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.
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