This paper deals with the problem of testing hypothesis when both the hypotheses and the available data are fuzzy. First, four different kinds of fuzzy hypotheses are defined. Then, a procedure is developed for constructing the fuzzy point estimation based on fuzzy data. Also, the concept of fuzzy test statistic is defined based on the -cuts of the fuzzy null hypothesis and the -cuts of the constructed fuzzy point estimation. Finally, by introducing a credit level, we propose a method to evaluate the fuzzy hypotheses of interest. The proposed method is employed to test the fuzzy hypotheses for the mean of a normal distribution, and the variance of a normal distribution. A practical example in lifetime testing is provided, to show the applicability of the proposed method in applied studies.

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