Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized an...Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. Grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.展开更多
Based on grey set, grey numbers and their operation properties, the grey numerical model of groundwater seepage system was set up for the first time, the whole grey solving method of the model was given and it was pro...Based on grey set, grey numbers and their operation properties, the grey numerical model of groundwater seepage system was set up for the first time, the whole grey solving method of the model was given and it was proved that the common solving method of the model was only a special case of the grey solving methods. At the same time, the grey solving method was compared widely with common solving method, classical numerical method. The study shows that the grey solving method is better in depicting the procedure of transporting grey data of groundwater system. On the basis of the theoretical study, two basic kinds of cases about groundwater seepage were selected: the prediction of pit yield and the evaluation of groundwater resources on a groundwater basin. In the cases, systematical analyses were made for generalization and greylization of the hydrogeologic conditions, setting up of the grey model, identification and correction of the model as well as its prediction and evaluation. It was pointed out that when the grey numerical model is used to predict pit yield, the upper limit of the “grey band” of groundwater level cannot be higher than planed safe groundwater level, when evaluating the groundwater resource, the lower limit of the “grey band” of groundwater level cannot be lower than controlled level of groundwater.展开更多
基金supported by the China Postdoctoral Science Foundation(200902321)a Marie Curie International Incoming Fellowship within the 7th European Community Framework Program(FP7-PIIFGA-2013-629051)
文摘Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. Grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.
基金the Ministry of National Lands and Resources (Grant No. 200010301-66).
文摘Based on grey set, grey numbers and their operation properties, the grey numerical model of groundwater seepage system was set up for the first time, the whole grey solving method of the model was given and it was proved that the common solving method of the model was only a special case of the grey solving methods. At the same time, the grey solving method was compared widely with common solving method, classical numerical method. The study shows that the grey solving method is better in depicting the procedure of transporting grey data of groundwater system. On the basis of the theoretical study, two basic kinds of cases about groundwater seepage were selected: the prediction of pit yield and the evaluation of groundwater resources on a groundwater basin. In the cases, systematical analyses were made for generalization and greylization of the hydrogeologic conditions, setting up of the grey model, identification and correction of the model as well as its prediction and evaluation. It was pointed out that when the grey numerical model is used to predict pit yield, the upper limit of the “grey band” of groundwater level cannot be higher than planed safe groundwater level, when evaluating the groundwater resource, the lower limit of the “grey band” of groundwater level cannot be lower than controlled level of groundwater.
