在实际生活中，我们经常需要去验证某个问题的一些假设是否正确。在概率统计中，随机假设检验就是解决这类决策问题的一个数学工具。由于随机假设检验的理论基础是概率论，因此其使用的前提是总体的分布函数与实际频率足够接近。大多数人相信分布函数能够很容易从历史数据中得到，因此我们应当使用随机假设检验，但是在实践中，由于问题和环境的复杂性，亦或是偶然事件 (例如洪水、地震、战争、意外、谣言、新冠疫情等) 的突发性，我们能够得到的分布函数与实际频率往往并不接近。在这种情况下，随机假设检验将不再适用。 为了研究当总体的分布函数和实际频率不接近时如何判断某些假设是否正确，本论文首次在不确定理论的框架下提出了不确定假设检验，并着重研究了如何检验一组观测数据是否服从正态不确定分布，然后将不确定假设检验分别应用到了不确定回归分析、不确定时间序列分析和不确定微分方程中。 总体来说，本文主要有如下的创新及贡献: 1. 提出了不确定假设检验，并给出了检验观测数据是否服从正态不确定分布的方法； 2. 在不确定回归分析中，给出了判断不确定回归模型与观测数据拟合得是否合理以及回归模型和系数是否显著的检验方法； 3. 在不确定时间序列分析中，构造了判断不确定时间序列模型与观测数据拟合得是否合理的检验方法，并针对拟合不合理的情形提出了差分的解决方案； 4. 在不确定微分方程中，设计了判断不确定微分方程与观测数据拟合得是否合理的检验方法。

In real life, it is usually necessary to decide whether some hypotheses about a problem are correct or not. To deal with these decision problems, there is a statistical tool in probability statistics called stochastic hypothesis test. Since the theoretical basis of stochastic hypothesis test is probability theory, it is used if the distribution function of the population is close enough to the real frequency. Most people believe that probability distribution is easy to obtain from the historical data, and then we should use probability theory. However, due to the complexity of problems and environments in practice, or the occurrence of emergencies (e.g., flood, earthquake, war, accident, rumor, and even COVID-19), the distribution function obtained in most practical problems is, unfortunately, not close enough to the real frequency. In this case, it is unreasonable to use stochastic hypothesis test. In order to study how to judge whether some hypotheses are correct when the distribution function of the population is not close to the real frequency, this dissertation proposes uncertain hypothesis test in the framework of uncertainty theory for the first time, and focuses on how to test whether a set of observed data follow the normal uncertainty distribution. Furthermore, uncertain hypothesis test is applied to uncertain regression analysis, uncertain time series analysis and uncertain differential equation. In summary, this dissertation has the following innovations and contributions. 1. It first proposes uncertain hypothesis test, and presents a method to test whether a set of observed data follows the normal uncertainty distribution. 2. In uncertain regression analysis, it provides some methods to test whether the uncertain regression model is a good fit to the observed data and whether the linear regression model and regression coefficients are significant. 3. In uncertain time series analysis, it introduces a method to test whether the uncertain time series model is a good fit to the observed data. For the case that the fit is not good, an approach of difference is proposed. 4. In uncertain differential equation, it designs a method to test whether the uncertain differential equation is a good fit to the observed data.