methoden, () · Zbl 0688.94006
[2] Bandemer, H.; Näther, W., Fuzzy data analysis, (1992), Kluwer Academic Publishers Dordrecht · Zbl 0758.62003
[3] Frühwirth-Schnatter, S., On fuzzy Bayesian inference, Fuzzy sets and systems, 60, 41-58, (1993) · Zbl 0796.62003
[4] Rommelfanger, H., Entscheiden bei unschärfe, (1988), Springer Heidelberg · Zbl 0657.90002
[5] Saade, J.J., Extension of fuzzy hypothesis testing with hybrid data, Fuzzy sets and systems, 63, 57-71, (1994) · Zbl 0843.62004
[6] Uhlmann, W., Statistische qualitätskontrolle, (1982), Teubner Stuttgart · Zbl 0137.37301
[7] Viertl, R., On Bayes’ theorem for fuzzy data, Statist. papers, 32, 115-122, (1991) · Zbl 0719.62011
[8] Viertl, R., Statistical methods for non-precise data, (1996), CRC Press London
[9] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
[10] Zimmermann, H.-J., Fuzzy set theory - and its applications, (1991), Kluwer Academic Publishers Dordrecht · Zbl 0719.04002
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