On Multi-Granulation Rough Sets with Its Applications

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

Multi-Granularity Neighborhood Fuzzy Rough Set Model on Two Universes

The two universes multi-granularity fuzzy rough set model is an effective tool for handling uncertainty problems between two domains with the help of binary fuzzy relations. This article applies the idea of neighborhood rough sets to two universes multi-granularity fuzzy rough sets, and discusses the two-universes multi-granularity neighborhood fuzzy rough set model. Firstly, the upper and lower approximation operators are defined in the two universes multi-granularity neighborhood fuzzy rough set model. Secondly, the properties of the upper and lower approximation operators are discussed. Finally, the properties of the two universes multi-granularity neighborhood fuzzy rough set model are verified through case studies.

Attribute Reduction of Neighborhood Rough Set Based on Discernment

For neighborhood rough set attribute reduction algorithms based on dependency degree,a neighborhood computation method incorporating attribute weight values and a neighborhood rough set attribute reduction algorithm using discernment as the heuristic information was proposed.The reduction algorithm comprehensively considers the dependency degree and neighborhood granulation degree of attributes,allowing for a more accurate measurement of the importance degrees of attributes.Example analyses and experimental results demonstrate the feasibility and effectiveness of the algorithm.

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.

Cost Sensitive Multi-Granulation Preference Relation Rough Set for Ordinal Decision System

The preference analysis is a class of important issues in multi-criteria ordinal decision making.The rough set is an effective approach to handle preference analysis.In order to solve the multi-criteria preference analysis problems,this paper improves the preference relation rough set model and expands it to multi-granulation cases.Cost is also an important issue in the field of decision analysis.Taking the cost into consideration,we also expand the model to the cost sensitive multi-granulation preference relation rough set.Some theorems are represented,and the granule structure selection based on approximation quality is investigated.The experimental results show that the multi-granulation preference rough set approach with the consideration of cost has a better performance in granule structure selection than that without cost consideration.

Multi-Span and Multiple Relevant Time Series Prediction Based on Neighborhood Rough Set

Rough set theory has been widely researched for time series prediction problems such as rainfall runoff.Accurate forecasting of rainfall runoff is a long standing but still mostly signicant problem for water resource planning and management,reservoir and river regulation.Most research is focused on constructing the better model for improving prediction accuracy.In this paper,a rainfall runoff forecast model based on the variable-precision fuzzy neighborhood rough set(VPFNRS)is constructed to predict Watershed runoff value.Fuzzy neighborhood rough set dene the fuzzy decision of a sample by using the concept of fuzzy neighborhood.The fuzzy neighborhood rough set model with variable-precision can reduce the redundant attributes,and the essential equivalent data can improve the predictive capabilities of model.Meanwhile VFPFNRS can handle the numerical data,while it also deals well with the noise data.In the discussed approach,VPFNRS is used to reduce superuous attributes of the original data,the compact data are employed for predicting the rainfall runoff.The proposed method is examined utilizing data in the Luo River Basin located in Guangdong,China.The prediction accuracy is compared with that of support vector machines and long shortterm memory(LSTM).The experiments show that the method put forward achieves a higher predictive performance.

Self-organizing Map Method Based on Real Rough Sets Space and Its Application of Pattern Recognition

This paper presents a real rough sets space and corresponding concepts of real lower and upper approximation sets which correspond to the real-valued attributes. Therefore, the real rough sets space can be investigated directly. A rhombus neighborhood for SOM is proposed, and the combination of SOM and rough sets theory is explored. According to the distance between the weight of winner node and the input vector in the real rough sets space, new weight learning rules are defined. The modified method makes the classification of the output of SOM clearer and the intervals of different classes larger. Finally, an example based on fault identification of an aircraft actuator is presented, The result of the simulation shows that this method is right and effective.

