## 4 Conclusions  
In this study, a new model for time-series forecasting was presented. The model was presented in two phases. The first phase was fuzzy linear regression that was used to replace the maximum likelihood method in parameter estimation. The second was the fuzzy window variance used to replace the long-run average variance component. Two datasets were used to test the performance of the proposed model; the first was from economics and the second was from agriculture. The forecasted values obtained from the use of the proposed model were compared to the benchmark models. The empirical results show that the proposed FLR-FSWGARCH model produced highly accurate forecasting values and a lower mean absolute percentage error (MAPE) than the SWGARCH, GARCH, ARIMA-GARCH, and EWMA models. This demonstrates that the FLR-FSWGARCH model was capable of giving a superior forecast compared to the benchmark models. Furthermore, the results also confirmed that the proposed model was highly reliable and significantly fit for forecasting time-series data as the R\({}^{2}\) were more than 90% for both datasets. These indicated that the combination of the FLR and FSW variance with the GARCH model was adept at addressing uncertainties and handling fluctuating information. The highlight of this work lies in the application of FLR and FSW variance, which overcomes the limitation of the GARCH. The FLR curbs the inter-correlation problem associated with independent variables, while the FSW variance captures the influence of the variance on each observation and determines the true window selection for the weight of the forecast to produce a highly accurate performance.  
In view of the need for a model that is easily understood by most people, particularly forecasters, the proposed model is computationally simple and practical as it does not involve any complex computations or simulations. The equations in the proposed model can be applied in Excel to obtain the estimated parameters of models and calculate the forecasts automatically. In addition, the application of the proposed model extends beyond the fields of economics to even include use in agriculture. Therefore, the proposed forecasting model could be used as an alternative to better forecast sustainable prices and growth, thereby improving a country's economy. The application of the FLR-FSWGARCH model will also facilitate the decision-making processes associated with forecasting practice. For further studies, more attention should be paid to the fuzzification process by imposing a bipolar fuzzy set to form the triangular fuzzy numbers. The bipolar fuzzy set is an extension of a fuzzy set whose membership degree range is (\(-1\),\(1\)), which is different from the current study, which uses a membership degree range of (\(0\),\(1\)). The performance of the proposed model will be more superior by using the bipolar fuzzy set as previous research has shown its advantages when handling vagueness and uncertainty over a fuzzy set.  
Conceptualization, A.L.M.H. and M.O.; project administration, A.L.M.H.; validation, N.R. and A.H.; formal analysis, R.S. and P.V.; funding acquisition, M.O. All authors have read and agreed to the published version of the manuscript.  
Universiti Teknologi PETRONAS, Malaysian Fundamental Research Grant Scheme (FRGS), cost center: 015 MA0-021.  
Thanks to the authors for the contributions and thanks to Universiti Teknologi PETRONAS and FRGS for providing financial support and good facilities.  
The authors declare no conflict of interest.