An Enhanced Interval Type-2 Fuzzy C-Means Algorithm for Fuzzy Time Series Forecasting of Vegetation Dynamics: A Case Study from the Aksu Region, Xinjiang, China

Accurate prediction of the Normalized Difference Vegetation Index (NDVI) is crucial for regional ecological management and precision decision-making. Existing methodologies often rely on smoothed NDVI data as ground truth, overlooking uncertainties inherent in data acquisition and processing. Fuzzy time series (FTS) prediction models based on the Fuzzy C-Means (FCM) clustering algorithm address some of these uncertainties by enabling soft partitioning through membership functions. However, the method remains limited by its reliance on expert experience in setting fuzzy parameters, which introduces uncertainty in the definition of fuzzy intervals and negatively affects prediction performance. To overcome these limitations, this study enhances the interval type-2 fuzzy clustering time series (IT2-FCM-FTS) model by developing a pixel-level time series forecasting framework, optimizing fuzzy interval divisions, and extending the model from unidimensional to spatial time series forecasting. Experimental results from 2021 to 2023 demonstrate that the proposed model outperforms both the Autoregressive Integrated Moving Average (ARIMA) and conventional FCM-FTS models, achieving the lowest RMSE (0.0624), MAE (0.0437), and SEM (0.000209) in 2021. Predictive analysis indicates a general ecological improvement in the Aksu region (Xinjiang, China), with persistent growth areas comprising 61.12% of the total and persistent decline areas accounting for 2.6%. In conclusion, this study presents an improved fuzzy model for NDVI time series prediction, providing valuable insights into regional desertification prevention and ecological strategy formulation.