基于两个集合上粗集模型的算法实现

为了处理人工智能中不精确和不确定的数据和知识,Pawlak 提出了粗集模型,之后粗集理论得到拓广,人们提出了许多新的粗集模型,拓广的方法主要有两种,一种是减弱对等价关系的依赖,另一种是把讨论问题的论域从一个拓展到两个,Y.Y.Yao 提出了一种基于两个论域的粗集模型,本文研究基于两个论域的粗集模型的具体算法实现,给出了上下近似的矩阵算法及其相应的焦点集的算法,并把相关结论及矩阵算法推广到模糊集上,还给出了相关模型的极为简洁的公理刻画,即仅用一条公理刻画该模型。     

一种基于模糊粗糙集的快速特征选择算法

模糊粗糙集由于能够处理实数值数据,甚至是混合值数据中的不确定性受到人们的广泛关注,其最重要的应用之一是特征选择,相关的特征选择方法已有不少研究,但其快速的特征选择算法研究很少。实际中的数据一般含有噪声点或信息含量低的样例,如果对数据集先筛选出代表样例,再对筛选的样例集进行数据挖掘便会降低挖掘计算量。本文基于模糊粗糙集,先根据样例的模糊下近似值对样例进行筛选,然后利用筛选样例的模糊粗糙信息熵构造特征选择的评估度量,并给出相应的特征选择算法,从而降低了算法的计算复杂度。数值试验表明该快速算法具有有效性,并且对控制筛选样例个数的参数给出了建议。     

基于粗糙近似的Web事务聚类方法研究

Web使用挖掘是数据挖掘技术在Web信息仓库中的应用.Web使用挖掘通过挖掘Web服务器日志获取的知识来预测用户浏览行为,是Web挖掘技术中的一个重要研究方向.通常发现的知识或一些意外规则很可能是不精确的、不完备的,这就需要用软计算技术如粗糙集来解决.提出一种基于粗糙近似的聚类方法,该方法能够实现从Web访问日志中聚类Web事务.通过这种方法可以有效地挖掘Web日志记录,从而发现用户存取Web页面的模式.     

Soft fuzzy rough set-based MR brain image segmentation

Fuzzy sets, rough sets are efficient tools to handle uncertainty and vagueness in the medical images and are widely used for medical image segmentation. Soft sets are a new mathematical approach to uncertainty and vagueness. In this paper, a hybrid segmentation algorithm based on soft sets namely soft fuzzy rough c-means is proposed to extract the white matter, gray matter and the cerebro spinal fluid from MR brain image with bias field correction. In this algorithm, soft fuzzy rough approximations are applied to obtain the rough regions of image. These approximations are free from defining thresholds, weight parameters and are less complex compared to the existing rough set based algorithms. Soft sets use similarity coefficients to find the similarity of the clusters formed in present and previous step. The proposed algorithm does not involve any negative region, hence all the pixels participate in clustering avoiding clustering mistakes. Also, the histogram based centroids choose the centroids close to the ground truth that in turn effect the definition of approximations, standardizing the clusters. The proposed algorithm evaluated through simulation, compared it with existing k-means, rough k-means, fuzzy c-means and other hybrid algorithms. The soft fuzzy rough c-means algorithm outperforms the considered algorithms in all analyzed scenarios even in extracting the tumor from the brain tissue.     

基于阴影集的粗糙模糊可能性C均值聚类算法

相对于硬聚类算法,软聚类算法可以更好地表示具有不精确边界的类簇。粗糙集和模糊集均是用于描述不确定数据的有效的数学工具,二者互为补充。研究人员已经将粗糙集和模糊集的概念相结合,并应用到聚类算法中,提出了粗糙模糊可能性C均值聚类算法。而文中通过引入阴影集,有效地解决了粗糙模糊可能性C均值聚类算法中的阈值选择问题。     

基于数据场的粗糙聚类算法

聚类分析是数据挖掘的研究热点.传统的聚类算法都是把一个对象精确地划分到一个聚类簇中,类别之间的界限是非常精确的.随着Web挖掘技术的发展,精确地划分每个对象的聚类算法面临着巨大的挑战.根据数据场理论和经典粗糙集理论所具有处理不精确与不确定性数据的特性,提出一种新的基于数据场的粗糙聚类算法,该粗糙聚类算法采用势值作为对象的划分依据,避免传统粗糙聚类算法一贯采用基于欧氏距离的划分方法.算法首先通过对数据对象进行粗分然后再不断迭代细分,直至形成稳定的聚类簇.实验分析过程中,把提出的算法与粗糙K-means算法和粗糙K-medoids算法进行了比较,结果表明该算法在交叉数据集上具有较好的聚类效果,而且收敛速度较快.     

