In this third paper of a series of reports on fuzzy differential equations, we consider the system of first-order, inhomogeneous fuzzy differential equations
with X(0) = Xo, where dX(t)/dt is an n-dimensional vector of first same-order (or reverse-order) derived functions of an n-dimensional vector,
x(t) = (x,(t) .... , x.(t)) T, of unknown fuzzy set-valued functions, that is, d (d d ; ~x(t)= ~x,(t) ..... ~x.(t) ; F(t), is an n-dimensional vector,
Lv, (t) ..... f.(t)) T, of known fuzzy set-valued functions; A (t) is an n x n matrix of known real functions. We introduce the time domain and frequency domain methods for the solutions of the system of first-order fuzzy differential equations (1), The solving processes of time domain and frequency domain for the system of first-order fuzzy differential equations with constant coefficients and variable coefficients are put forward. One example is considered in order to demonstrate the rationality and validity of the methods. The work provides an indispensable mathematical tool for setting up the theories of fuzzy stochastic differential equations [7], fuzzy dynamical systems [3], fuzzy random vibration [8], fuzzy stochastic dynamical systems [10,11,[14][15][16] and fuzzy stochastic systems [17][18][19].