F-规律推理与规律挖掘

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。     

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S-粗集与粗规律挖掘-分离

研究了函数S-粗集的本质和特性,及其用于挖掘系统的潜在规律。利用函数S-粗集(单向函数S-粗集,双向函数S-粗集)的数学结构和特性,给出系统中粗规律模型的生成方法。给出了利用函数S-粗集进行系统中的粗规律挖掘与分离的讨论,和系统中粗规律分离的应用。例子证明,函数S-粗集是系统规律挖掘的一个有力工具。     

(F)-风险属性入侵与承灾规律识别

针对公共突发事件的动态性、不确定性和危害性,利用单向S-粗集对偶(dual ofone direction sin-gular rough sets)给出承灾类、承灾量、F-承灾损失、F-承灾度、F-承灾损失规律、F-承灾度规律的概念,利用这些概念提出了F-承灾损失与F-承灾度关系定理,F-承灾损失规律与F-承灾度规律关系定理,F-风险属性入侵规律分辨定理,F-承灾度规律识别准则与应用.单向S-粗集是应急管理理论与方法研究中的一个新的有效的数学工具.     

■-风险属性入侵与承灾规律识别

针对公共突发事件的动态性、不确定性和危害性,利用单向S-粗集对偶(dual of one direction singular rough sets)给出承灾类、承灾量、■-承灾损失、■-承灾度、■-承灾损失规律、■-承灾度规律的概念,利用这些概念提出了■-承灾损失与■-承灾度关系定理,■-承灾损失规律与■-承灾度规律关系定理,■-风险属性入侵规律分辨定理,■-承灾度规律识别准则与应用。单向S-粗集是应急管理理论与方法研究中的一个新的有效的数学工具。     

一种基于单向变异S-概率粗集的动态决策方法

针对因决策因素个数的减少而导致的决策精度降低的情况,提出了一种基于单向变异S-概率粗集的动态决策方法。利用单向变异S-概率粗集的属性动态迁移特性,结合知识库中的统计信息,讨论了单向变异S-概率粗集模型的属性概率性质。利用上述性质的讨论,给出了一个具体的军事动态决策实例,从而证明该方法可以有效地提高决策精度。     

■-生成规律与系统规律识别

一个系统(控制系统、通讯系统)没有受到某个规律的干扰(或攻击),则系统处于稳定运动状态或者按预定的规律运动。未知规律进入到系统中,对系统进行干扰,使得系统的运动规律紊乱。利用函数单向S-粗集对偶(dual of function one direction singular rough sets),给出系统中■-生成规律的概念,给出■-生成规律的生成模型和对系统规律的识别。函数单向S-粗集对偶是识别系统中存在干扰规律,识别系统规律的一个新的理论与方法。     

-生成规律与系统规律识别

一个系统(控制系统、通讯系统)没有受到某个规律的干扰(或攻击),则系统处于稳定运动状态或者按预定的规律运动.未知规律进入到系统中,对系统进行干扰,使得系统的运动规律紊乱.利用函数单向S-粗集对偶(dual of function one direction singular rough sets),给出系统中(-F)-生成规律的概念,给出(-F)-生成规律的生成模型和对系统规律的识别.函数单向S-粗集对偶是识别系统中存在干扰规律,识别系统规律的一个新的理论与方法.     

(-F)-生成规律与系统规律识别

一个系统(控制系统、通讯系统)没有受到某个规律的干扰(或攻击),则系统处于稳定运动状态或者按预定的规律运动.未知规律进入到系统中,对系统进行干扰,使得系统的运动规律紊乱.利用函数单向S-粗集对偶(dual of function one direction singular rough sets),给出系统中(-F)-生成规律的概念,给出(-F)-生成规律的生成模型和对系统规律的识别.函数单向S-粗集对偶是识别系统中存在干扰规律,识别系统规律的一个新的理论与方法.     

单向S-粗集对偶与数据筛选-过滤的扩展应用

S-粗集(singular rough sets)是对Z.Pawlak粗集的改进,单向S-粗集对偶(dual of one direction sin-gular rough sets)是S-粗集的基本形式之一。利用单向S-粗集对偶,给出数据属性,数据筛选-过滤概念,数据筛选-过滤序定理,合成数据筛选-过滤定理,及数据筛选-过滤准则。利用这些结果,给出应用。单向S-粗集对偶是动态数据筛选-过滤研究的一个新工具。     

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.     

Rough law energy and measurement of ¯F-decomposition rough law

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 attribute ¯ f-interference degree are presented, which make the variation of rough law become measurable. ¯ f-decomposition law energy characteristic theorem, ¯ fdecomposition law energy inequality theorem, ¯ F-decomposition rough law energy characteristic theorem, and ¯ f-decomposition law energy mean value theorem are presented.     

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.     

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 hiding-dependence theorem of f-hiding laws, the hiding-dependence theorem of F-hiding laws, the hiding-dependence separation theorem, the hiding dependencs-discovery principle of unknown laws. Finally, the application of the hiding dependence of hiding laws in the discovery of system laws is given.     

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.     

S-粗集与F-隐藏知识发现

S-粗集具有三类形式:单向S-粗集,双向S-粗集,单向S-粗集对偶。S-粗集具有动态特性,遗传特性,记忆特性。利用单向S-粗集对偶与它的隐藏特性,本文给出f-隐藏知识,F-隐藏知识,隐藏度,隐藏依赖的概念,提出隐藏知识的隐藏定理,隐藏知识的隐藏依赖定理,给出F-隐藏与F-隐藏依赖在系统状态识别中的应用。     

Function S-Rough sets and its applications

1 .INTRODUCTIONBased on S-rough sets(singular rough sets)[3 ~14],Refs .[1 ,2] presented function S-rough sets (func-tion singular rough sets) and its two forms :func-tion one direction S-rough sets (function one direc-tion singular rough sets) and function two direc-tion S-rough sets (function two direction singularrough sets) . Function S-rough sets is obtained toresearch mining discovery . Let’s see a practicalsystem: The output state of a system can be de-scribed by the function set…     

Function S-rough sets and mining-discovery of rough law in systems

1. INTRODUCTION S-rough sets (singular rough sets) was presented in Ref. [3] in 2002, and defined on α -element equival- ence class [x] with dynamic characteristic. S-rough sets has more advantages than Z.Pawlak’s rough sets[24]. S-rough sets has been applied in dynamic object recognition[21], mechanical engineering[22] and information science[8-13]. In 2005, function S-rough sets was put forward in Refs. [1,2], and is defined on α -function equivalence class [u] with dynamic charact…     

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.