基于并不可约元的面向对象概念格的属性约简

概念格的属性约简是知识处理的重要研究问题之一。提出了一种面向对象概念格的属性约简方法。首先介绍了求面向对象概念格中并不可约元的方法,进而给出了面向对象概念格的并不可约元的外延集与面向对象概念格的协调集和约简集之间的关系,在此基础上,给出面向对象概念格的属性特征、并不可约元的外延集、属性等价类三者间的关系,最后利用这三者间的关系给出了面向对象概念格的约简集的构造。     

Reduction method based on a new fuzzy rough set in fuzzy information system and its applications to scheduling problems

In this paper, we present the concept of fuzzy information granule based on a relatively weaker fuzzy similarity relation called fuzzy T_L-similarity relation for the first time. Then, according to the fuzzy information granule, we define the lower and upper approximations of fuzzy sets and a corresponding new fuzzy rough set. Furthermore, we construct a kind of new fuzzy information system based on the fuzzy T_L-similarity relation and study its reduction using the fuzzy rough set. At last, we apply the reduction method based on the defined fuzzy rough set in the above fuzzy information system to the reduction of the redundant multiple fuzzy rule in the scheduling problems, and numerical computational results show that the reduction method based on the new fuzzy rough set is more suitable for the reduction of multiple fuzzy rules in the scheduling problems compared with the reduction methods based on the existing fuzzy rough set.     

一种基于规则的属性约简算法

Reduction of attributes is one of important topics in the research on rough set theory.Wong S K M and Ziarko W have proved that finding the minimal attribute reduction of decision table is a NP-hard problem.Algorithm A (the improved algorithm to Jelonek) choices optimal candidate attribute by using approximation quality of single attribute,it improves efficiency of attribute reduction,but yet exists the main drawback that the single atribute having maximum approxiamtion quality is probably optimal candidate attribute.Therefore,in this paper, we introduce the concept of compatible decision rule,and propose an attribute reduction algorithm based on rules (ARABR).Algorithm ARABR provides a new method that measures the relevance between extending attribute and the set of present attributes,the method assures that the optimal attribute is extended,and obviously reduces the search space.Theory analysis shows that algorithm ARABR is of lower computational complexity than Jelonek's algorithm,and overcomes effectively the main drawback of algorithm A.     

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。     

一种基于结构分解和因子分析的贝叶斯网络隐变量发现算法

通过研究粗糙集与图论的关系,提出了以集合为权的加权多重完全多部图的概念,定义了加权多重完全多部图的邻接矩阵,得到了加权完全多部图与决策表的映射关系;给出了粗糙集决策表信息系统的图论形式和决策表信息系统属性约简的图论方法,并根据图论理论对算法进行了优化;得到了在决策表信息系统中,属性的集合不可以约简的充分必要条件;并进一步提出了基于属性置信度的计算方法和多决策属性的处理方法。编程实验结果证明该方法能有效地降低时间和空间复杂度。     

概念层次中基于粗糙集的优化可信规则获取

随着系统中数据量剧增,规则太多以及不同决策者对规则有不同层次需求等问题,概念层次提供了一种解决方法。讨论条件属性具有概念层次的情况下,利用粗糙集理论分析属性在不同层次组合下的正域和规则关系,自顶向下提出了概念层次中基于粗糙集的优化可信规则获取的算法。该算法改进了现有的属性约简策略,借助描述子实现属性约简并获取优化可信规则。考虑到层次上正域为空和正域没有新增对象的特殊情况,提高了规则获取的效率。最后通过实例分析说明该算法的可行性。     

A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets

Traditional rough set theory is mainly used to extract rules from and reduce attributes in databases in which attributes are characterized by partitions, while the covering rough set theory, a generalization of traditional rough set theory, does the same yet characterizes attributes by covers. In this paper, we propose a way to reduce the attributes of covering decision systems, which are databases characterized by covers. First, we define consistent and inconsistent covering decision systems and their attribute reductions. Then, we state the sufficient and the necessary conditions for reduction. Finally, we use a discernibility matrix to design algorithms that compute all the reducts of consistent and inconsistent covering decision systems. Numerical tests on four public data sets show that the proposed attribute reductions of covering decision systems accomplish better classification performance than those of traditional rough sets.     

