Function S-rough Sets and Their Law Characteristic

Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory.

粗规律生成与它的分离

利用函数S-粗集(function singular rough sets),给出粗规律生成,粗规律生成定理;利用这些结果,提出粗规律分离与粗规律分离定理,粗规律带复合生成定理与粗规律带原理;给出粗规律分离在利润风险规律识别中的应用。

■-law collision and system state recognition

Using dual function one direction S-rough sets, this article gives the f-law, the F-law, law distance and the concept of system law collided by the F-law. The characteristics presented by the system law collided by the F-law, the recognition of these characteristics and recognition criterion are also proposed. The dual function one direction S-rough sets is one of the basic forms of function S-rough sets. Its basic theory and application in the study of system law collision are reviewed.

(F,■)-规律推理与规律挖掘

给出了(F,■)-规律推理以及(F,■)-规律推理的规律挖掘概念,提出了(F,■)-规律推理的规律挖掘定理与(F,■)-规律推理的规律挖掘原理.

粗规律能量与F-分解粗规律度量

函数单向S-粗集对偶具有规律特性、动态特性。应用函数单向S-粗集对偶,给出f-分解规律、F-分解粗规律、规律能量、属性f-扰动度的概念;研究了粗规律F-分解过程中的变化度量;给出f-分解规律能量特性定理、f-分解规律能量不等式定理、F-分解粗规律能量特性定理以及f-分解规律能量中值定理。

规律与它的^-f-属性控制

函数单向S-粗集对偶(dual of function one direction singular rough set),具有单向动态特性和规律特性;它是函数S-粗集(function singular rough set)的基本形式之一。函数S-粗集是在改进S-粗集的基础上提出的。利用函数单向S-粗集对偶的动态特性和规律特性,给出-f-规律,-f-规律的属性特征,属性距离,-f-冗余规律概念。利用这些概念,提出规律与它的-f-属性控制,并给出-f-属性控制定理,-f-属性控制判定定理,-f-属性控制识别准则与应用。

函数单向S-粗集对偶生成的■-模型

利用函数单向S-粗集对偶,给出R-函数等价类[u(x)]的-模型与-t阶单向动态模型的生成及有关概念,给出■-模型与■-单向动态模型生成及有关概念,提出■-单向动态模型序关系定理及动态分离定理,■-模型的动态特征依赖于属性集α上的属性删除。利用这些讨论,给出■-模型生成原理及应用。

函数单向S-粗集对偶与■-预测规律发现

函数S-粗集理论是粗集理论的拓展,函数单向S-粗集对偶是函数S-粗集的三类形式之一.函数S-粗集具有规律特性、动态特性、遗传特性、记忆特性与预测特性.利用函数单向S-粗集对偶的动态特征,给出-预测规律、■-预测规律和预测度概念,提出预测规律的预测定理,并在通信传输识别系统中给出应用.函数S-粗集(函数单向S-粗集、函数单向S-粗集对偶、函数双向S-粗集)与信息系统融合、交叉是粗集理论中的一个新的研究方向.

■-规律挖掘

函数单向S-粗集对偶(dual function one direction singular rough sets)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。利用函数单向S-粗集对偶的规律特征,给出■-规律挖掘的概念,提出■-规律挖掘定理。■-规律挖掘是寻找经济发展中未知规律的一个新的研究方向。

系统的_p-状态与它的动态识别

函数单向S-粗集对偶是函数S-粗集(function singular rough sets)的基本形式之一.函数单向S-粗集对偶是研究系统规律入侵预测的一个重要的理论与方法.利用函数单向S-粗集对偶(Dual of function one direction singular rough sets),本文给出p-状态,状态距离的概念,系统状态被p-规律随机入侵的概念.进而给出系统状态被p-规律入侵呈现的状态特征及对这些状态特征的识别准则和应用.

系统■-规律入侵与识别

利用函数单向S-粗集对偶(dual function one direction singular rough sets),本文给出■-规律,■-规律,规律距离,系统规律被■-规律入侵的概念.利用这些概念,本文给出系统被■-规律入侵呈现的特征与对这些特征的识别,识别准则与应用.函数单向S-粗集对偶是函数S-粗集(function singular rough sets)的基本形式之一.函数单向S-粗集对偶是研究系统规律入侵的一个重要的理论与方法.

F-rough law and the discovery of rough law

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.

F-Law collision and system state recognition

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.

F-generation law and recognition of system law

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.

Rough law generation and its separation-recognition

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.

Hiding dependence-discovery of F-hiding laws and system laws

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.

The Hiding Characteristic of F-interior Hiding Image and Its Applications

By using function one direction S-rough sets,the concept of F-interior hiding image is presented; the theorem of F-interior hiding and the recognition criteria of interior hiding are proposed; and the applications of F-interior hiding image are given. F-interior hiding image is a new application area of function S-rough sets,and function S-rough sets is a new theory and new tools for iconology research.

■-二重粗积分与系统识别

以函数单向S-粗集对偶的上、下近似生成的函数为基础,提出了粗区域的定义,二重粗积分的定义及其动态特征,通过动态特征给出了扩张度和扩张率的概念,并且通过计算扩张度和扩张率来度量系统受干扰的程度。

函数S-粗集对偶与F-粗边际规律

函数单向S粗集对偶(dual offunction one direction singular rough sets)是函数S粗集的基本形式之一,函数单向S-粗集对偶具有动态特性与规律(函数)特性.函数S粗集(function singular rough sets)是把函数概念引入到S粗集内(singular rough sets)改进S粗集得到的把导数概念与函数单向S粗集对偶交叉、渗透给出粗边际规律F-粗边际规律概念;给出粗边际规律F-粗边际规律特征;给出F-粗边际规律与粗边际规律的关系;