Building forecasting model for time series based on improvements in establishing fuzzy relationships and clustering algorithm

This research proposes a new forecasting model for time series with important improvements. The first improvement is the use of the variation between two consecutive times as a universal set and dividing it into intervals with an appropriate number using an automatic clustering technique. The second improvement is the establishment of fuzzy relationships between the built intervals and between each element in the series and these intervals. Finally, using the established relationships, a new forecasting rule is created. The model is presented step by step and detailed with numerical examples, and the proofs for algorithm convergence are provided. It outperforms existing models on well-known datasets including the M3 Competition with 3003 series and M4 Competition datasets with 100,000 series. Another important contribution of this study is the establishment of the R procedure to effectively apply the proposed model to real series.