基于FCM和粗糙集属性重要度理论的综合评价系统

应用FCM和粗糙集属性重要度理论研究了评价和预测问题中样本的聚类分析与各因素的合理赋权问题，提出了一种新的综合评判方法——基于FCM和粗糙集属性重要度理论的综合评判（FCM-WMRS方法）；并开发了基于FCM-WMRS方法的区域科技能力综合评判系统；最后，依据中国科学院可持续发展研究组所提供的评价指标体系和有关数据，并结合系统运行结果对各区域科技能力水平现状进行了分析。     

An efficient accelerator for attribute reduction from incomplete data in rough set framework

Feature selection (attribute reduction) from large-scale incomplete data is a challenging problem in areas such as pattern recognition, machine learning and data mining. In rough set theory, feature selection from incomplete data aims to retain the discriminatory power of original features. To address this issue, many feature selection algorithms have been proposed, however, these algorithms are often computationally time-consuming. To overcome this shortcoming, we introduce in this paper a theoretic framework based on rough set theory, which is called positive approximation and can be used to accelerate a heuristic process for feature selection from incomplete data. As an application of the proposed accelerator, a general feature selection algorithm is designed. By integrating the accelerator into a heuristic algorithm, we obtain several modified representative heuristic feature selection algorithms in rough set theory. Experiments show that these modified algorithms outperform their original counterparts. It is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets.     

基于拓展粗糙集的不完备表的规则挖掘及应用

实际应用中常存在缺省属性值的不完备信息系统,如何从不完备信息系统中挖掘有用规则是一个非常有价值的问题。粗糙集理论是一种有效的数据挖掘手段,但经典粗糙集缺乏对不完备信息系统的处理能力。在粗糙集拓展的基础上,设计出从不完备决策表中挖掘出有用规则的算法,并将其应用到银行贷款决策中不完备决策表的实例分析中。     

Towards a Software Change Classification System: A Rough Set Approach

The basic contribution of this paper is the presentation of two methods that can be used to design a practical software change classification system based on data mining methods from rough set theory. These methods incorporate recent advances in rough set theory related to coping with the uncertainty in making change decisions either during software development or during post-deployment of a software system. Two well-known software engineering data sets have been used as means of benchmarking the proposed classification methods, and also to facilitate comparison with other published studies on the same data sets. Two technologies in computation intelligence (CI) are used in the design of the software change classification systems described in this paper, namely, rough sets (a granular computing technology) and genetic algorithms. Using 10-fold cross validated paired t-test, this paper also compares the rough set classification learning method with the Waikato Environment for Knowledge Analysis (WEKA) classification learning method. The contribution of this paper is the presentation of two models for software change classification based on two CI technologies.     

Interval set clustering

Rough k-means clustering describes uncertainty by assigning some objects to more than one cluster. Rough cluster quality index based on decision theory is applicable to the evaluation of rough clustering. In this paper we analyze rough k-means clustering with respect to the selection of the threshold, the value of risk for assigning an object and uncertainty of objects. According to the analysis, clusters presented as interval sets with lower and upper approximations in rough k-means clustering are not adequate to describe clusters. This paper proposes an interval set clustering based on decision theory. Lower and upper approximations in the proposed algorithm are hierarchical and constructed as outer-level approximations and inner-level ones. Uncertainty of objects in out-level upper approximation is described by the assignment of objects among different clusters. Accordingly, ambiguity of objects in inner-level upper approximation is represented by local uniform factors of objects. In addition, interval set clustering can be improved to obtain a satisfactory clustering result with the optimal number of clusters, as well as optimal values of parameters, by taking advantage of the usefulness of rough cluster quality index in the evaluation of clustering. The experimental results on synthetic and standard data demonstrate how to construct clusters with satisfactory lower and upper approximations in the proposed algorithm. The experiments with a promotional campaign for the retail data illustrates the usefulness of interval set clustering for improving rough k-means clustering results.     

一种连续属性离散化的新方法

提出了一种基于聚类方法、结合粗集理论的连续属性离散化方法。在粗集理论中有一个重要概念：属性重要度（Attribute significance)，它常用来作为生成好的约简所采用的启发式评价函数。受此启发，在连续属性离散化方法中可把它用于属性选择，即从已离散化的属性集中选择出属性重要度最高的属性，再把它和待离散化的连续属性一起进行聚类学习，得到该连续属性的离散区间。文中介绍了该方法的算法描述，并通过实验与其他算法进行了比较。实验结果表明，由于这种方法在离散化过程中结合了粗集理论的思想,考虑了属性间的相互影响，从而产生了比较合理的划分点，提高了规则的分类精度。     

一种基于决策粗糙集的模糊C均值聚类数的确定方法

Fuzzy C-Means(FCM)是模糊聚类中聚类效果较好且应用较为广泛的聚类算法,但是其对初始聚类数的敏感性导致如何选择一个较好的C值 变得十分重要。因此,确定FCM的聚类数是使用FCM进行聚类分析时的一个至关重要的步骤。通过扩展决策粗糙集模型进行聚类的有效性分析,并进一步确定FCM的聚类数,从而避免了使用FCM时不好的初始化所带来的影响。文中提出了一种基于扩展粗糙集模型的模糊C均值聚类数的确定方法,并通过图像分割实验来验证聚类的效果。实验通过比对不同聚类数下分类结果的代价获得了一个较好的分割结果,并将结果与Z.Yu等人于2015年提出的蚁群模糊C均值混合算法(AFHA)以及提高的AFHA算法(IAFHA)进行对比,结果表明所提方法的聚类结果较好,图像分割效果较明显,Bezdek分割系数比AFHA和IAFHA算法的更高,且在Xie-Beni系数上也有较大优势。     

