Artificial Neural Network for Solving Fuzzy Differential Equations under Generalized H – Derivation

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.

Approximate Series Solution For Two-Point Fuzzy Boundary Value Problems

“…The general form of the two-point fuzzy boundary value problems for the ordinary differential equations is [9]:…”

“…during this work, we need many fundamental concepts in the fuzzy set theory, such as fuzzy number, fuzzy function and fuzzy derivative. These concepts can be found in detail in [6,9,12].…”

Fully Fuzzy Neural Network For Solving Fuzzy Differential Equations

“…,Otadi [15 ]. In (2016) Suhhiem [18] developed and used partially FANN for solving fuzzy and non-fuzzy differential equations.…”

Semi Analytical Solution for Fuzzy Autonomous Differential Equations

“…Researchers and scientists are continuing to develop this method for solving various types of the FIVBs because it represents an efficient and effective technique (For more details, see [1,2,3,4,6,7,8,10]).…”

“…In this work, we will need many basic concepts in the fuzzy theory. These concepts can be found in detail in [5,8,11].…”