Generalization Rough Set Theory

In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. Then, depending on the degree of general importance of attribute, the space distance can be measured with weighted method. At last, a generalization rough set theory based on the general near neighborhood relation is proposed. The proposed theory partitions the universe into the tolerant modules, and forms lower approximation and upper approximation of the set under general near neighborhood relationship, which avoids the discretization in Pawlak's rough set theory.

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.

一种属性变化局部变精度邻域粗糙集动态算法

传统的邻域粗糙集模型对混合型数据的抗噪能力和计算效率低下,基于矩阵理论建立了一种属性动态变化的局部变精度邻域粗糙集模型。在局部对角矩阵和中间矩阵的更新规律的基础上,构建了混合信息系统局部变精度邻域粗糙集下近似的动态更新机制,提出了一种新的属性变化的局部变精度邻域粗糙集动态算法。通过实验分析可知:所提出的动态算法具有较高的计算效率和良好的稳健性。

随机多属性子空间的ReliefF加权邻域粗糙集与属性约简

属性约简是一种重要的数据降维预处理方法,然而现有的属性约简方法大多没有考虑信息系统中属性权重的信息。ReliefF算法是一种实现简单且运算效率高的属性权重评估方法,提出一种随机多属性子空间的ReliefF加权邻域粗糙集和属性约简算法。该方法生成了多组具有相同大小随机子空间的属性集划分,并对每组划分的随机子空间利用ReliefF算法计算得到属性的局部权重,将所有组得到的属性局部权重求取平均值,得到了信息系统每个属性最终的全局权重;基于属性权重的结果,提出一种新的加权邻域粗糙集模型,并证明了相关理论和性质;在该模型的基础上通过加权邻域依赖度提出一种信息系统的属性约简算法。在公开数据集上的属性约简实验结果表明,所提出的属性约简算法比已有的同类型算法整体上具有更优的约简性能。

F-粗糙集的拓展与应用

F-粗糙集是第1个动态粗糙集模型,具有良好的兼容性、表达能力以及动态性,但绝大多数粗糙集模型动态性不足.为了明晰粗糙集模型的动态性,拓展F-粗糙集的应用,综述了F-粗糙集研究的现状和发展,证明了多粒度粗糙集、多粒度邻域粗糙集和多尺度信息系统中的粗糙集可以用F-粗糙集表示.此外,还研究了F-粗糙集的可拓性,并建议将其他粗糙集模型与F-粗糙集相结合,使它们在处理动态数据、增量数据和海量数据时具有更强的能力.研究结果将提高其他粗糙集模型的动态性,有利于粗糙集进一步应用到大数据领域.

基于Spark和NRSCA策略的并行深度森林算法

针对并行深度森林在大数据环境下存在冗余及无关特征过多、两端特征利用率过低、模型收敛速度慢以及级联森林并行效率低等问题,提出了基于Spark和NRSCA策略的并行深度森林算法——PDF-SNRSCA。首先,该算法提出了基于邻域粗糙集和Fisher score的特征选择策略(FS-NRS),通过衡量特征的相关性和冗余度,对特征进行过滤,有效减少了冗余及无关特征的数量;其次,提出了一种随机选择和等距提取的扫描策略(S-RSEE),保证了所有特征能够同概率被利用,解决了多粒度扫描两端特征利用率低的问题;最后,结合Spark框架,实现级联森林并行化训练,提出了基于重要性指数的特征筛选机制(FFM-II),筛选出非关键性特征,平衡增强类向量与原始类向量维度,从而加快模型收敛速度,同时设计了基于SCA的任务调度机制(TSM-SCA),将任务重新分配,保证集群负载均衡,解决了级联森林并行效率低的问题。实验表明,PDF-SNRSCA算法能有效提高深度森林的分类效果,且对深度森林并行化训练的效率也有大幅提升。

基于异类粒球分离度的自适应属性约简

属性约简是处理大规模数据集的关键步骤,与传统的邻域粗糙集(NRS)相比,粒球邻域粗糙集(GBNRS)可以显著提高属性约简的性能.然而,目前GBNRS属性约简算法生成了太多不必要的粒球;从而极大降低了算法运行效率.文章首先定义了一种新的粒球质量指标来控制生成自适应数量的粒球;然后通过粒球对样本集进行划分,将不同类别的样本点放入不同类别的粒球;最后根据不同属性集合下粒球中正域样本的数量来进行前向属性约简.为了验证算法的有效性,在12个真实数据集上将提出的算法与其他NRS属性约简算法进行了对比实验.实验结果表明,所提出的算法有更高的精度和更快的运行效率.

