基于K近邻隶属度的聚类算法研究

经典模糊C均值聚类算法（FCM）基于欧氏距离,存在不同规模类簇不能正确聚类问题,针对此问题提出一种基于[K]近邻隶属度的模糊C均值聚类算法（KNN_FCM）。讨论了基于[K]近邻隶属度的粗糙C均值聚类算法（KNN_RCM）和粗糙模糊C均值聚类算法（KNN_RFCM）,此方法避免了传统粗糙C均值聚类算法（RCM）和粗糙模糊C均值聚类算法（RFCM）中阈值选择问题。将KNN_FCM、KNN_RCM、KNN_RFCM分别与FCM、RFM、RFCM在UCI数据集上进行仿真比较,结果表明新方法是可行、有效的。     

基于聚类有效性分析的模糊粗糙集归纳学习方法

引入模糊C均值聚类算法进行连续属性模糊化,通过聚类有效性分析来确定最佳分类数目,克服了属性模糊化方法需要人为确定划分类数的缺点。用属性模糊化得到的属性隶属度矩阵约简模糊粗糙属性,由此提出一种基于模糊粗糙集的属性约简算法。实例验证了该方法的可行性和有效性。     

结合蚁群算法的改进粗糙K均值聚类算法

粗糙集理论是一种处理边界对象不确定的有效方法。将粗糙集与K均值结合的粗糙K均值聚类算法,具有简单高效且可处理聚类边界元素的特点,但同时存在缺陷。针对粗糙K均值聚类算法对初始点敏感,经验权重设置忽略数据差异性,阈值设置不合理导致聚类结果波动性大的缺陷,本文提出结合蚁群算法的改进粗糙K均值聚类算法,改进的算法中使用蚁群算法中随机概率选择策略和信息素更新的正负反馈机制,以及采用动态调整算法阈值和相关权重的方法,对粗糙K均值聚类算法进行优化。最后采用UCI的Iris、Balance-scale和Wine数据集分别对算法进行实验。实验结果表明,改进后的粗糙K均值聚类算法得到的聚类结果准确率更高。     

基于模糊聚类的图像分割方法

本文分析了模糊聚类在图像分割领域的应用,介绍了模糊集和聚类分析的作用,最后引出了模糊C均值聚类图像分割算法。     

基于HCM聚类的连续域模糊关联算法

针对粗糙集对于连续域属性决策表的处理能力差以及不容易获得模糊集之间关系等问题,提出一种基于连续型属性模糊关联规则约简算法。该算法引入三角隶属度函数将连续属性值转化为模糊值,并使用硬C均值聚类方法获得数据集之间关系,采用遗传算法优化该模型。仿真结果验证了该模型的有效性。     

基于粗糙集理论和FCM的图像聚类方法

提出一种将粗糙集方法与模糊C均值聚类(FCM)算法结合的图像聚类方法。借助于粗糙集理论在处理大数据量、消除冗余信息等方面的优点,减少模糊C均值聚类的训练数据量,克服其因为数据量大而处理速度慢等缺点,同时利用模糊C均值聚类好的聚类性能,对经过约简的最小属性子集进行聚类分析,实现图像聚类的快速、准确、鲁棒等优点。在人脸图像上的聚类实验取得了很好的效果。     

基于连续型决策表属性均值聚类约简算法

针对粗糙集对于连续域属性决策表的处理能力差以及不容易获得模糊集之间关系等问题,提出一种基于连续型属性的硬C均值(HCM)聚类约简算法。该算法首先引入三角隶属度函数将连续属性值转化为模糊值,并使用HCM聚类方法获得数据集之间关系。实例验证表明:采用该算法,用户可以根据实际决策需要和领域知识更改阈值,从而获得满意的属性结果。     

