科研之友
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摘要
In this study, the weakened fractional-order accumulation operator for alleviating the ill -condition of discrete grey system models with the aim of improving the grey system theory is proposed. It is found that the weakened fractional-order accumulation oper-ator composed of the improved fractional-order accumulation operator and the multi-plicative transformation can not only alleviate the ill-condition of the system by decreas-ing the differences between the elements of the columns (rows) in the coefficient ma-trix but also further enhance the prediction performance of the models. Therefore, the weakened fractional-order accumulation operator is an effective improvement measure. The demonstration of the unbiasedness and affine transformation property of the discrete grey forecasting models with the weakened fractional-order accumulation operator further strengthens the theoretical basis of this new system. Two real-world time series are used as cases to demonstrate the effectiveness of the discrete grey system models with the weakened fractional-order accumulation operator compared with discrete grey forecast-ing models based on five other different accumulation operators(1-order accumulation op-eration, new information accumulation operation, fractional-order accumulation operator, damping accumulative generating operator and the conformable fractional-order accumu-lation operator). The results of the comparative analysis show that the proposed weakened fractional order accumulation operator can not only substantially reduce the ill-condition of the models but also have good predictive performance, both of which confirm the fea-sibility and validity of the method.
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单位东北大学
