In this paper, a hybrid scheme based on recurrent neural networks for approximate coefficients (parameters) of ridge fuzzy regression model with LR-fuzzy output and crisp inputs is presented. Here a neural network is first constructed based on some concepts of convex optimization and stability theory. The suggested neural network model guarantees to find the approximate parameters of the ridge fuzzy regression problem. The existence and convergence of the trajectories of the neural network are studied. The Lyapunov stability for the neural network is also shown. To assess the ridge fuzzy regression estimator, the mean squared prediction error with three different well known distances are used. In order to depict the performance of the proposed ridge technique in the presence of multicollinear data, a Monte Carlo simulation is presented. To further determine, an example of a situation in which one variable is a perfect linear combination of the other variable is used to test the applicability of the proposed method. In this study, the performance of the model is evaluated by error parameters and visualized in the Taylor diagram. The predictive ability of the model thus obtained is examined by cross- validation to investigate how well the model fits and predicts every observations.

在本文中，提出了一种基于递归神经网络的混合方案，用于具有 LR 模糊输出和清晰输入的岭模糊回归模型的近似系数（参数）。这里首先基于凸优化和稳定性理论的一些概念构建神经网络。建议的神经网络模型保证找到岭模糊回归问题的近似参数。研究了神经网络轨迹的存在性和收敛性。还显示了神经网络的 Lyapunov 稳定性。为了评估岭模糊回归估计器，使用了具有三个不同已知距离的均方预测误差。为了在存在多重共线数据的情况下描述所提出的脊技术的性能，提出了蒙特卡罗模拟。为了进一步确定，以一个变量是另一个变量的完美线性组合的情况为例来测试所提出方法的适用性。在本研究中，模型的性能通过误差参数进行评估，并在泰勒图中进行可视化。通过交叉验证来检查由此获得的模型的预测能力，以研究模型对每个观察的拟合和预测的程度。