基于幂图的属性约简搜索式算法

粗糙集理论是一种新的处理不精确、不完全与不一致数据的数学工具.属性约简是粗糙集理论的重要研究内容之一,已有的属性约简算法主要是基于代数表示与信息表示的方法.同一问题在不同的知识表示下,其求解难度是不同的.文中从改变属性约简问题的知识表示人手,提出了该问题的一种新的表示方式--幂图;给出了基于幂图的属性约简搜索式算法,把属性约简计算问题转化为在幂图中的搜索问题.理论分析表明新算法是有效的,为属性约简研究提供了一条新的途径.     

Incremental feature selection based on rough set in dynamic incomplete data

Feature selection plays a vital role in many areas of pattern recognition and data mining. The effective computation of feature selection is important for improving the classification performance. In rough set theory, many feature selection algorithms have been proposed to process static incomplete data. However, feature values in an incomplete data set may vary dynamically in real-world applications. For such dynamic incomplete data, a classic (non-incremental) approach of feature selection is usually computationally time-consuming. To overcome this disadvantage, we propose an incremental approach for feature selection, which can accelerate the feature selection process in dynamic incomplete data. We firstly employ an incremental manner to compute the new positive region when feature values with respect to an object set vary dynamically. Based on the calculated positive region, two efficient incremental feature selection algorithms are developed respectively for single object and multiple objects with varying feature values. Then we conduct a series of experiments with 12 UCI real data sets to evaluate the efficiency and effectiveness of our proposed algorithms. The experimental results show that the proposed algorithms compare favorably with that of applying the existing non-incremental methods.     

Approximations in <Emphasis Type="Italic">n</Emphasis>-ary algebraic systems

Algebraic systems have many applications in the theory of sequential machines, formal languages, computer arithmetics, design of fast adders and error-correcting codes. The theory of rough sets has emerged as another major mathematical approach for managing uncertainty that arises from inexact, noisy, or incomplete information. This paper is devoted to the discussion of the relationship between algebraic systems, rough sets and fuzzy rough set models. We shall restrict ourselves to algebraic systems with one n-ary operation and we investigate some properties of approximations of n-ary semigroups. We introduce the notion of rough system in an n-ary semigroup. Fuzzy sets, a generalization of classical sets, are considered as mathematical tools to model the vagueness present in rough systems.     

Rough Sets, Their Extensions and Applications

Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge.Despite its recency,the theory and its extensions have been widely applied to many problems,including decision analysis,data mining,intelligent control and pattern recognition.This paper presents an outline of the basic concepts of rough sets and their major extensions,covering variable precision,tolerance and fuzzy rough sets.It also shows the diversity of successful applications these theories have entailed,ranging from financial and business,through biological and medicine,to physical,art,and meteorological.     

A survey of decision making methods based on certain hybrid soft set models

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.     

Approximations and reducts with covering generalized rough sets

The covering generalized rough sets are an improvement of traditional rough set model to deal with more complex practical problems which the traditional one cannot handle. It is well known that any generalization of traditional rough set theory should first have practical applied background and two important theoretical issues must be addressed. The first one is to present reasonable definitions of set approximations, and the second one is to develop reasonable algorithms for attributes reduct. The existing covering generalized rough sets, however, mainly pay attention to constructing approximation operators. The ideas of constructing lower approximations are similar but the ideas of constructing upper approximations are different and they all seem to be unreasonable. Furthermore, less effort has been put on the discussion of the applied background and the attributes reduct of covering generalized rough sets. In this paper we concentrate our discussion on the above two issues. We first discuss the applied background of covering generalized rough sets by proposing three kinds of datasets which the traditional rough sets cannot handle and improve the definition of upper approximation for covering generalized rough sets to make it more reasonable than the existing ones. Then we study the attributes reduct with covering generalized rough sets and present an algorithm by using discernibility matrix to compute all the attributes reducts with covering generalized rough sets. With these discussions we can set up a basic foundation of the covering generalized rough set theory and broaden its applications.     

属性序下基于优势关系灰色信息系统约简

粗糙集和灰色理论在数据挖掘领域各有优点,它们最终目标都是为了发现知识。将粗糙集和灰色系统结合,研究了区间灰色信息系统在优势关系下的约简方法。在现实世界中,属性之间可能存在着一种属性序的关系,将这种属性序关系引入到基于优势关系的灰色信息系统中,给出了两种属性约简的算法：一种基于分辨矩阵的算法,另一种不基于分辨矩阵的算法。较好地适应了不完备信息系统和大数据集信息系统约简。最后通过实例对比,得出两种算法的约简结果是一致的,并分析了各自的适用范围。