This paper concentrates on solving fuzzy dynamical differential equations (FDDEs) by use of unsupervised kernel least mean square (UKLMS). UKLMS is a nonlinear adaptive filter which works by applying kernel trick to LMS adaptive filter. UKLMS estimates multivariate function which is embedded to estimate the solution of FDDE. Adaptation mechanism of UKLMS helps for finding solution of FDDE in a recursive scenario. Without any desired response, UKLMS finds nonlinear functions. For this purpose, an approximate solution of FDDE is constructed based on adaptable parameters of UKLMS. An optimization algorithm, optimizes the values of adaptable parameters of UKLMS. The proposed algorithm is applied for solving Earth energy balance model (EBM) which is considered as a fuzzy differential equation for the first time. The method in comparison with the other existing approaches (such as numerical methods) has some advantages such as more accurate solution and also that the obtained solution has a functional form, thus the solution can be obtained at each time in training interval. Low error and applicability of developed algorithm are examined by applying it for solving several problems. After comparing the numerical results, with relative previous works, the superiority of the proposed method will be illustrated.

本文着重于通过使用无监督核最小均方（UKLMS）来解决模糊动力学微分方程（FDDE）。UKLMS是一种非线性自适应滤波器，通过将内核技巧应用于LMS自适应滤波器来工作。UKLMS估计多元函数，该函数被嵌入以估计FDDE的解。UKLMS的适应机制有助于在递归方案中找到FDDE的解决方案。没有任何期望的响应，UKLMS会发现非线性函数。为此，基于UKLMS的自适应参数构造了FDDE的近似解决方案。优化算法可优化UKLMS的自适应参数值。该算法被首次用于求解地球能量平衡模型（EBM）。与其他现有方法（例如数值方法）相比，该方法具有一些优点，例如更精确的解决方案，并且所获得的解决方案具有函数形式，因此可以在训练间隔中的每个时间获得解决方案。通过将其用于解决若干问题，检验了所开发算法的低误差和适用性。在将数值结果进行比较之后，与先前的相关工作一起，将说明所提出方法的优越性。