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Neyman-Pearson lemma for fuzzy hypotheses testing with vague data. (English) Zbl 1103.62021
Summary: In hypotheses testing, and other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise. This paper tries to develop a new approach for testing fuzzy hypotheses when the available data are fuzzy, too. First, some definitions are provided, such as: fuzzy sample space, fuzzy-valued random samples, and fuzzy-valued random variables. Then, the problem of fuzzy hypothesis testing with vague data is formulated. Finally, we state and prove a generalized Neyman-Pearson lemma for such problems. The proposed approach is illustrated by some numerical examples.

##### MSC:
 62F03 Parametric hypothesis testing 03E72 Theory of fuzzy sets, etc.
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