The benefits of social insurance system prediction using a hybrid fuzzy time series method

Decision-making in many industries relies heavily on accurate forecasts, including the insurance sector. The Social Insurance System (SIS) in Egypt, operating under a fully funded paradigm, depends on reliable predictions to ensure effective financial planning. This research introduces a hybrid predictive model that combines fuzzy time series (FTS) Markov chains with the tree partition method (TPM) and difference transformation to forecast total pension benefits within Egypt's SIS. A key feature of the proposed model is its ability to optimize the partitioning process, resulting in the creation of nine intervals that reduce computational complexity while maintaining forecasting accuracy. These intervals were consistently applied across all fuzzy time series models for comparison. The model's performance is evaluated using established metrics such as MAPE, Thiels' U statistic, and RMSE. Additionally, prediction interval coverage probability (PICP) and mean prediction interval length (MPIL) are used to assess the quality of prediction intervals, with a 95% prediction interval serving as the baseline. The proposed model achieved a PICP of approximately 95%, indicating wellcalibrated prediction intervals, although the MPIL of 424.5 reflects a wider uncertainty range. Despite this, the model balances coverage accuracy and interval precision effectively. The results demonstrate that the proposed model significantly outperforms traditional models like linear regression, ARIMA, and exponential smoothing and conventional FTS models like Song, Chen, Yu, and Cheng by achieving the lowest MAPE with the value of 11.8% for training and 10.65% for testing. This superior performance highlights the model's reliability and potential applicability to further forecasting tasks in the field of insurance and beyond.