In this paper, we propose a fuzzy adaptive lasso (least absolute shrinkage and selection operator) estimate for fuzzy linear regression with crisp inputs and fuzzy outputs. The proposed estimate is obtained by imposing an \(L_1\) penalty on the least-squares error. Compared with fuzzy lasso estimate proposed by Hesamian and Akbari (Int J Approx Reason 115:290–300, 2019), the estimate we proposed assigns different weights to different coefficients, which is reasonable to significant covariates. Some numerical experiments are conducted to evaluate the performance of the proposed estimate. In most cases, fuzzy adaptive lasso estimate outperforms five commonly used estimates, especially when the variances of the error terms are small.

在本文中，我们为具有清晰输入和模糊输出的模糊线性回归提出了一种模糊自适应套索（最小绝对收缩和选择算子）估计。建议的估计是通过对最小二乘误差施加\(L_1\)惩罚获得的。与 Hesa​​mian 和 Akbari (Int J Approx Reason 115:290–300, 2019) 提出的模糊套索估计相比，我们提出的估计为不同的系数分配了不同的权重，这对于显着的协变量是合理的。进行了一些数值实验来评估所提出的估计的性能。在大多数情况下，模糊自适应套索估计优于五种常用估计，尤其是当误差项的方差很小时。