Testing Fuzzy Hypotheses Using Fuzzy Data Based on Fuzzy Test Statistic

摘要

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 defined. Then, a procedure is developed for constructing the fuzzy point estimation based on fuzzy data. Also, the concept of fuzzy test statistic is defined based on the a-cuts of the fuzzy null hypothesis and the α-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.