There are several studies on fuzzy univariate hypothesis tests corresponding to a normal distribution. A fuzzy statistical test was proposed in this study for mean and variance–covariance matrix of a multivariate normal with fuzzy random variables. For this purpose, a notion of fuzzy multivariate normal random variable with fuzzy mean and non-fuzzy variance–covariance matrix was first developed. Then, the concepts of the fuzzy type-I error, fuzzy type-II error, fuzzy power, non-fuzzy significance level and fuzzy p-value were extended. A degree-based criterion was also suggested to compare the fuzzy p-values as well as a specific significance level to decide whether accepting or rejecting the underlying hypotheses. The effectiveness of the proposed fuzzy hypothesis test was also examined through some numerical examples.

有一些关于对应于正态分布的模糊单变量假设检验的研究。在这项研究中提出了一种模糊统计检验，用于模糊随机变量的多元正态的均值和方差-协方差矩阵。为此，首先开发了具有模糊均值和非模糊方差-协方差矩阵的模糊多元正态随机变量的概念。然后，扩展了模糊I型误差、模糊II型误差、模糊功效、非模糊显着性水平和模糊p值的概念。还建议使用基于度的标准来比较模糊p-values 以及特定的显着性水平来决定是接受还是拒绝潜在的假设。还通过一些数值例子检验了所提出的模糊假设检验的有效性。