Two-Layer Information Granulation:Mapping-Equivalence Neighborhood Rough Set and Its Attribute Reduction

Attribute reduction,as one of the essential applications of the rough set,has attracted extensive attention from scholars.Information granulation is a key step of attribute reduction,and its efficiency has a significant impact on the overall efficiency of attribute reduction.The information granulation of the existing neighborhood rough set models is usually a single layer,and the construction of each information granule needs to search all the samples in the universe,which is inefficient.To fill such gap,a new neighborhood rough set model is proposed,which aims to improve the efficiency of attribute reduction by means of two-layer information granulation.The first layer of information granulation constructs a mapping-equivalence relation that divides the universe into multiple mutually independent mapping-equivalence classes.The second layer of information granulation views each mapping-equivalence class as a sub-universe and then performs neighborhood informa-tion granulation.A model named mapping-equivalence neighborhood rough set model is derived from the strategy of two-layer information granulation.Experimental results show that compared with other neighborhood rough set models,this model can effectively improve the efficiency of attribute reduction and reduce the uncertainty of the system.The strategy provides a new thinking for the exploration of neighborhood rough set models and the study of attribute reduction acceleration problems.

Attribute Reduction in Decision Systems Based on Relation Matrix

This paper proposes,from the viewpoint of relation matrix,a new algorithm of attribute reduction for decision systems.Two new and relative reasonable indices are first defined to measure significance of the attributes in decision systems and then a heuristic algorithm of attribute reduction is formulated.Moreover,the time complexity of the algorithm is analyzed and it is proved to be complete.Some numerical experiments are also conducted to access the performance of the presented algorithm and the results demonstrate that it is not only effective but also efficient.

Rough set理论及其应用

Rough set理论能从数据间发现隐含的关联和规律，广泛应用于人工智能、模式识别、智能信息处理等领域，成为最受国际学术界重视的处理不确定数据的理论与方法。

Improved Rough Set Algorithms for Optimal Attribute Reduct

Feature selection（FS） aims to determine a minimal feature（attribute） subset from a problem domain while retaining a suitably high accuracy in representing the original features. Rough set theory（RST） has been used as such a tool with much success. RST enables the discovery of data dependencies and the reduction of the number of attributes contained in a dataset using the data alone,requiring no additional information. This paper describes the fundamental ideas behind RST-based approaches,reviews related FS methods built on these ideas,and analyses more frequently used RST-based traditional FS algorithms such as Quickreduct algorithm,entropy based reduct algorithm,and relative reduct algorithm. It is found that some of the drawbacks in the existing algorithms and our proposed improved algorithms can overcome these drawbacks. The experimental analyses have been carried out in order to achieve the efficiency of the proposed algorithms.

Methods for Lower Approximation Reduction in Inconsistent Decision Table Based on Tolerance Relation

It is well known that most of information systems are based on tolerance relation instead of the classical equivalence relation because of various factors in real-world. To acquire brief decision rules from the information systems, lower approximation reduction is needed. In this paper, the lower approximation reduction is proposed in inconsistent information systems based on tolerance relation. Moreover, the properties are discussed. Furthermore, judgment theorem and discernibility matrix are obtained, from which an approach to lower reductions can be provided in the complicated information systems.

Generalized binary discernibility matrix for attribute reduction in incomplete information systems

To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.

基于Rough集理论的模糊值属性信息表简化方法

为了有效地在信息表中处理取值为模糊术语的属性 ,解决Rough集对模糊值属性处理能力较弱的问题 ,提出了模糊不可分辨关系的概念 ,用于处理属性值为模糊术语的信息表 将约简、核、相对约简与相对核以及规则的约简与核等Rough集理论中一系列知识约简的概念推广到模糊环境下 ,提出了一种有效的模糊值信息表简化的启发式算法

一种基于Rough集的案例推理模型的构建

利用Rough集理论处理案例推理问题具有不需要外界信息和先验知识的优点,对案例库中冗余属性进行简化,能够起到优化案例库的作用,同时能够依赖于统计知识提炼规则并形成多个有效的案例索引,在进行案例检索时可针对不同的检索问题选择恰当的索引快速检索到相似的案例,并进行推理得出相应的问题解决方案。最后,以稀土萃取分离生产过程的产品纯度和料液处理量等生产指标的智能优化设定控制为例,验证了该模型的可行性和精确性。

基于RSDA的RDB与Rough集关系的研究

该文以Rough集数据分析技术(RSDA,RoughSetDataAnalysis)为基础,对关系数据库(RDB,relationaldatabase)和Rough集的关系进行了系统的研究。具体做法是,从Rough集与RDB产生的理论背景、关系与信息表的形式化语义、核心概念之间的关系、Rough度量与RRDM(roughrelationaldatabasemodel,简称RRDM)等方面对它们的关系进行了系统的、深入的探讨,并得出了相应的结论。

集值Rough扩展模型知识约简

基于吴鹏等提出的k度限制相容关系模型,讨论在集值不完备信息系统上的约简,给出集值不完备信息系统属性约简的判定定理和辨识矩阵,得到集值不完备信息系统知识约简的具体操作方法。

完备格上的广义Rough集模型

基于way-below关系和弱way-below关系,在具有逆合对应的完备格上建立了广义Rough上下近似算子,研究了它们的基本性质,并说明本文提出的广义Rough集模型是Pawlak标准粗糙集的推广.同时,在De Morgan代数上建立了广义Rough上下近似算子,给出了相应的基本性质.