Multi-level rough set reduction for decision rule mining

Most previous studies on rough sets focused on attribute reduction and decision rule mining on a single concept level. Data with attribute value taxonomies (AVTs) are, however, commonly seen in real-world applications. In this paper, we extend Pawlak’s rough set model, and propose a novel multi-level rough set model (MLRS) based on AVTs and a full-subtree generalization scheme. Paralleling with Pawlak’s rough set model, some conclusions related to the MLRS are given. Meanwhile, a novel concept of cut reduction based on MLRS is presented. A cut reduction can induce the most abstract multi-level decision table with the same classification ability on the raw decision table, and no other multi-level decision table exists that is more abstract. Furthermore, the relationships between attribute reduction in Pawlak’s rough set model and cut reduction in MLRS are discussed. We also prove that the problem of cut reduction generation is NP-hard, and develop a heuristic algorithm named CRTDR for computing the cut reduction. Finally, an approach named RMTDR for mining multi-level decision rule is provided. It can mine decision rules from different concept levels. Example analysis and comparative experiments show that the proposed methods are efficient and effective in handling the problems where data is associated with AVTs.     

基于OE-概念格的形式背景属性约简

在三支概念格的属性约简框架下,借助布尔矩阵理论,研究保持OE-对象粒矩阵不变的属性约简问题。给出OE-对象粒矩阵的概念以及OEG粒协调集的定义,在此基础之上讨论属性之间的相似性,并且刻画属性的内外重要度。针对对象导出三支概念格的形式背景设计基于矩阵理论的启发式属性约简算法。将上述理论结果应用于对象导出三支概念格的决策形式背景,提出三支协调决策形式背景及OEG粒协调集的概念,并且从规则提取的角度说明约简集对应的OE-概念格的决策形式背景的三支规则集比原背景的三支规则集更加简洁。通过数值实验阐明该理论的可行性和合理性。     

概念格中基于粗糙熵的属性约简方法

属性约简是概念格理论的研究重点内容之一。通过将粗糙熵引入概念格理论中,定义了一种粗糙熵约简。首先,基于所有概念外延定义了形式背景的粗糙熵,并分析了它的性质;其次,定义了形式背景的粗糙熵约简,并揭示了粗糙熵约简与概念格约简之间的关系;在此基础上,基于属性重要度设计了计算粗糙熵的启发式算法,并通过实验验证了该算法的有效性。     

基于粗糙集的教育网站综合评价研究

教育网站的综合评价对教育信息化资源建设与发展具有重要的意义.依据粗糙集理论的对象分类能力,通过属性约简,删除冗余属性,有效简化评价指标体系.以知识的信息量概念为基础对属性的重要性进行定义,得到了指标权重确定方法.在此基础上建立了教育网站的综合评价模型,由此对评价对象进行排序选优,从而得到教育网站综合评价的新方法.最后通过实例验证了该方法的实用性和可行性.     

基于粗集理论和神经网络的集成化数据挖掘方法研究

为了从大型数据库中获取有用的知识，本文提出了一种基于粗集理论和神经网络的集成化数据挖掘方法。论文以所提出的研究框架为基础，首先给出了一种改进的粗集属性约简的算法和消除冗余属性的方法，进而采用面向对象的概念泛化进一步对数据库进行属性约简，最后用相似权值法得到产生式规则，并将所得规则用决策树来表示，通过一个完整的应用实例演示了本文方法，证实了其有效性。     

