A new approach for solving first order fuzzy differential equation

Abstract

In this paper, a new approach for solving first order fuzzy differential equations (FDEs) with fuzzy initial value is considered under strongly generalized H-differentiability. In order to obtain solution of FDE, we extend the 1-cut solution of original problem. This extension is constructed based on the allocating some unknown spreads to 1-cut solution, then created value is replaced in the original FDE. However obtaining solutions of FDE is equivalent to determine the unknown spreads while 1-cut solution is derived via previous step (in general, 1-cut of FDE is interval differential equation). Moreover, we will introduce three new set solutions for FDEs based on the concepts of united solution set, tolerable solution set and controllable solution set. Indeed, our approach is designed to obtain such new solution sets while one of them has pessimistic/optimitic attitude. Finally, some numerical examples are solved to illustrate the approach. © Springer-Verlag Berlin Heidelberg 2010.