全粒度粗糙集属性约简

全粒度粗糙集是一种动静结合的粗糙集模型,在一定程度上可以表示人类认识的复杂性、多样性和不确定性.文中定义概念的全粒度属性约简,完善全粒度粗糙集属性约简的定义.探索概念的全粒度属性约简、全粒度绝对约简及全粒度Pawlak约简的性质,指明这些属性约简之间的关系,有助于全粒度属性约简的实际应用及启发式算法的产生.     

基于模糊邻域粗糙集的启发式属性约简算法

属性约简是机器学习等领域中常用的数据预处理方法。在基于粗糙集理论的属性约简算法中,大多是根据单一的方法来度量属性重要度。为了从多角度对属性达到更为优越的评估效果,首先在已有的模糊邻域粗糙集模型中定义属性依赖度度量,然后根据粒计算理论中知识粒度的概念,在模糊邻域粗糙集模型下提出了模糊邻域粒度度量。由于属性依赖度和知识粒度代表了不同视角的属性评估方法,因此将这两种方法结合起来用于信息系统的属性重要度评估,最后给出一种启发式属性约简算法。实验结果表明,所提出的算法具有较好的属性约简性能。     

决策表属性约简的相对划分粒度表示

粗糙集理论认为知识就是分类.本文对知识的分类能力给予了量化,提出利用划分粒度来定量地表示知识的分类能力.在划分粒度概念基础上,针对决策表定义了相对划分粒度并研究了它的性质,相对划分粒度可以定量表示决策表的条件属性子集相对于决策属性的分类能力的强弱;最后证明了对一致决策表的属性约简来说,相对划分粒度表示与Pawlak提出的代数表示是等价的.     

基于粒度计算的属性约简算法研究

从粒度计算的角度对粗糙集理论的属性约简进行研究,分别基于代数方法和信息论方法定义了粒度差和粒度熵的概念,并在此基础上提出了两种新的属性约简算法.实验分析表明,这两种可靠有效的粒度计算方法都能得到信息表的最小约简,为进一步研究知识的粒度计算提供了可行的方法.     

一种基于矩阵的知识粒度计算方法

不确定性是粗糙集理论研究中的热点问题之一,而知识粒度是度量知识系统不确定性的一种重要方法.文中从矩阵的视角探讨知识粒度、粗糙度和属性重要度等概念的计算方法并分析知识粒度矩阵算式的内在含义,揭示出知识粒度与等价关系矩阵之间的关系.在提出知识粒层次结构的基础上进一步探讨了属性增删时知识粒度的变化规律.最后结合属性增删时不可分辨关系矩阵的更新将属性重要度的矩阵计算方法应用于求属性集的核集和最小约简中,算例表明属性重要度的矩阵计算方法在属性约简中的有效性.     

可区分度与全粒度属性约简

全粒度粗糙集时空复杂度较高,难于计算属性约简.针对此问题,文中利用等价类定义信息系统中的可区分度,并研究其性质,证明基于可区分度的属性约简等价于绝对约简.定义决策系统中的正区域可区分度,并探究其性质,证明基于正区域可区分度约简是全粒度Pawlak约简的超集,但绝大部分情况下等于全粒度Pawlak约简,可作为全粒度Pawlak约简的近似.理论分析和实验表明,相比其它属性约简算法,基于正区域可区分度约简在计算复杂度和分类准确率等方面具有较大优势.     

粗糙集概念与运算的知识粒度表示

探讨了知识粒度的一些重要性质和定理。在此基础上,从知识粒度的角度对粗糙集进行研究,给出了粗糙集中主要概念与运算的知识粒度表示,最后证明了属性约简在知识粒度与代数两种不同表示下是等价的。     

F-粗糙集视角的概念漂移与属性约简

概念漂移探测是数据流挖掘具有挑战意义的研究难点,属性约简是粗糙集理论的研究核心.从概念漂移的角度研究了粗糙集理论的属性约简,从粗糙集属性约简的角度研究了概念漂移,将概念漂移和属性约简进行分析比较,指出了它们之间的区别和联系.提出了基于属性依赖度和条件熵的概念漂移探测准则,并将两种常用的概念漂移探测准则与属性依赖度、条件熵探测准则进行了比较.属性依赖度和条件熵兼具分类准确率的可实验检验和联合概率分布可进行理论分析的优点,还可以进行属性约简（或特征选择）.实验结果显示,属性依赖度、条件熵和分类准确率都能有效地探测概念漂移,但是,与分类准确率相比,属性依赖度和条件熵在探测概念漂移时可以增加可重用性,减少工作量.属性约简和概念漂移之间关系的研究为属性约简、概念漂移的研究提供了新方法,为粗糙集、粒计算进一步融入大数据时代潮流提供了新思路.     

基于粗糙集理论的粒度计算研究及其应用

经典的粗糙集理论提出知识是有粒度的,但它没有量化信息粒度所表示的信息量.本文定义了知识粒数,知识粒的微粒数,平均微粒数,近1系数,知识粒度的概念;提出了知识粒度的量化计算方法;提出了一种基于知识粒度的属性约简算法以避免选择约简子集的盲目性:给出了时间复杂度证明;通过海上交通事故的决策实例证明所提出的粒度计算方法是可行有效的.     

基于信息粒度的属性约简算法研究

该文从粒度计算的角度对粗糙集理论的属性约简进行研究,定义了粒度的概念,并在此基础上提出了一种新的属性约简算法。实验分析表明,这种粒度计算方法能得到信息系统的最小约简。     

F-邻域粗糙集及其约简

邻域粗糙集可以直接处理数值型数据,F-粗糙集是第一个动态粗糙集模型.针对动态变化的数值型数据,结合邻域粗糙集和F-粗糙集的优势,提出了F-邻域粗糙集和F-邻域并行约简.首先,定义了F-邻域粗糙集上下近似、边界区域;其次,在F-邻域粗糙集中提出了F-属性依赖度和属性重要度矩阵;根据F-属性依赖度和属性重要度矩阵分别提出了...     

Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets

Fuzzy rough sets are considered as an effective tool to deal with uncertainty in data analysis, and fuzzy similarity relations are used in fuzzy rough sets to calculate similarity between objects. On the other hand in kernel tricks, a kernel maps data into a higher dimensional feature space where the resulting structure of the learning task is linearly separable, while the kernel is the inner product of this feature space and can also be viewed as a similarity function. It has been reported there is an overlap between family of kernels and collection of fuzzy similarity relations. This fact motivates the idea in this paper to use some kernels as fuzzy similarity relations and develop kernel based fuzzy rough sets. First, we consider Gaussian kernel and propose Gaussian kernel based fuzzy rough sets. Second we introduce parameterized attribute reduction with the derived model of fuzzy rough sets. Structures of attribute reduction are investigated and an algorithm with discernibility matrix to find all reducts is developed. Finally, a heuristic algorithm is designed to compute reducts with Gaussian kernel fuzzy rough sets. Several experiments are provided to demonstrate the effectiveness of the idea.     

多粒度粗糙集的双层绝对约简*

多粒度粗糙集本质上是异构的,但是目前尚未运用于异构数据处理.从绝对约简的角度出发,提出多粒度粗糙集的双层绝对约简——多粒度绝对约简和多粒度绝对粒度约简.分析多粒度双层绝对约简的性质,特别是从异构数据约简的角度探究多粒度双层绝对约简的特性,提出多粒度双层绝对约简算法.理论分析和实例表明多粒度双层绝对约简算法的可行性.     

Induction of multiple fuzzy decision trees based on rough set technique

The integration of fuzzy sets and rough sets can lead to a hybrid soft-computing technique which has been applied successfully to many fields such as machine learning, pattern recognition and image processing. The key to this soft-computing technique is how to set up and make use of the fuzzy attribute reduct in fuzzy rough set theory. Given a fuzzy information system, we may find many fuzzy attribute reducts and each of them can have different contributions to decision-making. If only one of the fuzzy attribute reducts, which may be the most important one, is selected to induce decision rules, some useful information hidden in the other reducts for the decision-making will be losing unavoidably. To sufficiently make use of the information provided by every individual fuzzy attribute reduct in a fuzzy information system, this paper presents a novel induction of multiple fuzzy decision trees based on rough set technique. The induction consists of three stages. First several fuzzy attribute reducts are found by a similarity based approach, and then a fuzzy decision tree for each fuzzy attribute reduct is generated according to the fuzzy ID3 algorithm. The fuzzy integral is finally considered as a fusion tool to integrate the generated decision trees, which combines together all outputs of the multiple fuzzy decision trees and forms the final decision result. An illustration is given to show the proposed fusion scheme. A numerical experiment on real data indicates that the proposed multiple tree induction is superior to the single tree induction based on the individual reduct or on the entire feature set for learning problems with many attributes.     

两类关联约简构造性算法研究

关联约简由Dominik首次提出,其采用粗糙集理论属性约简思想,从全局属性依赖的角度,挖掘出信息系统中所隐含的关联规则。由于求取给定信息系统所有关联约简和最优关联约简已被证明为NP-难问题,针对特定属性（事务）给出了两类关联约简构造性算法：Multi-Single算法和Single-Multi算法,从而挖掘出针对特定事务的关联规则,有益于综合评价各事务在信息系统中的作用。实例分析表明了所提算法的有效性。     

Fuzzy preference based rough sets

Preference analysis is an important task in multi-criteria decision making. The rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations. The existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria. In this paper, we introduce a method to extract fuzzy preference relations from samples characterized by numerical criteria. Fuzzy preference relations are incorporated into a fuzzy rough set model, which leads to a fuzzy preference based rough set model. The measure of attribute dependency of the Pawlak’s rough set model is generalized to compute the relevance between criteria and decisions. The definitions of upward dependency, downward dependency and global dependency are introduced. Algorithms for computing attribute dependency and reducts are proposed and experimentally evaluated by using two publicly available data sets.     

Fuzzy rough set based attribute reduction for information systems with fuzzy decisions

Fuzzy rough set is a generalization of crisp rough set to deal with data sets with real value attributes. A primary use of fuzzy rough set theory is to perform attribute reduction for decision systems with numerical conditional attribute values and crisp (symbolic) decision attributes. In this paper we define inconsistent fuzzy decision system and their reductions, and develop discernibility matrix-based algorithms to find reducts. Finally, two heuristic algorithms are developed and comparison study is provided with the existing algorithms of attribute reduction with fuzzy rough sets. The proposed method in this paper can deal with decision systems with numerical conditional attribute values and fuzzy decision attributes rather than crisp ones. Experimental results imply that our algorithm of attribute reduction with general fuzzy rough sets is feasible and valid.     

基于动态加权的粗糙子空间集成

提出一种基于动态加权的粗糙子空间集成方法EROS-DW。利用粗糙集属性约简方法获得多个特征约简子集,并据此训练基分类器。在分类阶段,根据给定待测样本的具体特征动态地为每个基分类器指派相应的权重,采用加权投票组合规则集成各分类器的输出结果。利用UCI标准数据集对该方法的性能进行测试。实验结果表明,相较于经典的集成方法,EROS-DW方法可以获得更高的分类准确率。