Abstract This article provides a numerical method to solve a fuzzy differential equation via differential inclusions. The method obtains response solutions with their membership distribution functions. To do that, the fuzzy differential equation in the form of differential inclusions is transformed into the governing equation of the membership degree and the membership distribution of the fuzzy solution is composed of the membership degrees solved from the governing equation. In the procedure, no comparison or data storage is required, which makes the method have high computational efficiency and low memory cost. Since the governing equation of the membership degree is derived from the master equation of fuzzy dynamics, the method is validated by our theoretically proving the equivalence of the solution of the fuzzy differential equation via differential inclusions and that of the fuzzy master equation. Furthermore, the new method is verified by our comparing the numerical solution with the analytical solution in two examples. Finally, with use of the method, the response solutions are obtained for the Mathieu system and the rotor/stator contact system with fuzzy uncertainties.

中文翻译：

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一种利用微分包含求解模糊微分方程的数值方法

摘要 本文提供了一种通过微分包含求解模糊微分方程的数值方法。该方法通过其隶属度分布函数获得响应解。为此，将微分包含形式的模糊微分方程转化为隶属度的控制方程，模糊解的隶属度分布由从控制方程求解的隶属度组成。过程中不需要比较或数据存储，使得该方法具有较高的计算效率和较低的内存成本。由于隶属度的控制方程是从模糊动力学的主方程推导出来的，我们从理论上证明了模糊微分方程的微分包含解与模糊主方程的解的等价性，从而验证了该方法的有效性。此外，我们通过比较两个例子中的数值解和解析解来验证新方法。最后，利用该方法得到了具有模糊不确定性的Mathieu系统和转子/定子接触系统的响应解。