基于粗概念格模型的电子商务领域本体的构建研究

以构建电子商务系统中的本体为出发点,分析现有的本体构建技术中存在的缺陷。针对这些不足,综合考虑变精度粗糙集模型和形式概念分析的相关理论,提出基于粗概念格模型来构建本体。将变精度粗糙集的β选取算法和可辨识矩阵属性约简算法进行了改进,使β 上、下分布的约简方法适用于形式背景的约简,从而提出基于变精度粗糙集的概念格约减算法;然后计算语义概念相似度,并以联合国标准产品与服务分类代码的本体元模型为核心本体,结合领域专家知识,建立电子商务领域本体模型。实验表明了粗概念格构建本体的高效性。     

Conditional entropy for incomplete decision systems and its application in data mining

Rough set theory is a useful mathematic tool for dealing with vague and uncertain information. Shannon's entropy and its variants have been applied to measure uncertainty in rough set theory from the viewpoint of information theory. However, few studies have been carried out on information-theoretical measure of attribute importance in incomplete decision system (IDS) considering the relation between decision attribute and condition attributes. In this paper, we introduce the concept of conditional entropy together with entropy and joint entropy in IDSs. By using the new conditional entropy, we propose a measure for attribute importance. Based on the measure, a heuristic attribute reduction algorithm is presented. Some test experiments on real-lift data-sets show the effectiveness of the algorithm. The attribute importance measure and the attribute reduction algorithm can be used in data mining or machine learning for handling incomplete data.     

A vague-rough set approach for uncertain knowledge acquisition

By combining both vague sets and rough sets in fuzzy data processing, we propose a vague-rough set approach for extracting knowledge under uncertain environments. We compute all attribute reductions using the vague-rough lower approximation distribution, concepts of attribute reduction and the discernibility matrix in a vague decision information system (VDIS). Research results for extracting decision rules from the VDIS show the proposed approaches extend the corresponding method in classical rough set theory and provide a new avenue to uncertain vague knowledge acquisition.     

基于粗糙集理论与灰色理论的属性约简算法

约简是粗集理论的重要概念,由定义计算约简是一个典型的NP问题且由于约简的不唯一,在面对大数据集或高维数据集问题时获得的属性集往往并非是最小的属性约简集.文中针对Rough sets理论的属性约简进行了研究.研究了通过可辨识矩阵求得属性约简集,利用Rough sets与灰色理论相结合,提出一种属性约简的启发式算法,拟合结果表明本约简算法合有效.     

基于粗糙集理论与灰色理论的属性约简算法

约简是粗集理论的重要概念,由定义计算约简是一个典型的NP问题且由于约简的不唯一,在面对大数据集或高维数据集问题时获得的属性集往往并非是最小的属性约简集。文中针对Rough sets理论的属性约简进行了研究。研究了通过可辨识矩阵求得属性约简集,利用Rough sets与灰色理论相结合,提出一种属性约简的启发式算法,拟合结果表明本约简算法合有效。     

粗糙集在客户分类中的应用研究

粗糙集理论的主要思想是在保持分类能力不变的前提下,通过属性约简和值约简,提取决策规则。设计了一个基于粗糙集的客户分类模型,并利用粗糙集的知识约简和决策规则提取算法对超市客户进行了分析。通过决策表约简,剔除冗余属性、消除过剩规则。最后得出了属性约简的最小化结果以及决策规则。     

Graded dominance interval-based fuzzy objective information systems

Dominance interval-based fuzzy objective information systems are generalized models of single-valued fuzzy information systems. By introducing a graded dominance relation to dominance interval-valued fuzzy objective information systems, we establish a graded dominance interval-valued rough set model (RSM), which is mainly based on replacing the indiscernibility relation in classical rough set theory with the graded dominance interval-valued relation. Furthermore, in order to simplify knowledge representation and extract nontrivial simpler graded dominance interval fuzzy decision rules, we propose two attribute reduction approaches to eliminate the redundant condition attributes that are not essential from the viewpoint of graded dominance interval-valued fuzzy decision rules. These results are helpful for decision-making analysis in dominance interval-valued fuzzy objective information systems.