On the structure of solutions for fuzzy initial value problem

In this paper, by means of Banach Fixed-point Theorem we establish the existence and uniqueness of solutions for set differential equations, the continuous dependence of solutions on initial values, and the structural stability of solutions. On the basis of these results, we define level sets of solutions to fuzzy differential equations by the solutions of set differential equations, and then we obtain the corresponding results for the large solutions of the fuzzy initial value problem (FIVP). Finally, discuss the relationship between small solutions and large solutions of FIVP.

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