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。     

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。     

■-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。     

■-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。     

-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.     

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。     

(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.     

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。     

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。     

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-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.     

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…     

S-粗集与它的分解-还原

利用S-粗集(singular     

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.     

一种基于函数S-粗集的态势预测方法

针对态势评估中未来可能出现态势的优劣情况,提出了一种基于函数S-粗集的态势预测方法。利用函数S-粗集的粗规律挖掘功能,采用拉格朗日插值多项式,以函数单向S-粗集对偶为例,给出了应用该方法的具体步骤。最后通过态势评估中一个具体实例证明了该方法的有效性。得到了运用函数S-粗集能够找到隐藏在系统中的粗规律的结论。     

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.     

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。