Based on S-rough sets(singular rough sets), this paper presents function S-rough sets (function singular rough sets)and its mathematical structures and features. Function S-rough sets has two forms: function one ...Based on S-rough sets(singular rough sets), this paper presents function S-rough sets (function singular rough sets)and its mathematical structures and features. Function S-rough sets has two forms: function one direction S-rough sets (function one direction singular rough sets) and function two direction S-rough sets (function two direction singular rough sets). This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.展开更多
Function S-rough sets (function singular rough sets) is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives...Function S-rough sets (function singular rough sets) is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.展开更多
By using function one direction S-rough sets (function one direction singular rough sets), this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, thi...By using function one direction S-rough sets (function one direction singular rough sets), this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.展开更多
By using function S-rough sets(function singular rough sets), this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the ...By using function S-rough sets(function singular rough sets), this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.展开更多
Function one direction S-rough sets have dynamic characteristics and law characteristics. By using the function one direction S-rough sets, this article presents the concepts of the f-hiding law, F-hiding law, f-hidin...Function one direction S-rough sets have dynamic characteristics and law characteristics. By using the function one direction S-rough sets, this article presents the concepts of the f-hiding law, F-hiding law, f-hiding law dependence and F-hiding law dependence. Based on the concepts above, this article proposes the hidingdependence theorem of f-hiding laws, the hiding-dependence theorem of F-hiding laws, the hiding-dependence separation theorem, the hiding dependence-discovery principle of unknown laws. Finally, the application of the hiding dependence of hiding laws in the discovery of system laws is given.展开更多
基金This project was surpported by the Natural Science Foundation of Shandong Province of China (Y2004A94)
文摘Based on S-rough sets(singular rough sets), this paper presents function S-rough sets (function singular rough sets)and its mathematical structures and features. Function S-rough sets has two forms: function one direction S-rough sets (function one direction singular rough sets) and function two direction S-rough sets (function two direction singular rough sets). This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.
基金This project was supported by Natural Science Foundation of Shandong Province of China (Y2004A04), Natural ScienceFoundation of Fujian of China (Z051049) and Education Foundation of Fujian of China (JA04268),.
文摘Function S-rough sets (function singular rough sets) is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.
基金supported by the Natural Science Foundation of Shandong Province(Y2007H02)Natural Science Foundation of Fujian Province(S0650031)
文摘By using function one direction S-rough sets (function one direction singular rough sets), this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.
基金supported partly by the Natural Science Foundation of Shandong Province of China (Y2007Ho2)the Elementary and Advanced Technology Foundation of Henan Province of China (082300410040)
文摘By using function S-rough sets(function singular rough sets), this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.
基金supported partly by the Natural Science Foundation of Shandong Province(Y2004A04)Elementaryand Advanced Technology Foundation of Henan Province(082300410040)
文摘Function one direction S-rough sets have dynamic characteristics and law characteristics. By using the function one direction S-rough sets, this article presents the concepts of the f-hiding law, F-hiding law, f-hiding law dependence and F-hiding law dependence. Based on the concepts above, this article proposes the hidingdependence theorem of f-hiding laws, the hiding-dependence theorem of F-hiding laws, the hiding-dependence separation theorem, the hiding dependence-discovery principle of unknown laws. Finally, the application of the hiding dependence of hiding laws in the discovery of system laws is given.