Cauchy problem with fuzzy initial condition and its approximate solution with the help of fuzzy transform

We investigate the Cauchy problem for ordinary differential equation (ODE) with fuzzy initial condition. We define a solution to this problem and propose a new method of how an approximate solution can be constructed. The proposed method is based on the technique of fuzzy transforms and ends up with a solution of a system of fuzzy relation equations. The approximate solution is expressed symbolically and the quality of approximation is estimated.