Advances in Fuzzy Sets and Systems

The Advances in Fuzzy Sets and Systems publishes original research papers in the field of fuzzy sets and systems, covering topics such as artificial intelligence, robotics, decision-making, and data analysis. It also welcomes papers on variants of fuzzy sets and algorithms for computational work.

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FUZZY MODEL USING BERNSTEIN NEURAL NETWORK IN AN UNCERTAIN NON-LINEAR DIFFERENTIAL EQUATION

Authors

  • Jitendra Binwal
  • Arvind Maharshi
  • Anita Mundra

Keywords:

BNN, bisection method, harmonic Newton’s method, fuzzy model, non-linear differential equations.

DOI:

https://doi.org/10.17654/0973421X23001

Abstract

Nonlinear systems can also be simulated using fuzzy models, differential equations, and algebraic systems. Fuzzy systems are excellent models for uncertainty of nonlinear systems because nonlinear systems uncertainties can be converted into the fuzzy set concept. Fuzzy models employ many linear piecewise systems to approximate nonlinear systems with fuzzier outcomes. The fuzzy polynomial is an extended version of the fuzzy equation. The fuzzy equations are simpler to use than the standard fuzzy systems. There are a variety of ways to build fuzzy equations such as an interpolation technique, an iterative approach, and a Runge-Kutta technique that can be used to extract the statistical solution connected with fuzzy equations. In this work, it is studied that the previous research used fuzzy equations with Z-number coefficients to represent nonlinear systems with unknown parameters. A fuzzy model is suggested using Bernstein Neural Network (BNN) in uncertain non-linear differential equation in this research. The two methods bisection method and harmonic Newton’s method are used to solve the uncertain non-linear differential equations. Few non-linear differential equations are used in the work to acquire findings. The results reveal that the bisection method produces accurate roots that are approximately zero.

Received: September 29, 2022
Accepted: December 20, 2022

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Published

2023-01-10

Issue

Vol. 28 No. 1 (2023)

Section

Articles

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How to Cite

FUZZY MODEL USING BERNSTEIN NEURAL NETWORK IN AN UNCERTAIN NON-LINEAR DIFFERENTIAL EQUATION. (2023). Advances in Fuzzy Sets and Systems, 28(1), 1-19. https://doi.org/10.17654/0973421X23001

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