Hierarchical Granular Computing-Based Model and Its Reinforcement Structural Learning for Construction of Long-Term Prediction Intervals

Studying the evolutions, differences, and water security impacts of water demands under shared socioeconomic pathways: A SEMs-bootstrap-ANN approach applied to Sichuan Province

In this study, a SEMs-bootstrap-ANN method was presented for constructing prediction intervals (PIs) of water demand under shared socioeconomic pathways (SSPs). The primary objective was to examine the evolution, disparities, and impacts on water security. Initially, a bootstrap algorithm and an artificial neural network (ANN) were combined to form a bootstrap-ANN model, which determined the centres and widths of the PIs at a specified significance level by estimating the distributions of prediction values and errors. The water demand factors in SSPs were projected using socioeconomic models like Cobb-Douglas, based on the narratives of the International Institute for Applied Systems Analysis (IIASA). By incorporating these factors into the bootstrap-ANN model, the study obtained the temporal changes of water demand PIs in SSPs, while quantifying the differences and water security implications using the interval difference index (IDI) and surface water exploration index (SWEI). The case study focused on Sichuan province, and the model performance was evaluated via the evaluation indices and cross-validation. The results demonstrated five key findings. Firstly, the proposed method showed a greater PICP of 0.985, slightly larger PIRAW of 9.83%, and higher MAIS than other methods in the historical dataset, indicating a small disadvantage in width in return for better accuracy and overall performance. Secondly, the reliability of the results in the SSP period was supported by the PIRAWs (mostly within 15%), the cross errors (approximately 5%), and their performance in 2021 (the PIs in SSP2 almost covered all true values). Thirdly, the total water demands in all SSPs within Sichuan Province exhibited a consistent upward trajectory, with SSP5 displaying the highest increase of 44-63% compared to current water usage. Fourthly, among the four SSPs, the most substantial disparities were observed between SSP5 and SSP3, reaching a maximum difference of 32%. Conversely, the disparities between SSP2 and SSP1 fluctuated around zero, transitioning from negative to positive trends. Notably, from an environmental perspective, SSP1 was considered preferable to SSP2. Lastly, the SWEIs, which reflected water security conditions in Sichuan Province under the four SSPs, ranked in the following order: SSP3, SSP1, SSP2, and SSP5, indicating a progressively worsening situation. Despite not reaching stress thresholds even during dry years until 2100, the water security conditions could deteriorate by 28-46% compared to historical extremes and by 3-16% compared to extended extremes in dry years.

Establish a trend fuzzy information granule based short-term forecasting with long-association and k-medoids clustering

In the existing short-term forecasting methods of time series, two challenges are faced: capture the associations of data and avoid cumulative errors. For tackling these challenges, the fuzzy information granule based model catches our attention. The rule used in this model is fuzzy association rule (FAR), in which the FAR is constructed from a premise granule to a consequent granule at consecutive time periods, and then it describes the short-association in data. However, in real time series, another association, the association between a premise granule and a consequent granule at non-consecutive time periods, frequently exists, especially in periodical and seasonal time series. While the existing FAR can’t express such association. To describe it, the fuzzy long-association rule (FLAR) is proposed in this study. This kind of rule reflects the influence of an antecedent trend on a consequent trend, where these trends are described by fuzzy information granules at non-consecutive time periods. Thus, the FLAR can describe the long-association in data. Correspondingly, the existing FAR is called as fuzzy short-association rule (FSAR). Combining the existing FSAR with FLAR, a novel short-term forecasting model is presented. This model makes forecasting at granular level, and then it reduces the cumulative errors in short-term prediction. Note that the prediction results of this model are calculated from the available FARs selected by the k-medoids clustering based rule selection algorithm, therefore they are logical and accurate. The better forecasting performance of this model has been verified by comparing it with existing models in experiments.