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<p>In order to handle more uncertain information during machine learning, this paper proposes the concept of polygonal interval-valued fuzzy neural network (PIVFNN) and investigates its universal approximation property with operations of polygonal interval-valued fuzzy numbers. Secondly, we delineate the topology structure of the PIVFNN and rigorously derive its mathematical expression. Moreover, acknowledging the potential variability of connection weights and thresholds within neural networks, a modified gradient descent with momentum algorithm is introduced to address the parameter optimization problem within the PIVFNN framework. Among them, the function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{lor}(\cdot )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>lor</mtext> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is introduced to compute the gradient of the error function, and its convergence is proved. Finally, we carry out a simulation experiment of wind speed prediction with actual data comprising temperature difference, barometric pressure, and wind direction. The gradient descent (GD) algorithm, modified gradient descent with momentum (MGDM) algorithm, and BP neural network algorithm are employed for parameters optimization. By comparing and analyzing the residual, range, and accuracy in the statistical characteristics of several algorithms, it is determined that the proposed MGDM algorithm has the fastest convergence speed and higher stability.</p>

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Wind Speed Prediction Model Based on Polygonal Interval-Valued Fuzzy Neural Network and Modified Gradient Descent with Momentum Algorithm

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Chunfeng Suo,
  • Shu Sun,
  • Le Fu

摘要

In order to handle more uncertain information during machine learning, this paper proposes the concept of polygonal interval-valued fuzzy neural network (PIVFNN) and investigates its universal approximation property with operations of polygonal interval-valued fuzzy numbers. Secondly, we delineate the topology structure of the PIVFNN and rigorously derive its mathematical expression. Moreover, acknowledging the potential variability of connection weights and thresholds within neural networks, a modified gradient descent with momentum algorithm is introduced to address the parameter optimization problem within the PIVFNN framework. Among them, the function \(\textrm{lor}(\cdot )\) lor ( · ) is introduced to compute the gradient of the error function, and its convergence is proved. Finally, we carry out a simulation experiment of wind speed prediction with actual data comprising temperature difference, barometric pressure, and wind direction. The gradient descent (GD) algorithm, modified gradient descent with momentum (MGDM) algorithm, and BP neural network algorithm are employed for parameters optimization. By comparing and analyzing the residual, range, and accuracy in the statistical characteristics of several algorithms, it is determined that the proposed MGDM algorithm has the fastest convergence speed and higher stability.