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<p>Accurate forecasting of Sunspot Numbers (SSN) is essential for understanding solar activity and for mitigating the effects of space weather on technological systems. In this study, a Neutrosophic Fuzzy Time Series (NFTS) forecasting framework is developed to predict hemispherical 13-month smoothed SSN for both monthly and yearly datasets. The proposed approach maps the dataset into a universe of discourse and partitions it using a computational-based partitioning (CBP) technique. Triangular fuzzy sets are constructed, and neutrosophic membership components-truth, indeterminacy, and false are evaluated and aggregated using a score function. Fuzzy Logical Relationships (FLRs) and Fuzzy Logical Groups (FLGs) are then established to capture temporal dynamics, followed by defuzzification using the centroid method. The performance of the model is evaluated using statistical indicators such as Root Mean Square Error (RMSE), Mean Absolute Percentage error (MAPE), correlation coefficient (R), coefficient of determination (<InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">R</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\mathrm{R}^{2}$</EquationSource> </InlineEquation>), Theil’s inequality coefficient, Prediction Performance (PP), and Willmott index. The results demonstrate high predictive accuracy with low RMSE and MAPE values and strong agreement between observed and predicted values. The NFTS model reliably predicts solar cycles and space weather by accurately modeling nonlinear behavior and hemispherical asymmetry.</p>

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Prediction of Solar Activity Using Neutrosophic Fuzzy Time Series: A Study of Yearly and Monthly Hemispherical SSNs

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Geeta Mathpal,
  • Arvind Bhatt,
  • Rajesh Mathpal,
  • Meenakshi Rana

摘要

Accurate forecasting of Sunspot Numbers (SSN) is essential for understanding solar activity and for mitigating the effects of space weather on technological systems. In this study, a Neutrosophic Fuzzy Time Series (NFTS) forecasting framework is developed to predict hemispherical 13-month smoothed SSN for both monthly and yearly datasets. The proposed approach maps the dataset into a universe of discourse and partitions it using a computational-based partitioning (CBP) technique. Triangular fuzzy sets are constructed, and neutrosophic membership components-truth, indeterminacy, and false are evaluated and aggregated using a score function. Fuzzy Logical Relationships (FLRs) and Fuzzy Logical Groups (FLGs) are then established to capture temporal dynamics, followed by defuzzification using the centroid method. The performance of the model is evaluated using statistical indicators such as Root Mean Square Error (RMSE), Mean Absolute Percentage error (MAPE), correlation coefficient (R), coefficient of determination ( R 2 $\mathrm{R}^{2}$ ), Theil’s inequality coefficient, Prediction Performance (PP), and Willmott index. The results demonstrate high predictive accuracy with low RMSE and MAPE values and strong agreement between observed and predicted values. The NFTS model reliably predicts solar cycles and space weather by accurately modeling nonlinear behavior and hemispherical asymmetry.