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

We studied the Cauchy problem of fuzzy di erential equations on the basis of introducing the concept of di erentiation which is a generalization of the de nition of H-di erentiability due to Puri and Ralescu (1983), for fuzzy set-valued mappings of real variables whose values are in the fuzzy number space (E; D). The existence and uniqueness theorem is obtained for the Cauchy problem x′=f(t; x); x(t0)= x0, when f satis es the generalized Lipschitz condition. c © 2000 Elsevier Science B.V. All rights reserved.