Fuzzy differential equations by fuzzy-transform

摘要

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.