TIME-DOMAIN METHODS FOR THE SOLUTIONS OF N-ORDER FUZZY DIFFERENTIAL-EQUATIONS

In the first paper of a series of reports on fuzzy differential equati ons, we consider the nth-order fuzzy differential equation (X) under t ilde((n))(t) + a(n-1)(t)(X) under tilde((n-1))(t) + ... + a(o)(t)(X) u nder tilde(t) = (F) under tilde(t), (1) where (X) under tilde((n))(t), (X) under tilde((n-1)),(t),..., (X) under tilde((1))(t) are nth, (n - 1)th,..., 1st same-order (or reverse-order) derived functions of unkn own fuzzy set-valued function (X) under tilde(t), respectively; (F) un der tilde(t) is a known fuzzy set-valued function; a(i)(t), i = 0, 1,. ..,n - 1 are deterministic functions of time t. And the time domain me thods of the solutions of the n-order, inhomogeneous fuzzy differentia l equations with variable coefficients and constant coefficients are p ut forward. Two examples are considered in order to demonstrate the ra tionality and validity of the methods. The work provides an indispensa ble mathematical tool for setting up the theories of fuzzy stochastic differential equations [8], fuzzy dynamical systems [3], fuzzy random vibration [12], fuzzy stochastic dynamical systems [15, 18-20] and fuz zy stochastic systems [21-23]. (C) 1998 Elsevier Science B.V.