Generalized LU-fuzzy derivative and numerical solution of Fuzzy Differential Equations

AbstractWe present a representation of fuzzy numbers and its application to the numerical solution of fuzzy differential (initial value) equations (FDE). The generalized differentiability of a fuzzy-valued function g(x) of a real variable x 2]a; b[; as recently introduced by Bede and Gal, is expressed in terms of the differentiability of the lower and upper functions dening its level-cuts [g(x)] = [g (x); g+ (x)] where, for any membership level 2 [0; 1], g g+ are ordinary non-fuzzy functions that are monotonic with respect to . The representation uses a nite decomposition of the membership interval 0 = 0 < 1 <::: < N = 1 and models the level-cuts of the fuzzy numbers and functions to obtain the formulation of a fuzzy differential equation y0 = f(x; y) in terms of a set of ordinary differential equations y0i = i (x; y),