Topological approaches to covering rough sets

Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. This paper studies covering-based rough sets from the topological view. We explore the topological properties of this type of rough sets, study the interdependency between the lower and the upper approximation operations, and establish the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation. Lastly, axiomatic systems for the lower approximation operation and the upper approximation operation are constructed.     

Soft sets and soft rough sets

In this study, we establish an interesting connection between two mathematical approaches to vagueness: rough sets and soft sets. Soft set theory is utilized, for the first time, to generalize Pawlak’s rough set model. Based on the novel granulation structures called soft approximation spaces, soft rough approximations and soft rough sets are introduced. Basic properties of soft rough approximations are presented and supported by some illustrative examples. We also define new types of soft sets such as full soft sets, intersection complete soft sets and partition soft sets. The notion of soft rough equal relations is proposed and related properties are examined. We also show that Pawlak’s rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set. Moreover, an example containing a comparative analysis between rough sets and soft rough sets is given.     

几种粗糙集模型的推广研究

通过在经典粗糙集模型中引入函数,得到了一个广义的变精度粗糙集模型和一个广义的概率粗糙集模型。将这两个广义的模型进行比较研究,又得到了一个更广义的粗糙集模型,这个模型既是变精度粗糙集模型的推广也是概率粗糙集模型的推广,对推广模型的性质做了相应的研究。     

三支决策-基于粗糙集与粒计算研究视角

从三支决策3个历史发展阶段出发,通过粗糙集和粒计算两个研究视角对三支决策的发展踪迹和演化过程进行介绍。分析了三支决策与粗糙集理论的历史脉络、内在联系和相互关系,探讨了决策粗糙集、概率粗糙集、粗糙集和三支决策之间的包含关系;探讨了基于多层次粒计算和多视角粒计算下的三支决策方法;提出了一个基于三支决策的粒计算研究框架模型。最后,给出了三支决策的研究现状和未来发展方向。     

多粒度模糊粗糙集的表示与相应的信任结构

利用多粒度粗糙集的上、下近似及其性质,结合模糊集的分解定理,研究多粒度模糊粗糙集的上、下近似的表示及性质,根据多粒度模糊粗糙集的上、下近似构造信任函数与似然函数。     

Measures of general fuzzy rough sets on a probabilistic space

Fuzzy rough set is a generalization of crisp rough set, which deals with both fuzziness and vagueness in data. The measures of fuzzy rough sets aim to dig its numeral characters in order to analyze data effectively. In this paper we first develop a method to compute the cardinality of fuzzy set on a probabilistic space, and then propose a real number valued function for each approximation operator of the general fuzzy rough sets on a probabilistic space to measure its approximate accuracy. The functions of lower and upper approximation operators are natural generalizations of the belief function and plausibility function in Dempster-Shafer theory of evidence, respectively. By using these functions, accuracy measure, roughness degree, dependency function, entropy and conditional entropy of general fuzzy rough set are proposed, and the relative reduction of fuzzy decision system is also developed by using the dependency function and characterized by the conditional entropy. At last, these measure functions for approximation operators are characterized by axiomatic approaches.     

粗集中的粒计算模型

粒计算是一种基于问题概念空间划分的新的智能计算理论和方法,不相容决策表是粗集理论研究的一个重点,而粗集中的等价关系可以用来刻化等价粒.结合粒计算的处理方法给出了决策表信息系统的粒表示、粒运算规则和粒分解算法,同时结合粗集中的属性核计算方法,提出了决策表信息系统在粒表示下属性核的获取方法.     

基于粒计算与粗糙集的人工鱼群聚类算法

针对标准鱼群算法易受到初始鱼群随机性的影响,后期收敛速度减慢,处理边界数据能力低,聚类精度低等缺点,提出了基于粒计算与粗糙集的人工鱼群聚类算法。算法引入粒计算理论,并依据粒密度和最大最小距离积法选择初始化人工鱼群避免算法易受随机性的影响;通过结合粗糙集的决策系统和属性约简,提高算法解决边界数据的能力;采用类内紧致性和类间分离度的原则设计适应度函数,并将其作为算法的终止判断条件。实验结果表明：该算法提高了聚类精度,增强了获取全局极值的能力,具有良好的聚类效果。     

覆盖粗糙集的偏序关系研究

覆盖粒计算理论模型的研究大多停留在粒度空间的单个层面上进行讨论。已经有一些学者对覆盖粒度空间的层次进行了一些尝试。通过对目前已有的三种层次模型的分析,发现这些模型中存在一些问题。定义了一种新的覆盖上的偏序较细关系,对其性质进行研究,证明了覆盖近似空间下的概念近似具有偏序关系是覆盖近似空间本身具有偏序较细关系的充要条件。     

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。     

基于粒的二进制运算的最简规则获取算法

用粗糙集中的等价关系来刻化等价粒,结合粒计算的处理方法给出了决策表的粒表示、粒运算规则。提出了一种基于决策类逐渐细化条件粒直接获取最简规则的方法。该方法不仅考虑了属性相对独立性,而且能更加充分地挖掘决策表中的知识,并用实例验证了其可行性。     

