© Hindawi Publishing Corp. ON CAUCHY PROBLEMS FOR FUZZY DIFFERENTIAL EQUATIONS

Existence and uniqueness theorems are proved for Cauchy problems of second-order fuzzy differential equations. 2000 Mathematics Subject Classification: 34A30, 54A40, 26E50, 03E72. 1. Introduction. In 1972, Chang and Zadeh [2] first introduced the concept of fuzzy derivative, followed up ten years later by Dubois and Prade [5], who used the extension principle in their approach. In the mean time, Puri and Ralescu [12] used the notion of H-differentiability to extend the differential of set-valued functions to that of fuzzy functions. This led Seikkala [13] to introduce the notion of fuzzy derivative as an ex