一种构造模糊隶属度的新方法

传统的模糊支持向量机隶属度函数是基于样本点到类中心点的距离进行设计的,这对非规则形状分布数据很不合理.在基于粗糙集和支持向量机建立入侵检测模型里,使用粗糙集理论挖掘出各条件属性对决策属性的影响决策程度,提出基于样本点与类中心点属性比较加权的新隶属度函数构造方法.该方法用于此模型,可以有效降低隶属度函数对样本集几何形状的依赖,能够有效地区分样本点、噪音点以及孤立点.实验表明,与支持向量机和传统基于类中心距离的模糊支持向量机相比,新的基于属性相关的隶属度函数的模糊支持向量机达到最好的分类效果,而且新隶属度方法简单易行,运行速度快     

采用粒计算的属性权重确定方法

针对属性值为连续值且无单一决策属性的多属性决策问题,通过宏观和微观的粒计算理论模型的对比分析,提出了一种融合模糊商空间理论和粗糙集理论的属性权重确定方法。首先通过应用模糊商空间理论构建具有分层递阶结构的商空间族,将一系列粒度商空间的样本聚类结果作为相应粒度空间下单一决策属性的分类,然后采用粗糙集理论计算得出所有商空间下各个属性的重要度,综合不同粗细粒度商空间下的属性重要度大小确定了各属性的客观权重。应用实例验证了该方法的合理性、有效性和实用性。     

基于模糊化的决策粗糙集属性约简和分类

决策粗糙集是一种基于贝叶斯风险最小化原则的具有一定容忍度的概率粗糙集模型,但当前关于决策粗糙集模型的研究只局限于处理具有离散型数据的信息表.文中将模糊集和决策粗糙集理论相结合,在决策粗糙集模型中计算期望风险损失时,利用模糊隶属度函数代替传统的后验概率求解方法,这样可推导出新的决策规则,进而可高效处理那些包含连续型属性的信息系统.实验表明该方法是可行的,并且可通过调整隶属度函数,达到更佳分类效果.     

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。     

基于二进制可辨矩阵的知识粒度研究及应用

粗糙集理论是一种新型的处理模糊和不确定知识的数学工具，其对知识的理解是认为知识与分类相关、知识是有粒度的。文中利用粗糙集理论中的二进制可辨矩阵讨论知识的粒度计算及其应用，得到了二进制可辨矩阵若干定理及推论，并提出计算知识的分辨度和属性重要度的新方法，利用这些理论和公式、可快速计算出知识的分辨度和属性重要度，相对正域和负域等．为以后的属性约简和规则提取打下基础。并给出这些方法的应用，表明了文中提出的方法的有效性。     

不确定性工艺知识的模糊粗糙隶属度函数表示方法*

分析了工艺知识不确定性和模糊性的特点,提出了基于模糊粗糙隶属度函数的工艺不确定性知识的表示与应用模型。实现了对各类用数值和符号描述的工艺不确定知识的表示,通过隶属度值代替粗糙集中的实数值作为模糊粗糙集的属性,依照属性的依赖度和属性表的核进行了工艺知识属性的约简,得到了工艺知识规则集,并以LED芯片制造领域的工艺知识表示为实例,验证了该方法的可行性与有效性。     

基于连续型条件属性的模糊规则约简算法*

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,提出一种将模糊集和粗糙集结合起来的连续型条件属性模糊规则约简算法。该算法首先引入三角隶属度函数将连续属性值转换为模糊值,并使用离散模糊神经网络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,从而获得满意的模糊规则结果。     

基于最佳分类数和粗糙集的故障诊断方法

提出了一种基于最佳分类数和粗糙集理论的汽轮机轴系振动故障诊断方法。该方法利用模糊C均值聚类算法（FCM）把数据的连续属性离散化,以形成隶属度矩阵及属性分类数,根据隶属度矩阵及属性分类数进行划分系数和划分熵的有效性评判,最终找到连续属性的最佳分类数。然后根据最佳分类数对数据的连续属性进行实际的离散化,将离散化后形成的离散数据根据粗糙集理论,进行数据挖掘,得到诊断规则,有效提高了汽轮机轴系振动故障的诊断水平。     

基于模糊集的连续域决策表属性约简算法

把模糊集和粗糙集结合起来,对连续域决策表属性约简算法进行研究。使用三角隶属度函数将连续属性值转化为模糊值。定义两模糊对象间的相似度、模糊对象的相似类以及连续属性在对象集上划分所形成的相似类集组成的特征向量。给出连续型属性的数字特征向量,以此为基础建立连续型属性间的相似矩阵。提出一个新的属性约简算法,并用一个实例加以验证。     

基于包含度的直觉模糊粗糙集模型

将直觉模糊包含度引入粗糙集与直觉模糊集的融合建模。首先,介绍直觉模糊集在特殊格L上的定义;其次,将模糊包含度拓展到直觉模糊环境下,提出取值于特殊格L的直觉模糊包含度定义和计算公式;在此基础上,分别利用直觉模糊包含度的隶属度与非隶属度定义了上下近似算子,建立了直觉模糊相似关系下的直觉模糊粗糙集模型,并对近似算子的重要性质进行了证明。     

Improved feature selection algorithm with fuzzy-rough sets on compact computational domain

The aim of this paper is to provide an efficient input feature selection algorithm for modeling of systems based on modified definition of fuzzy-rough sets. Some of the critical issues concerning the complexity and convergence of the feature selection algorithm are discussed in detail. Based on some natural properties of fuzzy t-norm and t-conorm operators, the concept of fuzzy-rough sets on compact computational domain is put forward, which is then utilized to construct improved Fuzzy-Rough Feature Selection algorithm. Various mathematical properties of this new definition of fuzzy-rough sets are discussed from pattern classification viewpoint. Speedup factor as high as 622 has been achieved with proposed algorithm compared to recently proposed FRSAR, with improved model performance on selected set of features.     

