A novel forecasting model for time series using optimized interval division and fuzzy relationships

This study builds an effective forecasting model for time series based on significant improvements of the fuzzy clustering algorithm. Firstly, we use the universal set, which is the percentage change between two consecutive time points, and divide it into unequal intervals using the automatic clustering algorithm that adjusts the number of clusters. Next, we propose the networks so that establish the fuzzy relationship of the elements in the universal set and the intervals based on the improved inverse fuzzy number. Finally, a new principle for future forecasting is built based on these two improvements. The proposed model details the steps and is clearly illustrated through a specific numerical. The convergence of the proposed algorithm is also considered and addressed. The proposed model has demonstrated effectiveness by outperforming many other models applied to the M3 dataset with 3,003 series, the M4 dataset with 100,000 series, and the well-known benchmark dataset. The proposed model is also applied to forecast the number of people infected and deceased due to COVID-19 in Southeast Asian countries. This application also demonstrates the advantages of the proposed model over many existing models.