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 one-directional 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。     

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…     

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-粗集与它的分解-还原

利用S-粗集(singular     

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…     

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。     

函数S-粗集与图像识别

函数S-粗集是以函数等价类定义的,它具有规律特性,图像具有特征,特征存在着规律,将函数S-粗集的规律特性嫁接,应用到识别理论中。给出图像特征F-下近似规律,F-上近似规律的生成,及规律模型,给出图像特征规律F-识别对结构,并对图像F-识别给出特性分析。图像F-识别是一种新的识别方法,已经成为识别理论研究中的一个新的研究方向。     

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.     

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…     

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-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.     

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-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−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.     

Security transmission and recognition of F-knowledge

The concept of F-knowledge is presented by employing S-rough sets. By engrafting and penetrating between the F-knowledge generated by S-rough sets and the RSA algorithm, the security transmission and recognition of multi-agent F-knowledge are proposed, which includes the security transmission of multi-agent F-knowledge with positive direction secret key and the security transmission of multi-agent F-knowledge with reverse direction secret key. Finally, the recognition criterion and the applications of F-knowledge are presented. The security of F-knowledge is a new application research direction of S-rough sets in information systems.     

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.     

面向证券投资的动态知识发现系统设计与实现

针对传统证券投资技术分析方法所存在的不足，通过对粗集理论、神经网络学习机理的研究。提出了面向证券投资的动态知识发现系统的基本框架．基于此框架，设计出面向证券投资的动态知识发现系统，并详细阐述了系统的各组成部分的设计思想及实现．最后结合实例，验证了系统的有效性、可行性．     

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS II： M（n）/G/1/K

We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M（n）/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O（K^3）.     

Fault-tolerant control of linear uncertain systems using H∞ robust predictive control

The robust fault-tolerant control problem of linear uncertain systems is studied. It is shown that a solution for this problem can be obtained from a H∞ robust predictive controller （RMPC） by the method of linear matrix inequality （LMI）. This approach has the advantages of both H∞ control and MPC： the robustness and ability to handle constraints explicitly. The robust closed-loop stability of the linear uncertain system with input and output constraints is proven under an actuator and sensor faults condition. Finally, satisfactory results of simulation experiments verify the validity of this algorithm.