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
Using function one direction S-rough sets （function one direction singular rough sets）, f-law and F- law and the concept of law distance and the concept of system law collided by F-law are given. Using these concept...Using function one direction S-rough sets （function one direction singular rough sets）, f-law and F- law and the concept of law distance and the concept of system law collided by F-law are given. Using these concepts, state characteristic presented by system law collided by F-law and recognition of these states characteristic and recognition criterion and applications are given. Function one direction S-rough sets is one of basic forms of function S-rough sets （function singular rough sets）. Function one direction S-rough sets is importance theory and is a method in studying system law collision.展开更多
If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the...If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the system and leads it into turbulence. Using function one direction S-rough sets, this article gives the concept of the F-generation law in the system, the generation model of the F-generation law and the recognition method of the system law. Function one direction singular rough sets is a new theory and method in recognizing the disturbance law existing in the system and recognizing the system law.展开更多
对S-粗集给出改进,把函数这个分析工具引入到S-粗集中,提出函数S-粗集(function singularrough sets)。函数单向S-粗集(function one direction singular rough sets)是函数S-粗集的基本形式之一,它是以R-函数等价类[u]定义的;ui∈[u]...对S-粗集给出改进,把函数这个分析工具引入到S-粗集中,提出函数S-粗集(function singularrough sets)。函数单向S-粗集(function one direction singular rough sets)是函数S-粗集的基本形式之一,它是以R-函数等价类[u]定义的;ui∈[u]是一个函数,函数是一个规律。函数单向S-粗集具有单向动态特性与规律特征:利用函数单向S-粗集的规律特征,给出F-规律推理与F-规律推理的规律挖掘概念,提出F-规律推理的规律挖掘定理,F-规律推理的规律挖掘原理与F-规律推理的规律挖掘应用。F-规律推理的规律挖掘是寻找系统中未知规律研究的一个新的研究方向。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
By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law var...By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ^-F-decomposition is researched. The concepts of law energy and attdbute ^-f-interference degree are presented, which make the variation of rough law become measurable. ^-f-decomposition law energy characteristic theorem, ^-f- decomposition law energy inequality theorem, ^-F-decomposition rough law energy characteristic theorem, and ^-f-decomposition law energy mean value theorem are presented.展开更多
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the Natural Science Foundation of Shandong Province of China (Y2004A04)the Natural Science Foundation of Fujian Province of China (Z0511049).
文摘Using function one direction S-rough sets （function one direction singular rough sets）, f-law and F- law and the concept of law distance and the concept of system law collided by F-law are given. Using these concepts, state characteristic presented by system law collided by F-law and recognition of these states characteristic and recognition criterion and applications are given. Function one direction S-rough sets is one of basic forms of function S-rough sets （function singular rough sets）. Function one direction S-rough sets is importance theory and is a method in studying system law collision.
基金This project was supported by the Ministry of Education of China (206089)Shangdong Provincial Natural Science Foundation of China (Y2004A04)Fujian Provincial Natural Science Foundation of China (Z051049).
文摘If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the system and leads it into turbulence. Using function one direction S-rough sets, this article gives the concept of the F-generation law in the system, the generation model of the F-generation law and the recognition method of the system law. Function one direction singular rough sets is a new theory and method in recognizing the disturbance law existing in the system and recognizing the system law.
文摘对S-粗集给出改进,把函数这个分析工具引入到S-粗集中,提出函数S-粗集(function singularrough sets)。函数单向S-粗集(function one direction singular rough sets)是函数S-粗集的基本形式之一,它是以R-函数等价类[u]定义的;ui∈[u]是一个函数,函数是一个规律。函数单向S-粗集具有单向动态特性与规律特征:利用函数单向S-粗集的规律特征,给出F-规律推理与F-规律推理的规律挖掘概念,提出F-规律推理的规律挖掘定理,F-规律推理的规律挖掘原理与F-规律推理的规律挖掘应用。F-规律推理的规律挖掘是寻找系统中未知规律研究的一个新的研究方向。
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.
基金supported by the Natural Science Foundation of Shandong Province (Y2007H02)
文摘By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ^-F-decomposition is researched. The concepts of law energy and attdbute ^-f-interference degree are presented, which make the variation of rough law become measurable. ^-f-decomposition law energy characteristic theorem, ^-f- decomposition law energy inequality theorem, ^-F-decomposition rough law energy characteristic theorem, and ^-f-decomposition law energy mean value theorem are presented.
