Parametric testing statistical hypotheses for fuzzy random variables

In this paper, a method is proposed for testing statistical hypotheses about the fuzzy parameter of the underlying parametric population. In this approach, using definition of fuzzy random variables, the concept of the power of test and p value is extended to the fuzzy power and fuzzy p value. To do this, the concepts of fuzzy p value have been defined using the α -optimistic values of the fuzzy observations and fuzzy parameters. This paper also develop the concepts of fuzzy type-I, fuzzy type-II errors and fuzzy power for the proposed hypothesis tests. To make decision as a fuzzy test, a well-known index is employed to compare the observed fuzzy p value and a given significance value. The result provides a fuzzy test function which leads to some degrees to accept or to reject the null hypothesis. As an application of the proposed method, we focus on the normal fuzzy random variable to investigate hypotheses about the related fuzzy parameters. An applied example is provided throughout the paper clarifying the discussions made in this paper.