基于邻域粗集神经网络的大数据特征分类系统

为提升主机元件对大数据的分类准确性,尽可能地避免数据误传,提出基于邻域粗集神经网络的大数据特征分类系统。在邻域粗集神经网络中,完成对邻域系数的粒化处理,通过逼近运算的方式,使神经网络模型快速趋于稳定。选取大数据特征调制信息,借助调制识别器元件控制大数据特征的导出方向,结合关联信道组织完成数据特征的多标合并处理。实验表明,利用该系统可将大数据的单位召回率提升至65%,能够促进主机元件对大数据的准确分类。

广义多粒度双量化邻域粗糙集

针对实数型数据的信息量化问题,引入相对概念和绝对基数构建了广义多粒度双量化邻域粗糙集模型.首先,通过I型和II型广义多粒度上、下邻域特征支撑函数构建两类广义多粒度上、下邻域近似算子并讨论其性质;其次,讨论了两种广义多粒度邻域粗糙集的关系;最后,通过传染病案例实证分析了模型的实用性和有效性.

基于自适应密度邻域关系的多标签在线流特征选择

流特征选择指从以流形式到来的特征数据中选出最优特征子集,现有方法大多在模型训练中需要事先学习领域信息并预设给定参数值。实际应用中,由于不同的数据集数据结构和来源不同,在模型学习过程中研究人员无法提前获取相关领域知识且针对不同类型数据集指定一个统一参数存在巨大挑战。基于此,提出一种基于自适应密度邻域关系的多标签在线流特征选择方法(multi-label online stream feature selection based on adaptive density neighborhood relation,ML-OFS-ADNR),基于邻域粗糙集理论,所提方法在特征依赖计算时无需任何先验领域信息。此外,提出了一种新的自适应密度邻域关系,使用周围实例的密度信息,可以在流特征选择过程中自动选择适当数量的邻域,不需要事先指定任何参数。通过模糊等价约束,ML-OFS-ADNR可以选择高依赖低冗余度的特征。实验表明在10种不同类型的数据集上,所提方法在特征数量相同的情况下优于传统特征选择方法和先进的在线流特征选择方法。

基于最大联盟粗糙集的三支聚类

针对邻域粗糙集模型受邻域参数影响大、刻画样本信息时不够精细等问题,提出了一种基于最大联盟理论的粗糙集模型。在标准化邻域信息系统后,引入最大联盟集来描述邻域颗粒信息,使得邻域粗糙集模型对信息的划分更加精细,从而显著降低了边界域的不确定性。将该模型与三支聚类相结合,设计了一种基于最大联盟粗糙集的三支聚类算法。在6个UCI公共数据集上进行对比实验,结果表明,所提算法相较于对比算法具有更好的聚类质量,在处理边界域样本时具有更高的比较正确率。

基于测试代价的三支邻域属性约简算法

针对粗糙集属性约简时很少考虑属性自身的测试代价等问题,提出了一种基于测试代价的三支邻域属性约简算法。算法根据各属性在邻域分辨矩阵中出现的频次和比例来计算属性重要性,并结合属性自身的测试代价来构造性价比指标,以此指导属性的甄选。三支决策方法被用于划分属性集,为属性的约简处理提供数据支撑。在7个UCI公共数据集上进行对比实验,结果表明,该算法可得到比对比算法更小的属性约简集合,在分类精度不降低的情况下,该算法具有更少的运行时间和更小的测试代价。基于财政收入的预测应用实例进一步证明了所提算法的有效性和实用性。