Predicting Sunspot Numbers Based on Neutrosophic Time Series

Abstract

Neutrosophic Time Series applies Neutrosophic principles for resolving forecasting problems. It can be applied to analyze ambiguous or imprecise data that are difficult to process using conventional methods. 1D Convolutional Long Short-Term Memory Network (Conv1D-LSTM) is a hybrid of two approaches that are frequently employed to manage time series data and produce an accurate predictive model. The monthly Sunspot number data were used from the WDC-SILSO, Royal Observatory of Belgium, from January 1900 to December 2024. The dataset consists of 125 years, including 1500 months. Data normalization (Min-Max Scaling) was used to uniformly scale sunspot values to enhance model performance and stabilize training for predictive modeling. The data was divided from January 1900 to June 1987 as a training set (70%) and from July 1987 to December 2024 as a test set (30%). A hybrid method was proposed to improve the accuracy of predictions by integrating the outputs of a neutrosophic model as an input for the Conv1D-LSTM model. We compared the proposed method with neutrosophic, and Conv1D-LSTM. The evaluation metrics highlight that the proposed model outperforms other models across all performance metrics, indicating its superior forecasting ability.  It is sufficiently flexible and can be readily extended to other phenomena exhibiting comparable characteristics. The neutrosophic model closely follows the Conv1D-LSTM model, indicating highly competitive results. The highest number of sunspots is predicted for June, July, September, and October 2026