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
This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on th...This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model(NDGM), the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence(MAPEM) and mean percent of interval sequence simulating value set covered(MPSVSC), are defined and, the procedure of the interval grey number sequence based the NDGM(IG-NDGM) is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM(1,1) model and GM(1,1) model.展开更多
To incorporate indeterminacy in spatio-temporal database systems, grey modeling method is used for the calculations of the discrete models of indeterminate two dimension continuously moving objects. The Grey Model GM...To incorporate indeterminacy in spatio-temporal database systems, grey modeling method is used for the calculations of the discrete models of indeterminate two dimension continuously moving objects. The Grey Model GM( 1,1 ) model generated from the snapshot sequence reduces the randomness of discrete snapshot and generates the holistic measure of object's movements. Comparisons to traditional linear models show that when information is limited this model can be used in the interpolation and near future prediction of uncertain continuously moving spatio-temporal objects.展开更多
In the DGM(1, 1) model modeling process, the influencing factors are uncertain. But the solution of DGM(1, 1) model with uncertain information is unique, which conflicts with the nonuniqueness principle of solution in...In the DGM(1, 1) model modeling process, the influencing factors are uncertain. But the solution of DGM(1, 1) model with uncertain information is unique, which conflicts with the nonuniqueness principle of solution in grey theory. In view of this situation, this paper makes an in-depth analysis of the meaning of grey action quantity β_(2) in DGM(1, 1) model and regards β_(2) as an interval grey number. The maximum possibility whitenization value is given to estimate the kernel of grey number,and the typical possibility function is constructed to describe the possibility of grey number taking different values. A new DGM(1, 1) model with a grey parameter is then proposed, whose simulation results are interval grey numbers. The proposed model is compatible with the DGM(1, 1) model in model structure and simulation results. Finally, the practical example results show the applicability and effectiveness of the proposed model.展开更多
The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredient...The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredients of the method are:(1)use of three meshes,(2)use of the Gauss-Green theorem for the approximation of derivatives,(3)discrete integration by parts.In this article we propose to extend this method to the coupled grey thermal-P_(N) radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with radiation.The stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are proved while the experimental second-order accuracy is observed with manufactured solutions.Several numerical experiments are reported which show the good behavior of the method.展开更多
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.
基金supported by the National Natural Science Foundation of China(7090104171171113)the Aeronautical Science Foundation of China(2014ZG52077)
文摘This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model(NDGM), the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence(MAPEM) and mean percent of interval sequence simulating value set covered(MPSVSC), are defined and, the procedure of the interval grey number sequence based the NDGM(IG-NDGM) is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM(1,1) model and GM(1,1) model.
文摘To incorporate indeterminacy in spatio-temporal database systems, grey modeling method is used for the calculations of the discrete models of indeterminate two dimension continuously moving objects. The Grey Model GM( 1,1 ) model generated from the snapshot sequence reduces the randomness of discrete snapshot and generates the holistic measure of object's movements. Comparisons to traditional linear models show that when information is limited this model can be used in the interpolation and near future prediction of uncertain continuously moving spatio-temporal objects.
基金Supported by the National Natural Science Foundation of China(11771172)。
文摘In the DGM(1, 1) model modeling process, the influencing factors are uncertain. But the solution of DGM(1, 1) model with uncertain information is unique, which conflicts with the nonuniqueness principle of solution in grey theory. In view of this situation, this paper makes an in-depth analysis of the meaning of grey action quantity β_(2) in DGM(1, 1) model and regards β_(2) as an interval grey number. The maximum possibility whitenization value is given to estimate the kernel of grey number,and the typical possibility function is constructed to describe the possibility of grey number taking different values. A new DGM(1, 1) model with a grey parameter is then proposed, whose simulation results are interval grey numbers. The proposed model is compatible with the DGM(1, 1) model in model structure and simulation results. Finally, the practical example results show the applicability and effectiveness of the proposed model.
文摘The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredients of the method are:(1)use of three meshes,(2)use of the Gauss-Green theorem for the approximation of derivatives,(3)discrete integration by parts.In this article we propose to extend this method to the coupled grey thermal-P_(N) radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with radiation.The stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are proved while the experimental second-order accuracy is observed with manufactured solutions.Several numerical experiments are reported which show the good behavior of the method.