Using S-rough sets, this paper gives the concepts off-heredity knowledge and its heredity coefficient, and f-variation coefficient of knowledge; presents the theorem of f-attribute dependence of variation coefficient ...Using S-rough sets, this paper gives the concepts off-heredity knowledge and its heredity coefficient, and f-variation coefficient of knowledge; presents the theorem of f-attribute dependence of variation coefficient and the relation theorem of heredity-variation. The attribute dependence of f-variation coefficient and the relation of heredity-variation are important characteristics of S-rough sets. From such discussion, this paper puts forward the heredity mining off-knowledge and the algorithm of heredity mining, also gives its relative application.展开更多
By the inductive relations,this paper first obtains some existence theorems of solutions for generalized quasi-variational relation problems,which are different from other papers.As applications,some existence theorem...By the inductive relations,this paper first obtains some existence theorems of solutions for generalized quasi-variational relation problems,which are different from other papers.As applications,some existence theorems of solutions for generalized quasi-equilibrium problems and NS-equilibria for noncooperative games under uncertainty are obtained.展开更多
The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundl...The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.展开更多
基金This project was supported by the National Natural Science Foundation of China (60364001), the Shandong ProvincialNatural Science Foundation of China (Y2004A04) and Fujian Provincial Education Foundation of China(JA04268).
文摘Using S-rough sets, this paper gives the concepts off-heredity knowledge and its heredity coefficient, and f-variation coefficient of knowledge; presents the theorem of f-attribute dependence of variation coefficient and the relation theorem of heredity-variation. The attribute dependence of f-variation coefficient and the relation of heredity-variation are important characteristics of S-rough sets. From such discussion, this paper puts forward the heredity mining off-knowledge and the algorithm of heredity mining, also gives its relative application.
基金supported the Chen Guang Project Sponsored by the Shanghai Municipal Education Commission and Shanghai Education Development Foundation under Grant No.13CG35Open Project of Key Laboratory of Mathematical Economics(SUFE),Ministry of Education under Grant No.201309KF02
文摘By the inductive relations,this paper first obtains some existence theorems of solutions for generalized quasi-variational relation problems,which are different from other papers.As applications,some existence theorems of solutions for generalized quasi-equilibrium problems and NS-equilibria for noncooperative games under uncertainty are obtained.
文摘The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.