模糊粗糙集在音频检索中的应用

音频具有数据量大、维数高等特点,直接进行音频检索会造成“特征维数灾难”,因此有必要从音频提取最能表现音频特征的音频帧。提出一种基于模糊粗糙集模型（Fuzzy Rough Set Model,FRSM）的音频数据约简算法,根据隶属度对音频数据进行模糊离散,基于知识表达能力约简属性,以等价划分计算具有等同分类能力的知识核。实验结果表明,该算法能够得到最小约简,并且最大程度地保持音频特征,提高检索效率。     

Classification and rule induction using rough set theory

Rough set theory (RST) offers an interesting and novel approach both to the generation of rules for use in expert systems and to the traditional statistical task of classification. The method is based on a novel classification metric, implemented as upper and lower approximations of a set and more generally in terms of positive, negative and boundary regions. Classification accuracy, which may be set by the decision maker, is measured in terms of conditional probabilities for equivalence classes, and the method involves a search for subsets of attributes (called 'reducts') which do not require a loss of classification quality. To illustrate the technique, RST is employed within a state level comparison of education expenditure in the USA.     

变精度多粒度粗糙集近似集更新的矩阵算法

随着信息大爆炸时代的到来,数据集的巨大化和数据集结构的复杂化已经成为近似计算中不能忽视的问题,而动态计算是解决这些问题的一种行之有效的途径。对现有的应用于经典多粒度粗糙集动态近似集更新方法进行了改进,提出了应用于变精度多粒度粗糙集（VPMGRS）的向量矩阵近似集计算与更新方法。首先,提出了一种基于向量矩阵的VPMGRS近似集静态计算算法;其次,重新考虑了VPMGRS近似集更新时的搜索区域,并根据VPMGRS的性质缩小了该区域,有效地提升了近似集更新算法的时间效率;再次,根据新的搜索区域,在VPMGRS近似集静态计算算法的基础上提出了一种新的VPMGRS近似集更新的向量矩阵算法;最后,通过实验验证了所提算法的有效性。     

基于粗糙集的焊接类型关联规则提取

为了从大量工艺数据中获得潜在的、有价值的工艺知识,提出了基于粗糙集的焊接类型关联规则提取方法。分析与焊接类型相关的属性,建立焊接类型选择的决策表,应用粗糙集属性约简删除对焊接类型选择没有影响的属性。应用Apriori算法获取频繁项集,为了减少冗余项集产生,采用不同属性的项集进行联接;应用较低的支持度和较高的置信度提取强规则。以具体的实例验证了该方法,提取的规则对焊接类型的选择有很好的参考价值。     

Sequential covering rule induction algorithm for variable consistency rough set approaches

We present a general rule induction algorithm based on sequential covering, suitable for variable consistency rough set approaches. This algorithm, called VC-DomLEM, can be used for both ordered and non-ordered data. In the case of ordered data, the rough set model employs dominance relation, and in the case of non-ordered data, it employs indiscernibility relation. VC-DomLEM generates a minimal set of decision rules. These rules are characterized by a satisfactory value of the chosen consistency measure. We analyze properties of induced decision rules, and discuss conditions of correct rule induction. Moreover, we show how to improve rule induction efficiency due to application of consistency measures with desirable monotonicity properties.     

Rudiments of rough sets

Worldwide, there has been a rapid growth in interest in rough set theory and its applications in recent years. Evidence of this can be found in the increasing number of high-quality articles on rough sets and related topics that have been published in a variety of international journals, symposia, workshops, and international conferences in recent years. In addition, many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs. Rough set theory has led to many interesting applications and extensions. It seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences, especially in research areas such as machine learning, intelligent systems, inductive reasoning, pattern recognition, mereology, knowledge discovery, decision analysis, and expert systems. In the article, we present the basic concepts of rough set theory and point out some rough set-based research directions and applications.     

基于粗糙集的多维关联规则挖掘方法

海量的数据使得关联规则挖掘非常耗时,而并非所有的规则都是用户感兴趣的,应用传统的挖掘方法会挖掘出许多无关信息。此外,目前大部分算法是针对单维规则的。因此,定义了一种挖掘语言使得用户可以指定感兴趣的项以及关联规则的参数（如支持度,置信度等）,并提出一种基于粗糙集理论的多维关联规则挖掘方法,动态生成频繁集和多维关联规则,减少频繁项集的生成搜索空间。实例分析验证该算法的可行性与有效性。     

基于概率覆盖决策粗糙集模型的中医菜谱分析

针对营养决策表规则提取中规则矛盾多、覆盖样例冗余多,导致有效规则遗漏的问题,提出概率覆盖决策粗糙集模型.首先,对决策粗糙集相关理论进行简要介绍,给出对应的属性约简和值约简理论和算法.然后,在决策粗糙集基础上,提出概率覆盖模型,根据值约简需求提出一、二、三度覆盖矩阵,以解决规则矛盾和冗余问题.最后,通过中医菜谱数据提取营养学规则实验,证明所提模型可有效解决规则矛盾问题,相比其他常用规则提取模型,概率覆盖模型所得规则约简力度较高,矛盾个数较少.     

Textural approach to generalized rough sets based on relations

This paper presents a discussion on rough set theory from the textural point of view. A texturing is a family of subsets of a given universal set U satisfying certain conditions which are generally basic properties of the power set. The suitable morphisms between texture spaces are given by direlations defined as pairs (r,R) where r is a relation and R is a corelation. It is observed that the presections are natural generalizations for rough sets; more precisely, if (r,R) is a complemented direlation, then the inverse of the relation r (the corelation R) is actually a lower approximation operator (an upper approximation operator).