In this paper, a novel stepwise learning approach based on estimating desired premise parts' outputs by solving a constrained optimization problem is proposed. This learning approach does not require backpropagating the output error to learn the premise parts' parameters. Instead, the near best output values of the rules premise parts are estimated and their parameters are changed to reduce the error between current premise parts' outputs and the estimated desired ones. Therefore, the proposed learning method avoids error backpropagation, which lead to vanishing gradient and consequently getting stuck in a local optimum. The proposed method does not need any initialization method. This learning method is utilized to train a new Takagi-Sugeno-Kang (TSK) Fuzzy Neural Network with correlated fuzzy rules including many parameters in both premise and consequent parts, avoiding getting stuck in a local optimum due to vanishing gradient. To learn the proposed network parameters, first, a constrained optimization problem is introduced and solved to estimate the desired values of premise parts' output values. Next, the error between these values and the current ones is utilized to adapt the premise parts' parameters based on the gradient-descent (GD) approach. Afterward, the error between the desired and network's outputs is used to learn consequent parts' parameters by the GD method. The proposed paradigm is successfully applied to real-world time-series prediction and regression problems. According to experimental results, its performance outperforms other methods with a more parsimonious structure.

翻译：在本文中, 提出了一个基于通过解决限制优化问题估算理想前提部分产出的新颖的渐进式学习方法。 这种学习方法不需要对输出错误进行反演, 以学习前提部分参数。 相反, 对规则前提部分的近最佳产出值进行了估计, 并对参数进行了修改, 以减少当前前提部分产出与估计理想部分产出之间的错误。 因此, 拟议的学习方法避免了错误反演, 导致梯度消失, 从而卡在本地最佳状态中。 拟议的方法不需要任何初始化方法。 使用这种学习方法来训练一个新的输出错误( TSK) Fuzzy Neural 网络, 配有相关的模糊规则, 包括前提部分和随后部分的许多参数, 避免由于渐渐渐变而陷入当地最佳状态。 因此, 要学习拟议的网络参数, 首先, 引入了限制优化问题, 来估计前提部分产出值的理想值。 下一步, 这些数值和当前值之间的错误被用来调整基于梯度( GGD) 的前提部分参数。 之后, 将理想的网络和模型错误应用到真实的模型序列中。 。 之后, 将 选择的方法 将 将 学习到实际结果, 选择 将 方法 选择 将 方法 走向 走向 走向 走向 。