Testing statistical hypotheses is very important for making decisions in scientific and practical issues. In conventional methods of testing statistical hypotheses, data, hypotheses, parameters, and other elements of the problem are accurate. But in applied sciences such as economics, agriculture, and the social sciences, we may encounter vague definitions and fuzzy concepts such as patient tolerance threshold and a taxi driver's monthly income. In such cases, classical methods need to be generalized in fuzzy environments. Ambiguity in the problem of hypothesis testing can be done through data or hypotheses. Therefore, the following three main problems can be considered: (1) testing accurate hypotheses based on fuzzy data, (2) testing fuzzy hypotheses based on accurate data, (3) testing fuzzy hypotheses based on fuzzy data. In this paper, we discuss the p-value approach in the above three issues using the Fuzzy.p.value software package in R. Calculating the p-value of the fuzzy membership function, comparing it with the level of fuzzy significance and the final decision of the fuzzy in testing the hypothesis is one of the main tasks of this software package, which is examined with some numerical examples.