文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例...文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例应用结果表明,其建模精度和预测效果均优于无偏GM(1,1)模型和离散GM(1,1)模型。为将适宜建模序列拓展至近似非齐次指数序列和季节波动序列,同时保留幂函数变换可以有效降低背景值误差对建模精度影响的优势,将幂函数变换与平移变换相结合构建了PFNGM(1,1)模型,将幂函数变换与季节性GM(1,1)模型(SGM(1,1)模型)相结合构建了PFSGM(1,1)模型。实例应用结果表明,PFNGM(1,1)模型的建模精度和预测效果均优于背景值改进的NGM(1,1, k )模型和ONGM(1,1, k,c )模型,PFSGM(1,1)模型的建模精度和预测效果均优于SGM(1,1)模型,验证了两种模型的有效性。展开更多
For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the backgrou...For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the background value as a variable related to k.At the same time,the initial value is set as a variable,and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error(MRE).Combined with the domestic natural gas annual consumption data,the classical model and the improved GM(1,1)model are applied to the calculation and error comparison respectively.It proves that the improved model is better than any other models.展开更多
Firstly, the research progress of grey model GM （1,1） is summarized, which is divided into three development stages： assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study th...Firstly, the research progress of grey model GM （1,1） is summarized, which is divided into three development stages： assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study the modeling mechanism of GM （1,1）, which decomposes the modeling data matrix into raw data transformation matrix, accumulated generating operation matrix and background value selection matrix. The changes of these three matrices are the essential reasons affecting the modeling and the accuracy of GM （1,1）. Finally, the paper proposes a generalization grey model GGM （1,1）, which is a extended form of GM （1,1） and also a unified form of model GM （1,1）, model GM （1,1,α）, stage grey model, hopping grey model, generalized accumulated model, strengthening operator model, weakening operator model and unequal interval model. And the theory and practical significance of the extended model is analyzed.展开更多
Based on the optimization method, a new modified GM (1,1) model is presented, which is characterized by more accuracy prediction for the grey modeling.
The basic difference non-equal interval model GM(1,1) in grey theory was used to fit and forecast data series with non-equal lengths and different inertias, acquired from oil monitoring of internal combustion engines....The basic difference non-equal interval model GM(1,1) in grey theory was used to fit and forecast data series with non-equal lengths and different inertias, acquired from oil monitoring of internal combustion engines. The fitted and forecasted results show that the length or inertia of a sequence affects its precision very much, i.e. the bigger the inertia of a sequence is, or the shorter the length of a series is, the less the errors of fitted and forecasted results are. Based on the research results, it is suggested that short series should be applied to be fitted and forecasted; for longer series, the newer datum should be applied instead of the older datum to be analyzed by non- equalinterval GM(1,1) to improve the forecasted and fitted precision, and that data sequence should be verified to satisfy the conditions of grey forecasting.展开更多
This paper expresses the efficient outputs of decisionmaking unit（DMU） as the sum of ＂average outputs＂ forecasted by a GM（1,N） model and ＂increased outputs＂ which reflect the difficulty to realize efficient ou...This paper expresses the efficient outputs of decisionmaking unit（DMU） as the sum of ＂average outputs＂ forecasted by a GM（1,N） model and ＂increased outputs＂ which reflect the difficulty to realize efficient outputs.The increased outputs are solved by linear programming using data envelopment analysis efficiency theories,wherein a new sample is introduced whose inputs are equal to the budget in the issue No.n ＋ 1 and outputs are forecasted by the GM（1,N） model.The shortcoming in the existing methods that the forecasted efficient outputs may be less than the possible actual outputs according to developing trends of input-output rate in the periods of pre-n is overcome.The new prediction method provides decision-makers with more decisionmaking information,and the initial conditions are easy to be given.展开更多
In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.B...In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.展开更多
文摘文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例应用结果表明,其建模精度和预测效果均优于无偏GM(1,1)模型和离散GM(1,1)模型。为将适宜建模序列拓展至近似非齐次指数序列和季节波动序列,同时保留幂函数变换可以有效降低背景值误差对建模精度影响的优势,将幂函数变换与平移变换相结合构建了PFNGM(1,1)模型,将幂函数变换与季节性GM(1,1)模型(SGM(1,1)模型)相结合构建了PFSGM(1,1)模型。实例应用结果表明,PFNGM(1,1)模型的建模精度和预测效果均优于背景值改进的NGM(1,1, k )模型和ONGM(1,1, k,c )模型,PFSGM(1,1)模型的建模精度和预测效果均优于SGM(1,1)模型,验证了两种模型的有效性。
基金supported by the National Natural Science Foundation of China (71871106)the Blue and Green Project in Jiangsu Provincethe Six Talent Peaks Project in Jiangsu Province (2016-JY-011)
文摘For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the background value as a variable related to k.At the same time,the initial value is set as a variable,and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error(MRE).Combined with the domestic natural gas annual consumption data,the classical model and the improved GM(1,1)model are applied to the calculation and error comparison respectively.It proves that the improved model is better than any other models.
基金supported by the National Natural Science Foundation of China(70971103)the Specialized Research Fund for the Doctora Program of Higher Education(20120143110001)
文摘Firstly, the research progress of grey model GM （1,1） is summarized, which is divided into three development stages： assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study the modeling mechanism of GM （1,1）, which decomposes the modeling data matrix into raw data transformation matrix, accumulated generating operation matrix and background value selection matrix. The changes of these three matrices are the essential reasons affecting the modeling and the accuracy of GM （1,1）. Finally, the paper proposes a generalization grey model GGM （1,1）, which is a extended form of GM （1,1） and also a unified form of model GM （1,1）, model GM （1,1,α）, stage grey model, hopping grey model, generalized accumulated model, strengthening operator model, weakening operator model and unequal interval model. And the theory and practical significance of the extended model is analyzed.
文摘Based on the optimization method, a new modified GM (1,1) model is presented, which is characterized by more accuracy prediction for the grey modeling.
文摘The basic difference non-equal interval model GM(1,1) in grey theory was used to fit and forecast data series with non-equal lengths and different inertias, acquired from oil monitoring of internal combustion engines. The fitted and forecasted results show that the length or inertia of a sequence affects its precision very much, i.e. the bigger the inertia of a sequence is, or the shorter the length of a series is, the less the errors of fitted and forecasted results are. Based on the research results, it is suggested that short series should be applied to be fitted and forecasted; for longer series, the newer datum should be applied instead of the older datum to be analyzed by non- equalinterval GM(1,1) to improve the forecasted and fitted precision, and that data sequence should be verified to satisfy the conditions of grey forecasting.
基金supported by the Research Start Funds for Introducing High-level Talents of North China University of Water Resources and Electric Power
文摘This paper expresses the efficient outputs of decisionmaking unit（DMU） as the sum of ＂average outputs＂ forecasted by a GM（1,N） model and ＂increased outputs＂ which reflect the difficulty to realize efficient outputs.The increased outputs are solved by linear programming using data envelopment analysis efficiency theories,wherein a new sample is introduced whose inputs are equal to the budget in the issue No.n ＋ 1 and outputs are forecasted by the GM（1,N） model.The shortcoming in the existing methods that the forecasted efficient outputs may be less than the possible actual outputs according to developing trends of input-output rate in the periods of pre-n is overcome.The new prediction method provides decision-makers with more decisionmaking information,and the initial conditions are easy to be given.
基金supported by the National Natural Science Foundation of China(7084001290924022)the Ph.D.Thesis Innovation and Excellent Foundation of Nanjing University of Aeronautics and Astronautics(2010)
文摘In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.