特征逐减的可能性模糊聚类算法

模糊C均值聚类（FCM）和可能性模糊C均值聚类（PFCM）没有考虑样本特征项及每个样本对聚类的贡献程度，存在对噪声较敏感的问题。特征减少的模糊聚类算法FRFCM可剔除数据集中无效特征量，且考虑了剩余特征量的权重，具有更好的聚类性能。对此，在可能性模糊C均值聚类算法（PFCM）的基础上将其与FRFCM算法相结合，提出新的特征逐减的可能性模糊C均值聚类算法（FRPFCM）。该算法解决了PFCM算法参数依赖的问题，且在迭代过程中可自动淘汰无效特征项并更新各特征项对聚类的贡献程度。对人工数据集以及UCI数据集进行测试的结果表明，提出的FRPFCM算法可得到更高的聚类准确率，所需迭代次数更少，算法收敛速度更快。     

直觉模糊C-均值聚类算法研究

鉴于直觉模糊集理论作为模糊理论的推广已得到广泛的应用,研究了将模糊C-均值聚类推广为直觉模糊C-均值聚类（IFCM）的途径和方法,分析了现有的几种IFCM算法,并提出了一种基于直觉模糊集的模糊C-均值聚类算法．该算法首先定义了直觉模糊集之间的距离;然后构造了聚类的目标函数;最后给出了聚类算法步骤．将算法用于目标识别,实验结果表明了算法的有效性．     

一种新的带模糊权的粗糙聚类算法

针对粗糙聚类算法缺乏对数据比例变换的鲁棒性的问题，在粗糙聚类的框架下融合模糊聚类的思想，将临界区域中对象的模糊隶属度作为它们对于聚类中心调整的作用权值，得到一种带有模糊权的粗糙聚类算法（fuzzy weighing rough clustering algorithm, FWRCA）．实验表明，该算法不仅对于数据的比例变化具有鲁棒性，且在一定程度上克服了粗糙C均值聚类算法对划分阈值ε的敏感性，在性能上优于传统粗糙C均值聚类算法(如RCMCA)，可应用于水电工程科学等以原型模型为研究手段并有大量需做比例变换的观测数据的领域．     

粗糙support-intuitionistic模糊集及其聚类分析应用

粗糙集和模糊集理论已经被用于各种类型的不确定性建模中。Dubois和Prade研究了将模糊集和粗糙集结合的问题。提出了粗糙support-intuitionistic模糊集。介绍了粗糙集、粗糙直觉模糊集和support-intuitionistic模糊集等的概念;定义了在Pawlak近似空间中的support-intuitionistic模糊集的上下近似,讨论了一些粗糙support-intuitionistic模糊集近似算子的性质,给出了其相似度表达式;将其应用到聚类分析问题中,并通过一个实例验证其合理性。     

Rough set based generalized fuzzy c-means algorithm and quantitative indices.

A generalized hybrid unsupervised learning algorithm, which is termed as rough-fuzzy possibilistic c-means (RFPCM), is proposed in this paper. It comprises a judicious integration of the principles of rough and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy sets enables efficient handling of overlapping partitions. It incorporates both probabilistic and possibilistic memberships simultaneously to avoid the problems of noise sensitivity of fuzzy c-means and the coincident clusters of PCM. The concept of crisp lower bound and fuzzy boundary of a class, which is introduced in the RFPCM, enables efficient selection of cluster prototypes. The algorithm is generalized in the sense that all existing variants of c-means algorithms can be derived from the proposed algorithm as a special case. Several quantitative indices are introduced based on rough sets for the evaluation of performance of the proposed c-means algorithm. The effectiveness of the algorithm, along with a comparison with other algorithms, has been demonstrated both qualitatively and quantitatively on a set of real-life data sets.     

粗糙的方向性模糊聚类算法

根据高维数据具有方向性的特征,结合概率模糊聚类算法与粗糙集理论提出了一种粗糙的方向性模糊聚类算法。该算法在概率模糊聚类算法中引入了数据方向相似性函数,能对不确定数据进行处理。在算法中利用粗糙集中的下近似集与边界集来确定目标对象函数,属于下近似集的数据在聚类时是确定的,属于边界的数据具有模糊性。实验结果表明,该算法能有效地对高维的方向性数据进行聚类。     

Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators

The fuzzy rough set model and interval-valued fuzzy rough set model have been introduced to handle databases with real values and interval values, respectively. Variable precision rough set was advanced by Ziarko to overcome the shortcomings of misclassification and/or perturbation in Pawlak rough sets. By combining fuzzy rough set and variable precision rough set, a variety of fuzzy variable precision rough sets were studied, which cannot only handle numerical data, but are also less sensitive to misclassification. However, fuzzy variable precision rough sets cannot effectively handle interval-valued data-sets. Research into interval-valued fuzzy rough sets for interval-valued fuzzy data-sets has commenced; however, variable precision problems have not been considered in interval-valued fuzzy rough sets and generalized interval-valued fuzzy rough sets based on fuzzy logical operators nor have interval-valued fuzzy sets been considered in variable precision rough sets and fuzzy variable precision rough sets. These current models are incapable of wide application, especially on misclassification and/or perturbation and on interval-valued fuzzy data-sets. In this paper, these models are generalized to a more integrative approach that not only considers interval-valued fuzzy sets, but also variable precision. First, we review generalized interval-valued fuzzy rough sets based on two fuzzy logical operators: interval-valued fuzzy triangular norms and interval-valued fuzzy residual implicators. Second, we propose generalized interval-valued fuzzy variable precision rough sets based on the above two fuzzy logical operators. Finally, we confirm that some existing models, including rough sets, fuzzy variable precision rough sets, interval-valued fuzzy rough sets, generalized fuzzy rough sets and generalized interval-valued fuzzy variable precision rough sets based on fuzzy logical operators, are special cases of the proposed models.     

基于混合蛙跳与阴影集优化的粗糙模糊聚类算法

针对粗糙模糊聚类算法对初值敏感、易陷入局部最优和聚类性能依赖阈值选择等问题, 提出一种混合蛙跳与阴影集优化的粗糙模糊聚类算法(SFLA-SRFCM). 通过设置自适应调节因子, 以增加混合蛙跳算法的局部搜索能力; 利用类簇上、下近似集的模糊类内紧密度和模糊类间分离度构造新的适应度函数; 采用阴影集自适应获取类簇阈值. 实验结果表明, SFLA-SRFCM 算法是有效的, 并且具有更好的聚类精度和有效性指标.

     

Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory

The primitive notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation and satisfying many interesting properties. Many types of generalized rough set models have been proposed in the literature. This paper discusses the rough approximations of Atanassov intuitionistic fuzzy sets in crisp and fuzzy approximation spaces in which both constructive and axiomatic approaches are used. In the constructive approach, concepts of rough intuitionistic fuzzy sets and intuitionistic fuzzy rough sets are defined, properties of rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are examined. Different classes of rough intuitionistic fuzzy set algebras and intuitionistic fuzzy rough set algebras are obtained from different types of fuzzy relations. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of crisp/fuzzy relations which produce the same operators.     

On generalized intuitionistic fuzzy rough approximation operators

In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak’s rough approximations have been made in the literature over the years. This paper proposes a general framework for the study of relation-based intuitionistic fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper intuitionistic fuzzy rough approximation operators induced from an arbitrary intuitionistic fuzzy relation are defined. Basic properties of the intuitionistic fuzzy rough approximation operators are then examined. By introducing cut sets of intuitionistic fuzzy sets, classical representations of intuitionistic fuzzy rough approximation operators are presented. The connections between special intuitionistic fuzzy relations and intuitionistic fuzzy rough approximation operators are further established. Finally, an operator-oriented characterization of intuitionistic fuzzy rough sets is proposed, that is, intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of intuitionistic fuzzy relations which produce the same operators.     

基于阴影集的粗糙聚类闭值选择

粗糙聚类思想自提出以来,在软划分聚类方面取得了广泛应用,但其阂值参数常主观确定,未能考虑数据集 本身的特性。基于阴影集((Shadowed Sets)的优化理论给出了一种客观的阂值选择方法,并将其应用于粗糙模糊C均 值聚类算法。人工数据与UCI数据实验结果表明了所提方法的有效性。     

新的模糊粗糙集的模糊性度量方法

研究了模糊粗糙集的模糊性度量方法。首先从模糊集支集的角度,给出了一般模糊关系下模糊集的粗糙隶属函数;在此基础上,设计了一种合理的模糊粗糙集的模糊性度量方法,并对其相关性质进行了详细的讨论。