Testing fuzzy hypotheses based on fuzzy test statistic
A new approach for testing fuzzy parametric hypotheses based on fuzzy test statistic is introduced. First, we define some models representing the extended versions of the simple, the one-sided and the two-sided crisp hypotheses to the fuzzy ones. Then, we provide a confidence interval for interested parameter, and using alpha-cuts of the fuzzy null hypothesis, we construct the related fuzzy test statistic. Finally, by introducing a credit level, we can decide to accept or reject the fuzzy hypothesis. The method is applied to test the fuzzy hypotheses for the mean of a normal distribution, the variance of a normal distribution, and the mean of a Poisson distribution.
fuzzy test statistic credit level fuzzy hypothesis testing hypothesis