Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations

We studied the Cauchy problem of fuzzy dierential equations on the basis of introducing the concept of dierentiation which is a generalization of the denition of H-dierentiability due to Puri and Ralescu (1983), for fuzzy set-valued mappings of real variables whose values are in the fuzzy number space (E n ;D). The existence and uniqueness theorem is obtained for the Cauchy problem x 0 =f(t;x) ;x ( t 0)=x0, when f satises the generalized Lipschitz condition. c 2000