Adaptive fuzzy time series forecasting with slime mould algorithm

Accurate crude oil price forecasting is essential due to the significant impact of crude oil on the global economy. Precise forecasts help investors, businesses, and policymakers make better-informed decisions. In this study, we propose a hybrid forecasting model called SMA-FTS, which combines the Slime Mould Algorithm (SMA) and Fuzzy Time Series (FTS), aiming to optimize the selection of fuzzy relationships and enhance prediction accuracy. Additionally, we introduce a new method for assigning temporal weights during the Defuzzification step, called the Exponential Increasing Weight Function, which prioritizes fuzzy sets based on their temporal proximity to the current time. This enhancement is designed to reduce uncertainty and improve the forecasting precision of the model. The model is trained on historical monthly Dubai crude oil prices from May 1, 2014, to December 1, 2024. Model performance is evaluated using Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Error (MAE). Experimental results show that the SMA-FTS with the Exponential Increasing Weight Function outperforms the traditional FTS approach, achieving the lowest RMSE, MAPE, and MAE of 5.6264, 5.3367%, and 4.6197, respectively. Moreover, we conduct a comprehensive evaluation using synthetic time series data generated under 84 different experimental conditions, varying the number of data points, noise levels, and missing data rates. The results demonstrate that the proposed SMA-FTS model with the Exponential Increasing Weight Function significantly outperforms baseline models. Furthermore, statistical tests show that the missing rate clearly affects the optimal value of the parameter h, which adjusts the final forecast. This indicates the model's ability to adapt under uncertainty, confirming the robustness of the SMA-FTS approach in real-world forecasting environments.