Modeling and Control Using Fuzzy Differential Equations
Wen Yu, Raheleh Jafari · 2019
This chapter utilizes a new model based on a Bernstein neural network, which has the good properties of the Bernstein polynomial for fuzzy differential equations (FDEs). Two types of neural networks are used: static and dynamic models, to approximate the solutions of FDEs. These numerical methods use the generalized differentiability of FDEs. The solutions of FDEs are substituted into four ordinary differential equations.Then the corresponding Bernstein neural networks are applied. Furthermore, a new method based on the fuzzy Sumudu transform (FST) is used to obtain the approximate solutions of FDEs. Significant theorems are suggested in order to explain the properties of the FST. The FST reduces the FDE to an algebraic equation. A very important property of the FST is that it can solve the equation without resorting to a new frequency domain. By utilizing the proposed technique, the fuzzy boundary value problem can be resolved directly without determining a general solution.