Static rough similarity degree and its applications

The definition of rough similarity degree is given based on the axiomatic similarity degree, and the properties of rough similarity degree are listed. Using the properties of rough similarity degree, the method of clustering in rough systems can be obtained. After clustering, a new sample can be recognized by the principle of maximal rough similarity degree.     

基于粗糙集的信息粗传递

针对实际中两种信息传递情况,提出了两种信息粗传递概念—下近似和上近似信息粗传递。利用粗糙集理论对这两种信息粗传递进行了讨论,分析了粗传递信息保持不变、发生损失和发生增益的条件,得到了下近似和上近似粗传递信息不变定理,下近似粗传递信息损失定理,上近似粗传递信息增益定理,下近似和上近似信息粗传递原理以及提高信息粗传递精确性的方法。信息粗传递是粗糙集理论的一个新的应用。     

基于模糊聚类和粗糙集的仿真可信性模糊综合评估

为客观有效地解决仿真可信性评估问题,提出基于模糊聚类和粗糙集的仿真可信性模糊综合评估方法。阐述了基于模糊传递闭包法进行模糊聚类分析的基本步骤,分析了粗糙集中属性重要性的相关原理;提出了基于模糊聚类和粗糙集的可信性模糊综合评估模型,利用模糊聚类和粗糙集中的属性重要性原理客观地进行各因素权重分配,结合模糊综合评判进行仿真可信性综合评估;以某飞行视景仿真系统为例,进行可信性综合评估。结果表明,该方法具有一定的合理性和可行性。     

Transformation and entropy for fuzzy rough sets

A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.     

Method to determine α in rough set model based on connection degree

An improvement of tolerance relation is proposed in regard to rough set model based on connection degree by which reflexivity of relation can be assured without loss of information. Then, a method to determine optimal identity degree based on relative positive region is proposed so that the identity degree can be computed in an objective method without any preliminary or additional information about data, which is consistent with the notion of objectivity in rough set theory and data mining theory. Subsequently, an algorithm is proposed, and in two examples, the global optimum identity degree is found out. Finally, in regard to optimum connection degree, the method of rules extraction for connection degree rough set model baaed on generalization function is presented by which the rules extracted from a decision table are enumerated.     

双论域上的直觉模糊概率粗糙集模型及其应用

基于一个直觉模糊关系,给出了双论域上的直觉模糊概率粗糙集模型的定义,同时也给出了逆下近似、上近似算子的概念. 研究了它们的若干性质,为粗糙集的应用提供了新的理论基础与操作手段.最后,通过在临床诊断系统中的具体应用阐述了本文提出的直觉模糊概率粗糙集模型的有效性和优越性.     

基于粗糙集-神经网络的城市产业生命周期识别

以城市经济为背景,提出了基于粗糙集-RBF神经网络的城市产业生命周期识别方法.首先运用基于MDV函数与信息熵的模糊聚类算法进行连续属性离散化处理,然后采用粗糙集理论约简出重要指标体系,最后将训练样本输入RBF神经网络进行学习和训练,并对检验样本的产业生命周期阶段进行判断.对大连市669组样本产业的分析结果表明:基于MDV函数与信息熵的模糊聚类算法能够有效改善离散化效果,且与通常采用的模糊评价法相比,该方法对检验样本预测精度更高,是一种有效和实用的城市产业生命周期识别工具.     

基于粗糙集和证据理论的设备状态评估方法

为准确判定复杂设备健康状态，提出一种基于粗糙集理论和证据理论的健康状态评估方法。鉴于粗糙集只能处理离散指标，首先提出一种基于动态模糊C-均值聚类算法的连续型评估指标的离散化方法；再通过基于互信息的属性约简算法对复杂设备健康状态评估指标进行约简；然后对约简的评估决策表进行处理，构建基本信度分配函数；最后利用D-S合成规则进行多指标合成得到健康状态，进一步挖掘评估指标与健康状态间的关系。实例研究及对比分析表明该方法能有效提高决策可信度，减少评估的不确定性。     

不完备信息系统中基于相似度的变精度粗糙集模型

提出了一种基于相似度的变精度粗糙集模型,该模型是变精度粗糙集模型在不完备信息系统中的拓展.定义了这种模型上的知识约简,并给出了求约简的两种一般算法.最后通过实例分析说明了算法的有效性.     

