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.
Radi, D., Stefanini, L., Fuzzy differential equations by fuzzy-transform, in Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS, (Redmond, Washington, USA, 2023-08-17), Institute of Electrical and Electronics Engineers Inc., Redmond 2015:2015- 1-6. [10.1109/NAFIPS-WConSC.2015.7284180] [https://hdl.handle.net/10807/238074]
Fuzzy differential equations by fuzzy-transform
Radi, DavidePrimo
Methodology
;
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.
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