In fuzzy regression modeling, when the sample size is small, resampling methods are appropriate and useful for improving model estimation. However, in the commonly used bootstrap method, the standard errors of estimates are also random because of randomness existing in samples. This paper investigates the use of Jackknife-after-Bootstrap (JB) in fuzzy regression modeling to address this problem and produce estimates with smaller mean prediction errors. Performance analysis is carried out through some numerical illustrations and some interactive graphs to illustrate the superiority of the JB method compared to the bootstrap. Moreover, it is demonstrated that using the JB method, we have a significant model, with some sense; however, this is not the case using the bootstrap method.

中文翻译：

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通过 Jackknife-after-Bootstrap (JB) 在模糊回归中重采样

在模糊回归建模中，当样本量较小时，重采样方法适用于改进模型估计。然而，在常用的 bootstrap 方法中，由于样本存在随机性，估计的标准误也是随机的。本文研究了在模糊回归建模中使用 Jackknife-after-Bootstrap (JB) 来解决这个问题并产生具有较小平均预测误差的估计值。性能分析通过一些数值插图和一些交互图来说明JB方法相对于bootstrap的优越性。此外，证明了使用JB方法，我们有一个有意义的模型；但是，使用引导方法并非如此。