The fuzzy transform setting (F-transform), as a tool for general continuous approximation of functions, is proposed to approximate the solution of ordinary, interval or fuzzy (levelwise) differential equations; in particular, one of the basic properties of inverse F-transform allows a good approximation of the solution x(t), starting with the uniform approximation of the derivative x'(t) via F-transform. First, the ordinary initial value problem is considered and a global second order approximation is obtained. Then, the interval and fuzzy cases are considered, in the setting of generalized differentiability, and an efficient numerical procedure is proposed.
Fuzzy differential equations by fuzzy-transform
STEFANINI, LUCIANO
2015
Abstract
The fuzzy transform setting (F-transform), as a tool for general continuous approximation of functions, is proposed to approximate the solution of ordinary, interval or fuzzy (levelwise) differential equations; in particular, one of the basic properties of inverse F-transform allows a good approximation of the solution x(t), starting with the uniform approximation of the derivative x'(t) via F-transform. First, the ordinary initial value problem is considered and a global second order approximation is obtained. Then, the interval and fuzzy cases are considered, in the setting of generalized differentiability, and an efficient numerical procedure is proposed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