一种基于信息熵的模糊粗糙集知识获取方法

模糊粗糙集融合了模糊集和粗糙集的思想,是一种新的处理模糊和不确定性知识的软计算工具。针对属性为模糊值的信息系统,提出了一种基于熵的模糊粗糙集知识获取方法:首先通过模糊相似度量计算出各属性下对象的模糊相似值,再根据模糊相似关系构造模糊等价关系,然后根据模糊等价关系建立属性集的信息熵表示,继而使用基于信息熵的决策表属性约简算法获取规则。最后,通过一个实例,分析说明了这种算法的合理有效性。     

Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR

Linguistic hesitant intuitionistic fuzzy set, which allows an element having several linguistic evaluation values and each linguistic argument having several intuitionistic fuzzy memberships, is a power tool to model uncertain information existing in multiple attribute decision-making problems. In this paper, we propose new methods by using TOPSIS and VIKOR for multiple attribute decision-making problems, in which evaluation values are in the form of linguistic hesitant intuitionistic fuzzy elements. Different situations of attribute weight information are considered. If attribute weights are partly known, a linear programming model is set up based on the idea that reasonable weights should make the relative closeness of each alternative evaluation value to the linguistic hesitant intuitionistic fuzzy positive ideal solution as large as possible. If attribute weights are unknown completely, an optimization model is set up based on the maximum deviation method. A numerical example is presented to illustrate feasibility and practical advantages of the proposed method. We compare the alternatives’ rankings derived from the linguistic hesitant intuitionistic fuzzy TOPSIS method with those derived from the hesitant fuzzy linguistic TOPSIS and the hesitant intuitionistic fuzzy TOPSIS approach to further illustrate their advantages.

     

Fuzzy rough set based attribute reduction for information systems with fuzzy decisions

Fuzzy rough set is a generalization of crisp rough set to deal with data sets with real value attributes. A primary use of fuzzy rough set theory is to perform attribute reduction for decision systems with numerical conditional attribute values and crisp (symbolic) decision attributes. In this paper we define inconsistent fuzzy decision system and their reductions, and develop discernibility matrix-based algorithms to find reducts. Finally, two heuristic algorithms are developed and comparison study is provided with the existing algorithms of attribute reduction with fuzzy rough sets. The proposed method in this paper can deal with decision systems with numerical conditional attribute values and fuzzy decision attributes rather than crisp ones. Experimental results imply that our algorithm of attribute reduction with general fuzzy rough sets is feasible and valid.     

A method based on preference degrees for handling hybrid multiple attribute decision making problems

In this paper, we investigate hybrid multiple attribute decision making problems with various forms of attribute values (real numbers, linguistic labels, interval numbers, intuitionistic fuzzy numbers and interval intuitionistic fuzzy numbers). We propose a method based on preference degrees which may take the forms of fuzzy numbers, intuitionistic fuzzy numbers and interval intuitionistic fuzzy numbers. The method first normalizes various forms of attribute values into preference degrees, and then uses a preference degree-based weighted averaging operator to aggregate the normalized preference degrees. Meanwhile, for convenience of calculation, a new linguistic representation model is presented, whose feasibility is verified by comparing it with the traditional 4-tuple linguistic representation model, and from our model, the mapping relationship between interval intuitionistic fuzzy numbers and linguistic labels can be constructed. Finally, we illustrate the rationality and practicality of the proposed method by an application example.     

Tolerance analysis using fuzzy sets

A method for the analysis of the effects of subjective and objective tolerances in networks and systems is presented in this paper. The imprecision of the components is represented using fuzzy sets and then the value of the desired attribute is computed. The resulting attribute is also fuzzy and is obtained in the form of a fuzzy set. This fuzzy set contains the extremal and other values of the desired attribute along with their grades of membership. Thus, apart from getting the extremel values, we get the overall picture of the attribute. Since this method is directly applicable for the analysis of subjective tolerances, networks representing humanistic systems may be analysed using this method.     

一种对方案有偏好的Vague集多属性决策方法

研究了方案属性值和偏好值均为Vague值的多属性决策问题。针对相关文献中,将由Vague值表示的方案属性值与偏好值转化为直觉模糊数,并根据直觉模糊数表示的方案属性值与偏好值之间的偏差建立规划模型并求解属性权重这一过程,分析了建立的规划模型的不合理性。提出通过最小化直觉模糊数表示的方案综合值与偏好值的偏差,建立并求解一个规划模型计算属性权重的改进方法。通过将Vague值转化为模糊值,利用模糊值矩阵的线性序构造模糊优先矩阵,并对其进行分割,从而实现方案的排序择优。通过一个实例说明了该方法的可行性。     

Fuzzy quartile encoding as a preprocessing method for biomedical pattern classification

A fuzzy set based preprocessing method is described that may be used in the classification of patterns. This method, dispersion-adjusted fuzzy quartile encoding, determines the respective degrees to which a feature (attribute) belongs to a collection of fuzzy sets that overlap at the respective quartile boundaries of the feature. The fuzzy sets are adjusted to take into account the overall dispersion of values for a feature. The membership values are subsequently used in place of the original feature value. This transformation has a normalizing effect on the feature space and is robust to feature outliers. This preprocessing method, empirically evaluated using five biomedical datasets, is shown to improve the discriminatory power of the underlying classifiers.     

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。