<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Bearing in mind the considerable importance of fuzzy differential equations (FDEs) in different fields of science and engineering, in this paper, nonlinear <italic>nth</italic> order FDEs are approximated, heuristically. The analysis is carried out on using Chebyshev neural network (ChNN), which is a type of single layer functional link artificial neural network (FLANN). Besides, explication of generalized Hukuhara differentiability (gH-differentiability) is also added for the <italic>nth</italic> order differentiability of fuzzy-valued functions. Moreover, general formulation of the structure of ChNN for the governing problem is described and assessed on some examples of nonlinear FDEs. In addition, comparison analysis of the proposed method with Runge-Kutta method is added and also portrayed the error bars that clarify the feasibility of attained solutions and validity of the method.</p></abstract>

Bearing in mind the considerable importance of fuzzy differential equations (FDEs) in different fields of science and engineering, in this paper, nonlinear nth order FDEs are approximated, heuristically. The analysis is carried out on using Chebyshev neural network (ChNN), which is a type of single layer functional link artificial neural network (FLANN). Besides, explication of generalized Hukuhara differentiability (gH-differentiability) is also added for the nth order differentiability of fuzzy-valued functions. Moreover, general formulation of the structure of ChNN for the governing problem is described and assessed on some examples of nonlinear FDEs. In addition, comparison analysis of the proposed method with Runge-Kutta method is added and also portrayed the error bars that clarify the feasibility of attained solutions and validity of the method.

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

Department of Humanities and Social Sciences

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Bearing in mind the considerable importance of fuzzy differential equations (FDEs) in different fields of science and engineering, in this paper, nonlinear nth...

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

Published Online: Dec 07, 2018

Page range: 3 - 22

Received: Mar 14, 2016

Accepted: Nov 04, 2017

DOI: https://doi.org/10.2478/awutm-2018-0001

Keywords
gH-differentiability, fuzzy-valued function, nonlinear fuzzy differential equation, neural network

© 2018 Asmat Ara et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

Published Online: Dec 07, 2018

Page range: 3 - 22

Received: Mar 14, 2016

Accepted: Nov 04, 2017

DOI: https://doi.org/10.2478/awutm-2018-0001

KeywordsgH-differentiability, fuzzy-valued function, nonlinear fuzzy differential equation, neural network

© 2018 Asmat Ara et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
gH-differentiability, fuzzy-valued function, nonlinear fuzzy differential equation, neural network