Rough Computational Approach to UAR based on Dominance Matrix in IOIS

Rough set theory is a new mathematical tool to deal with vagueness and uncertainty. The classical rough set theory based on equivalence relation has made a great progress, while the equivalence relation is too harsh to meet and is extended to dominance relation in real world. It is important to investigate rough computational methods for rough set theory, which is one of the bottleneck problems in the development of rough set theory. In this article, rough computational approach to upper ap-proximation reduction (UAR) is discussed based on dominance matrix in inconsistent ordered information systems (IOIS). The algorithm of upper approximation reduction is obtained, from which we can provide approach to upper approximation reduction operated simply in inconsistent systems based on dominance relations. Finally, an example illustrates the validity of this method, and shows the method is excellent to a complicated information system.

基于邻域优势粗糙集的区分度动态属性约简算法

为解决动态环境下数值型偏序关系数据的属性约简问题,利用优势粗糙集的区分度提出一种增量式属性约简算法。在数值型信息系统环境下,定义邻域优势区分度度量,通过邻域优势区分度设出一种非增量式属性约简算法;研究和分析对象变化场景下邻域优势区分度进行增量式更新的原理;分别提出数据对象增加和减少情形下数据集属性约简的增量式更新算法。在多个UCI数据集上进行实验验证,实验结果表明,该增量式算法能够有效完成动态数据的属性约简任务。

区间值决策表中基于相对优势邻域粒度的属性约简

现实生活中大量数据以区间值形式存在,此时区间值决策表并不是基于等价关系,传统的决策方法并不能解决这一问题.为此,本文在区间值决策表中引入相邻关系、相邻类的定义,进而由相邻类建立了区间决策表的相对优势邻域粒度,拓展了经典决策信息系统的相关方法,并利用相对优势邻域粒度研究了区间决策表属性约简的启发式算法,通过具体案例将得到的属性约简结果与代数约简进行了有效性验证,进一步丰富和完善了信息系统属性约简理论.

基于多核模糊条件熵的多类型混合数据属性约简算法

对数据进行有效属性约简是数据挖掘中一个具有挑战性的任务。当前,粗糙集理论是构造属性约简的一种常用方法。然而,现有的属性约简方法都侧重于单类型的数据,对现实环境下多类型混合的数据并不适用。为了解决这一问题,提出一种多核模糊条件熵的多类型混合数据属性约简算法。首先,针对标记型、数值型、区间型和集值型混合的多类型数据,提出了一种多核模糊相似关系。然后,基于这种多核模糊相似关系,定义了一种多核模糊条件熵模型,并讨论了它的单调性和有界性。最后,利用多核模糊条件熵的单调性提出了一种多类型混合数据的属性约简算法。通过UCI数据集的实验分析验证了该算法的有效性。

基于不可区分度的启发式快速完备约简算法

在已有的粗糙集属性约简算法基础上,给出了一个新的度量属性重要性的不可区分度函数,分析了不可区分度的性质,提出了一种能有效处理噪声的基于不可区分度的快速完备约简算法,最坏时间复杂度为max(O(|A||U|),O(|A|2|U/A|))。理论分析和实验结果表明,该约简算法在效率上较现有算法有显著提高,能较好抵制数据噪声,适于对大数据集进行处理。

不完备信息系统下的属性约简算法

传统的粗糙集模型是处理完全信息系统的有力工具,但对于不完全信息系统却显得无能为力。因此对不完备信息系统的研究也是粗集理论研究领域之一。本文在M.Kryszkiewcz提出的一个容差关系的基础上提出改进,使之更加具有灵活性。然后以该改进模型为基础,运用属性重要性理论,给出属性约简算法,并通过一个实例来验证。最后将该算法和经典算法进行了比较。

基于邻域粒化和粗糙逼近的数值属性约简

对于空间中的任一子集,通过基本邻域信息粒子进行逼近,由此提出了邻域信息系统和邻域决策表模型.分析了该模型的性质,并且基于此模型构造了数值型属性的选择算法.利用UCI标准数据集与现有算法进行了比较分析,实验结果表明,该模型可以选择较少的特征而保持或改善分类能力.

不一致决策表的知识约简方法研究

目前计算不一致决策表的分布约简、最大分布约简和分配约简的方法均基于可辨识属性矩阵,在大数据集下耗时较多.为此,提出转化算法,将计算原不一致决策表的上述3种约简转化为计算3种一致决策表的Paw lak约简.通过应用针对后者的高效启发式算法,有效地减少了计算时间.此外,引入λ-约简的概念,通过调节λ的值,能得到一族反映决策矢量不同水平相似程度的知识约简.该方法降低了分布约简对决策表区分能力的过高要求,较上述3种约简更为灵活.