The Initial Value Problems Of Fuzzy Differential Equations

In this paper, we discuss the relations between approximate solutions and solutions for the initial value problems of the fuzzy differential equations by the embedding theorem of fuzzy number space. Using two different ways, we prove the existence of initial value problems under compactness-type conditions on closed set in (E~n,D). Using the comparative theorem and partial orders in (E~n, D), we discuss the existence of maximal and minimal solutions of initial value problems under compactness-type conditions. Finally, we defined the L-D type function of fuzzy number value function, and we discuss the existence of initial value problems under dissipation-type conditions. We expanded this result on a closed set in (E~n, D).