On Fuzzy differential equation (original) (raw)

Quantum fuzzy genetic algorithm with Turing to solve DE

Periodicals of Engineering and Natural Sciences (PEN), 2023

In this study, we create the quantum fuzzy Turing machine (QFTM) approach for solving fuzzy differential equations under Seikkala differentiability by combining it with a differential equation and a genetic algorithm. A theoretical model of computation called a quantum fuzzy Turing machine (QFTM) incorporates aspects of fuzzy logic and quantum physics.

A numerical method to solve Fuzzy Differential Equation

In this research paper, we presented an approximate method to solve the delay differential equations under the fuzzy domain. Delay differential equation is a differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. To handle this equation, used an approximate method called Adomian decomposition method. The analysis is accompanied by numerical example. The obtained results demonstrate reliability and efficiency of the proposed method.

Euler method for solving hybrid fuzzy differential equation

Soft Computing, 2011

In this paper, we study the numerical method for solving hybrid fuzzy differential using Euler method under generalized Hukuhara differentiability. To this end, we determine the Euler method for both cases of H-differentiability. Also, the convergence of the proposed method is studied and the characteristic theorem is given for both cases. Finally, some numerical examples are given to illustrate the efficiency of the proposed method under generalized Hukuhara differentiability instead of suing Hukuhara differentiability.

Numerical Solution of Fuzzy Differential Equations Based on Semi-Taylor by Using Neural Network

2013

In this paper, a new approach is proposed for solving the differential equations of fuzzy initial value based on the feedforward neural network fuzzy differential equation is first replaced by a system of ordinary differential equations. A trial Solution of this System involves two parts. The first part Semi-Taylor method and involves no adjustable parameters. And The second part Satisfies the neural network and adjustable parameters (the weights). Finally, This proposed method is compared with some numerical methods. The examples indicate the application of neural network provides solutions better and much accuracy in comparison with existing numerical methods.

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

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.

A Review on Fuzzy Differential Equations

IEEE ACCESS, 2021

Since the term ''Fuzzy differential equations'' (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential applications. This paper presents a chronological survey on fuzzy differential equations of integer and fractional orders. Attention is concentrated on the FDEs in which a definition of fuzzy derivative of a fuzzy number-valued function has been taken into account. The chronological rationale behind considering FDEs under each concept of fuzzy derivative is highlighted. The pros and cons of each approach dealing with FDEs are also discussed. Moreover, some of the proposed FDEs applications and methods for solving them are investigated. Finally, some of the future perspectives and challenges of fuzzy differential equations are discussed based on our personal view point.

Solving fuzzy differential equations by differential transformation method

Information Sciences, 2009

In this paper, we are going to solve Fuzzy integral equations (FI)s by differential transformation method(DTM). Intrinsically, DTM evaluates the approximating solution by the finite Taylor series. The differential transformation method does not evaluate the derivative symbolically; instead, it calculates the relative derivatives by an iteration procedure described by the transformed equations obtained from the original equations using differential transformation. The proposed method provides the Taylors series expansion solution for the domain between any adjacent grid points. Some numerical examples are given to illustrated the proposed extension of DTM to solve fuzzy Fredholm integral equations.

Numerical Solution of Fuzzy Differential Equations and its Applications

Advances in computational intelligence and robotics book series, 2014

Theory of fuzzy differential equations is the important new developments to model various science and engineering problems of uncertain nature because this theory represents a natural way to model dynamical systems under uncertainty. Since, it is too difficult to obtain the exact solution of fuzzy differential equations so one may need reliable and efficient numerical techniques for the solution of fuzzy differential equations. In this chapter we have presented various numerical techniques viz. Euler and improved Euler type methods and Homotopy Perturbation Method (HPM) to solve fuzzy differential equations. Also application problems such as fuzzy continuum reaction diffusion model to analyse the dynamical behaviour of the fire with fuzzy initial condition is investigated. To analyse the fire propagation, the complex fuzzy arithmetic and computation are used to solve hyperbolic reaction diffusion equation. This analysis finds the rate of burning number of trees in bounds where wave variable/ time are defined in terms of fuzzy. Obtained results are compared with the existing solution to show the efficiency of the applied methods.

Numerical solution of fuzzy initial value problems using continuous genetic algorithms

2008

Fuzzy di¤erential equations are one of the most important modern mathematical …elds that result from modeling of uncertain physical, engineering, and economical problems. Two main classical numerical techniques are widely used for the solution of such problems: the classical fourth-order Runge-Kutta method and fourth-order Predictor-Corrector method. The solution accuracy of these methods in many cases is poor for fuzzy di¤erential equations and these methods provide unsatisfactory solutions for sti¤ problems. Furthermore, the error in the approximated nodal values obtained using these methods increase as the node of concern is moved away from the given initial condition. In this paper, a novel approach is proposed to solve fuzzy di¤erential equations, which is based on the use of continuous genetic algorithms where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed algorithm has the following distinct advantages over the conventional methods. First, it does not require any modi…cation while switching from the linear to the nonlinear case. Second, it requires the minimal amount of informations about speci…c problems. Third, the method is not a mathematically guided scheme. Fourth, the algorithm is of global nature in terms of the solutions obtained as well as it is ability to solve other mathematical problems based on ordinary as well as partial fuzzy di¤erential equations. Numerical example presented in this paper illustrate the applicability, accuracy, and generality of the proposed method.