Abstract
The aim of this work is to present a novel approach based on the artificial neural network for finding the numerical solution of first order fuzzy differential equations under generalized H-derivation. The differentiability concept used in this paper is the generalized differentiability since a fuzzy differential equation under this differentiability can have two solutions. The fuzzy trial solution of fuzzy initial value problem is written as a sum of two parts. The first part satisfies the fuzzy condition, it contains no adjustable parameters. The second part involves feed-forward neural networks containing adjustable parameters. Under some conditions the proposed method provides numerical solutions with high accuracy.
Highlights
Nowadays, fuzzy differential equations (FDEs) is a popular topic studied by many researchers since it is utilized widely for the purpose of modeling problems in science and engineering
For solving FDE Under Generalized H – Derivation, we present modified method which relies on the function approximation capabilities of feed-forward neural networks (FFNN) and results in the construction of a solution written in a differentiable, closed analytic form
We have presented numerical method based on artificial neural network for solving first order fuzzy initial value problem under generalized H-derivation
Summary
Fuzzy differential equations (FDEs) is a popular topic studied by many researchers since it is utilized widely for the purpose of modeling problems in science and engineering. For solving FDE Under Generalized H – Derivation, we present modified method which relies on the function approximation capabilities of FFNN and results in the construction of a solution written in a differentiable, closed analytic form. This form employs FFNN as the basic approximation element, whose parameters (weights and biases) are adjusted to minimize an appropriate error function. To train the ANN which we design, we employ optimization techniques, which in turn require the computation of the gradient of the error with respect to the network parameters In this proposed approach the model function is expressed as the sum of the two terms: the first term satisfies the fuzzy initial / fuzzy boundary conditions and contains no adjustable parameters.
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