Nonlinear Optimization Problems with Bipolar Fuzzy Relation Equations using Neural Networks

Document Type : Research Article

Authors

1 School of Mathematics and Computer Science, Damghan University, Damghan, Iran

2 Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran; International Business University,Toronto, Canada

Abstract

In this paper, we present a novel application of neural networks for solving nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set for these problems is generally non-convex, which makes conventional nonlinear optimization methods less suitable for solving them. To address this challenge, we propose the use of neural networks {and some rules for simplification of the problem}. To find an input vector \( x \in [0,1]^n \) that satisfies the constraints and minimizes (or maximizes) the objective function, \( n \) neural networks are trained simultaneously. Each neural network identifies the corresponding variable of the vector \( x \in [0,1]^n \). The loss function integrates both the constraints and the objective function. Our experiments demonstrate that the proposed method can solve these problems with high accuracy and reasonable computational time. The proposed method is compared to the existing methods.

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 10, Issue 2
December 2025
Pages 237-254

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History

  • Receive Date: 24 November 2025
  • Revise Date: 26 December 2025
  • Accept Date: 27 December 2025
  • Publish Date: 30 December 2025

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