Solution of Fuzzy Problems Under Generalized H-Derivation. Artificial Neural Network For Solving Fuzzy Differential Equations Under Generalized H- Derivation

      Аннотация: Nowadays , fuzzy differential equation FDE is a popular topic studied by many researchers since it is utilized widely for the purpose of modeling problems in science and engineering . Most of the practical problems require the solution of FDE which satisfies fuzzy initial or fuzzy boundary conditions , therefore, the fuzzy problem should be solved . However , many FDE could not be solved exactly , sometimes it is even impossible to find their analytical solutions. Thus , considering their approximate solutions is becoming more important . In this work, for solving FDE Under Generalized H – Derivation , we present modified numerical method which relies on the function approximation capabilities of artificial neural network (ANN) and results in the construction of a solution written in a differentiable, closed analytic form. This form employs ANN as the basic approximation element, whose parameters weights and biases are adjusted to minimize an appropriate error function. This method can result in improved numerical methods for solving FDE .

Ключевые слова: Fuzzy Differential Equations, Artificial Neural Network, Generalized H – Derivation, Error Function, Trial Solution, BFGS Quasi-Newton Method