The Transform Method to Solve Fuzzy Differential Equation via Differential Inclusions

This chapter dedicates to offer a numerical method, named transform method, to solve fuzzy differential equation (FDE) via differential inclusions. The method acquires response solutions with their membership distribution functions. To do that, the FDE in form of differential inclusions is transformed into the governing equation of membership degree and the membership distribution of the fuzzy solution is composed by the membership degrees solved from the governing equation. In the procedure, no comparison or data storage is required, which makes the method possess 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 theoretically proving the equivalence of the solution of the FDE via differential inclusions and that of the fuzzy master equation. Furthermore, the transform method is verified by comparing the numerical solution with the analytical solution in two examples. At last, with the help of the method, the response solutions are obtained for the Mathieu system and the rotor/stator contact system with fuzzy uncertainties.