Approximate Solutions, Existence, and Uniqueness of the Cauchy Problem of Fuzzy Differential Equations*

The Cauchy problem of fuzzy differential equations is investigated by the use of the concept of H-differentiability due to M. L. Puri and D. A. Ralescu J. Math. Anal. Appl. 91, 1983, 552]558.. The existence and uniqueness theorem is obtained for the solution of the Cauchy problem x9 t.sf t, x t.., x t0.sx0, for the fuzzy-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported fuzzy sets in Rn, where the function f satisfies the generalized Lipschitz condition