模糊粗交流及其应用

提出了变异模糊粗集的概念,并给出了变异模糊粗集的相关性质和定理。将Amin Mousavi提出的粗交流进行了推广,提出了模糊粗交流。建立了模糊粗交流网络最优传递序列的数学模型,应用模糊粗交流理论给出了解决这类数学模型的算法。最后利用提出的算法解决了通讯网络中选择最优通讯线路的实例,从而验证了算法的有效性。     

模糊度与贴近度的关系研究

针对描述模糊集合的两个重要概念（模糊度和贴近度）,详细讨论了二者之间的关系,得到了它们相互刻划的两个定理,并且指出模糊度是模糊集和它的余的贴近度,这些结果可在模式识别、决策科学中得到应用．     

粗糙近似算子的拓扑性质

通过闭包与内部算子研究模糊粗糙集的拓扑结构,证明了自反、传递关系下的近似空间中模糊集的上、下近似算子分别为一个模糊拓扑的闭包、内部算子,且相应的模糊拓扑满足(TC)条件;反之,满足(TC)条件的模糊拓扑的闭包与内部算子也恰为一自反、传递关系下的近似空间中的上、下近似算子.     

粗糙集-神经网络集成在编队空战中的应用

为了提高空战决策的实时性和准确度,将粗糙集理论和神经网络引入到编队协同空战战术决策研究中,提出了应用SOM网络—粗糙集—BP网络集成进行编队协同空战战术决策的方案:应用SOM网络离散化决策系统输入数据的连续属性值;利用粗糙集数据分析方法,从数据中提取出规则将输入映射到输出的子空间上;在这个子空间上用BP网络进行逼近。2∶4编队空战实例仿真结果验证该方案的可行性,在数据充分的条件下,该方案可以推广应用于其它空战决策系统。     

New judging model of fuzzy cluster optimal dividing based on rough sets theory

To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory: information system discrete algorithm (algorithm 1) and samples representatives judging algorithm (algorithm 2). On the principle of the farthest distance, algorithm i transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.     

Rough law energy and measurement of ¯F-decomposition rough law

By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ¯ f-decomposition law and ¯ F-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ¯ F-decomposition is researched. The concepts of law energy and attribute ¯ f-interference degree are presented, which make the variation of rough law become measurable. ¯ f-decomposition law energy characteristic theorem, ¯ fdecomposition law energy inequality theorem, ¯ F-decomposition rough law energy characteristic theorem, and ¯ f-decomposition law energy mean value theorem are presented.     

Rough function model and rough membership function

Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.     

基于模糊粗糙近似的web浏览模式的聚类

提出一种模糊的粗糙近似法用于对web日志中的用户浏览模式进行聚类.在聚类过程中,一个网页是否被访问反映了用户的浏览兴趣,一个网页上的浏览时间反映了用户浏览兴趣的程度,它被刻画成模糊语言变量以忽略时间值之间的细小差别.每个用户浏览模式被表示成等长的模糊向量的形式以表示该用户访问过的网页及网页上的浏览时间.最后使用粗糙近似的方法对这些表示用户浏览模式的模糊向量进行聚类.这种方法可以把具有相似浏览行为的用户聚成一类.     

Pawlak粗糙集的公理系统

粗糙集合理论是一种新的有效处理不精确、不确定、含糊信息的理论,粗集公理系统研究是粗集理论及应用研究的基础。利用模糊关系及其运算的矩阵表示,建立Pawlak粗近似空间的公理体系,该公理系统由三条相互独立的非常简洁的表达式构成。获得的结果深刻地揭示了经典等价关系与模糊等价关系的本质区别,进一步深化了Pawlak粗集理论。     

基于改进IFRS相似度和信息熵的反导作战目标威胁评估

针对现有反导目标威胁评估方法忽略目标属性犹豫度和权重并造成评估精度不高的问题,引入直觉模糊粗糙集(intuitionistic fuzzy rough set, IFRS)理论,提出基于改进IFRS相似度和信息熵的反导作战目标威胁评估方法。首先,细分IFRS犹豫度,提出改进的IFRS相似度模型,并证明其性质。之后,针对现有的IFRS信息熵存在与直觉事实不相符的问题,提出基于余弦函数的IFRS信息熵,确定目标属性权重。在此基础上,构建并量化反导作战目标威胁评估体系,并通过比较威胁目标的各个属性值与正、负理想解的相似度,实现目标威胁排序。仿真实例验证了该方法的可行性和有效性,可为不确定环境下反导作战威胁评估提供新的参考和尝试。     

基于模糊粗糙k-均值的用户访问模式的聚类

Web用户访问过的网页以及在该网页上的浏览时间体现了用户的访问兴趣.为了更好的衡量任意两个用户访问模式之间的相似/相异度,每个用户访问模式都被转换成具有相等长度的模糊向量,其中每个元素要么是0要么是模糊语言变量,它体现了用户是否访问过该网页及在该网页上的浏览时间.由于类的边界可能是模糊的,因而使用粗糙k-均值法对这些代表用户浏览特征的模糊向量进行聚类.最后使用Davies-Bouldin指标来衡量聚类的效果.