S-rough sets and the discovery of F-hiding knowledge

Singular rough sets （S-rough sets） have three classes of forms： one-directional S-rough sets, dual of onedirectional S-rough sets, and two-directional S-rough sets. Dynamic, hereditary, mnemonic, and hiding properties are the basic characteristics of S-rough sets. By using the S-rough sets, the concepts of f-hiding knowledge, F-hiding knowledge, hiding degree, and hiding dependence degree are given. Then, both the hiding theorem and the hiding dependence theorem of hiding knowledge are proposed. Finally, an application of hiding knowledge is discussed.     

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。     

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.     

f-heredity knowledge and f-heredity mining

1. INTRODUCTION Professor Z.Pawlak, a Poland mathematician, putforward rough sets theory in 1982[1] and gave aprimary discussion about it. Ref. [2] developed roughsets into S-rough sets and gave a further discussion; Refs[3~5] put forward the heredity characteristics (F-heredity, F -heredity, F-heredity)of S-roughsets.There exists such a phenomena in S-rough sets:Suppose U={x1,x2,x3,x4,x5} is an element universe,α={α1,α2} is the attributes in U,[x]α is the knowledgewith attribute…     

f-heredity knowledge and f-heredity mining

Using S-rough sets, this paper gives the concepts of f-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 of f-knowledge and the algorithm of heredity mining, also gives its relative application.     

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。     

S-rough sets and knowledge separation

1.INTRODUCTION GivensetX U,Risanequivalencerelationfamily ofU;[x]R;isanR equivalenceclass,andwehave Z.Pawlakroughsets(R-(X),R-(X))[10].Inset Uthereareriskelementswhichexistinriskestima tionsystem,earlywarninganalysissystem,etc.We can’tascertaintheirincursionorintrusiontosetX Uinprevious;theseelementshavethefollowingtwo features:u∈U,u∈-X f(u)=x∈X;x∈X f(x)=u∈-X.Inotherwords,duetotheeffectof f∈F,elementuwhichisnotinXturnsintof(u)=x,f(u)goesintoX;elementxwhichisinX,turnsinto f…     

S-粗集与它的分解-还原

利用S-粗集(singular     

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…     

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-interference law generation and its feature recognition

By using two-directional S-rough sets, the concepts of (f, ¯ f)-interference generation and (f, ¯ f)- interference law generation of knowledge, F-interference generation and F-interference law generation of two-directional S-rough sets are proposed. Based on the concepts above, the relation theorems between F- interference loss and F-interference degree, the relation theorems between F-interference loss law and F-interference degree law, the discernibility theorems between F-interference and F-interference law are presented. At last, the recognition criterion of F-interference law and its application are given.     

单向S-粗决策规律与决策规律挖掘

利用单向S-粗集,给出单向S-粗决策规律生成方法;给出上决策规律,下决策规律,单向S-粗决策规律核,单向S-粗决策规律带,单向S-粗决策规律壳的概念;利用这些概念,提出下决策规律传递定理,上决策规律传递定理,F-分离的属性定理,粗决策规律挖掘定理,与粗决策规律挖掘准则。     

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。     

S-Rough communication and its characteristics

In view of certain defects of common rough communication, using the S-rough sets, this article presents a S-rough communication model. The S-rough communication model is the extension of the common rough communication model. S-rough communication has two kinds of forms: one-direction S-rough communication and two-direction S-rough communication. The mathematical structure and characteristics of the one-direction S-rough communication and the two-direction S-rough communication, the relationship theorem between the one-direction S-rough communication and the two-direction S-rough communication are also presented. The S-rough communication is a dynamic communication method, and it is a novel research direction in rough sets field.     

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.     

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.     

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…     

P-集合与动态信息的依赖-发现

P-集合是一个集合对,它是由内P-集合(internal packet set)与外P-集合(outer packet set)共同构成。P-集合具有动态特征,是通过改进普通集合得到的,或者用动态特性代替普通集合的静态特性,也可得到P-集合。利用P-集合的结构与动态特性,给出动态信息生成和动态度的概念,提出动态信息生成的依赖特性、动态信息依赖、信息依赖-发现定理和信息依赖-发现准则等。最后,给出动态信息依赖-发现在信息状态识别中的应用。     

S-粗集与新材料发现-识别

S-粗集(singular rough sets)具有两类形式:单向S-粗集(one direction S-rough sets)和双向S-粗集(two direction S-rough sets)。S-粗集具有遗传特征、记忆特征。把S-粗集与材料科学进行学科渗透,互补共享,给出新金属材料的发现-识别的讨论,利用属性生成模型给出新金属材料的属性值分析,给出的结果与实际相符。S-粗集是粗集研究的一个新方向,是新材料发现-识别的一个新的数学工具。     

基于S-粗集的图像阈值分割方法

介绍了S-粗集的概念, 结合其动态迁移特性给出了可以适应复杂背景和含噪环境的图像S-粗集表示模型, 使静态目标可以将"不好"特性像素点迁移出去. 利用粗糙熵平衡目标和背景粗糙度对边界的影响, 提出一种更具适应性的 图像阈值分割算法. 为了适应离散点的迁移, 同时避免粒度大小的选择, 结合包含度概念给出了图像变精度S-粗集表示模型, 利用精度参数来 控制调节获取最佳分割阈值, 实现目标提取. 仿真实验表明, 所提出算法具有更好的图像分割效果.