Comparison of Fuzzy, Intuitionistic Fuzzy, and Picture Fuzzy Regression Function Approaches for Forecasting the Dow Jones Financial Time Series

Uncertainty observed in financial time series makes it difficult to obtain accurate and stable forecasts. In this study, the forecasting performances of Fuzzy Regression Functions (FRF), Intuitionistic Fuzzy Regression Functions (IFRF), and Picture Fuzzy Regression Functions (PFRF) approaches are comparatively examined using Dow Jones index time series with different data lengths. These methods incorporate membership, non-membership, and rejection degrees into the modeling process in different ways, and all experiments are conducted under the same data structure and identical experimental conditions. Forecasting performance is evaluated using RMSE and MAPE metrics. The results indicate that, particularly when different test lengths are considered, the IFRF approach produces more stable forecasts with lower error values. The findings demonstrate that intuitionistic fuzzy regression functions provide a strong and reliable alternative for forecasting financial time series under uncertainty.