SOLVING PROCESSES FOR A SYSTEM OF FIRST-ORDER FUZZY DIFFERENTIAL-EQUATIONS

In this third paper of a series of reports on fuzzy differential equat ions, we consider the system of first-order, inhomogeneous fuzzy diffe rential equations d/dt (X) under tilde(t) + A(t)(X) under tilde(t) = ( F) under tilde(t) with (X) under tilde(O) = (X) under tilde(o), where d (X) under tilde(t)/dt is an n-dimensional vector of first same-order (or reverse-order) derived functions of an n-dimensional vector, (X) under tilde(t) = ((X) under tilde 1(t),...,(X) under tilde(n)(t))(T), of unknown fuzzy set-valued functions, that is, d/dt (X) under tilde(t ) = (d/dt (X) under tilde(1)(t),...,d/dt (X) under tilde(n)(t))(T); (F ) under tilde(t), is an n-dimensional vector, ((F) under tilde(1)(t),. ..(F) under tilde(n)(t))(T), of known fuzzy set-valued functions; A(t) is an n x n matrix of known real functions. We introduce the time dom ain and frequency domain methods for the solutions of the system of fi rst-order fuzzy differential equations (1). The solving processes of t ime domain and frequency domain for the system of first-order fuzzy di fferential equations with constant coefficients and variable coefficie nts are put forward. One example is considered in order to demonstrate the rationality and validity of the methods. The work provides an ind ispensable mathematical tool for setting up the theories of fuzzy stoc hastic differential equations [7], fuzzy dynamical systems [3], fuzzy random vibration [8], fuzzy stochastic dynamical systems [10,11,14-16] and fuzzy stochastic systems [17-19]. (C) 1998 Elsevier Science B.V. All rights reserved.