中文摘要：

以模糊随机变量理论为指导,视模糊随机变量的均值为模糊数,基于小样本理论推导了均值模糊数模糊变化范围与样本数的关系式。采用截集敏感性分析法进行了边坡稳定的模糊随机有限元可靠度分析,得到了边坡的模糊随机可靠指标及模糊滑面的位置,研究了样本数与边坡模糊随机可靠指标的关系。分析表明,基于模糊随机变量理论的模糊随机可靠度分析方法是随机可靠度分析方法的自然推广;模糊随机可靠指标与样本数有关,随着样本数的改变,模糊随机可靠指标的中值也会发生微小变化,不是定值;在相同的置信度情况下,模糊随机可靠指标的变化范围随着样本数的增加而减小,可通过增加样本数的方式来减小模糊随机可靠指标的模糊性。

英文摘要：

Considering the means of fuzzy random variables are fuzzy numbers,the relationship between the variation ranges of the means of fuzzy random variables and sample size is obtained based on the theory of fuzzy random variables and the theory of small sample size.Through the fuzzy random finite element reliability analysis of slope stability using the cutting method of sensitivity,the fuzzy random reliability indices and the fuzzy slip surfaces of slopes can be calculated;and the relationship between sample size and fuzzy random reliability indices can be obtained.It is demonstrated that the method of fuzzy random reliability analysis based on the theory of fuzzy random variables are the natural extension of the normally used method of stochastic reliability analysis.The normal value of fuzzy reliability indices is not a constant for it will change a little with the changing of sample size.Under the same confidence level,the variation ranges of the reliability indices will decrease with the increasing of sample size.Then,we can decrease the fuzziness of fuzzy random reliability indices by increasing the number of sample size.