The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey inciden...The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey incidence model, the grey cluster model based on endpoint triangular whitenization functions, the grey cluster model based on center-point triangular whitenization functions, the grey prediction model of the model GM （ 1,1）, and the weighted multi-attribute grey target decision model.展开更多
In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the wh...In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n).展开更多
An unequal time interval sequence or a sequence with blanks is usually completed with average generation in grey system theory. This paper discovers that there exists obvious errors when using average generation to ge...An unequal time interval sequence or a sequence with blanks is usually completed with average generation in grey system theory. This paper discovers that there exists obvious errors when using average generation to generate internal points of non-consecutive neighbours. The average generation and the preference generation of the sequence are discussed, the concave and convex properties show the status of local sequence and propose a new idea for using the status to build up the criteria of choosing generation coefficient. Compared with the general average method of the one-dimensional data sequence, the two-dimensional data sequence is defined and its average generation is discussed, and the coefficient decision method for the preference generation is presented.展开更多
基金Supported by the Joint Research Project of Both the National Natural Science Foundation of Chinaand the Royal Society(RS)of UK(71111130211)the National Natural Science Foundation of China(90924022,70971064,70901041,71171113)+7 种基金the Major Project of Social Science Foundation of China(10ZD&014)the Key Project of Social Science Foundation of China(08AJY024)the Key Project of Soft Science Foundation of China(2008GXS5D115)the Foundation of Doctoral Programs(200802870020,200902870032)the Foundation of Humanities and Social Sciences of Chinese National Ministry of Education(08JA630039)the Science Foundation ofthe Excellent and Creative Group of Science and Technology in Jiangsu Province(Y0553-091)the Foundation of Key Research Base of Philosophy and Social Science in Colleges and Universities of Jiangsu Province(2010JDXM015)the Foundation of Outstanding Teaching Group of China(10td128)~~
文摘The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey incidence model, the grey cluster model based on endpoint triangular whitenization functions, the grey cluster model based on center-point triangular whitenization functions, the grey prediction model of the model GM （ 1,1）, and the weighted multi-attribute grey target decision model.
文摘In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n).
文摘An unequal time interval sequence or a sequence with blanks is usually completed with average generation in grey system theory. This paper discovers that there exists obvious errors when using average generation to generate internal points of non-consecutive neighbours. The average generation and the preference generation of the sequence are discussed, the concave and convex properties show the status of local sequence and propose a new idea for using the status to build up the criteria of choosing generation coefficient. Compared with the general average method of the one-dimensional data sequence, the two-dimensional data sequence is defined and its average generation is discussed, and the coefficient decision method for the preference generation is presented.
