三支半概念的广义结构及粗糙集近似算子

随着形式概念分析理论的发展,经典半概念理论也受到了广泛关注。三支半概念是将经典半概念与三支决策相结合而产生的新理论,也是一个知识发现与数据挖掘的有效工具。本文主要对三支半概念的结构和性质两个方面进行研究,首先将三支半概念拓广到了广义三支半概念——OE-半概念和AE-半概念,给出了寻找二者的算法,接下来分别针对两种广义三支半概念构建了纯双布尔代数结构。此外,研究了三支半概念与经典半概念之间的关系,分别证明了它们之间的保运算以及序同构关系。最后利用粗糙集理论分别构建了经典半概念的两对算子,给出该算子的相关性质,并证明这两对算子为粗糙集近似算子。     

基于对象导出三支概念格的决策背景规则获取

规则获取是当前形式概念分析领域的研究热点.首先给出了基于对象导出三支概念格间的细于关系,定义了基于对象导出三支概念格的三支弱协调性,并研究了其与经典概念格下的二支弱协调性之间的关系.然后,研究了基于对象导出三支概念格的规则获取,并与经典概念格的规则获取进行了比较.最后,定义了对象导出三支概念的弱闭标记,研究了基于弱闭标记的三支弱协调决策形式背景的规则获取,剔除了冗余规则,并且得到一些新的更为精简的三支规则.     

基于直觉模糊决策粗糙集的三支决策

基于决策粗糙集的三支决策是解决风险决策问题的一种经典方法,利用贝叶斯决策理论生成决策规则。决策规则具有正域、边界域、负域三个区域特征,对应的决策分别为接受决策、延迟决策和拒绝决策。本文将决策粗糙集模型对象之间的等价关系转变为具有自反性和对称性的直觉模糊关系,通过直觉模糊事件概率度量,定义了贝叶斯决策理论中对象状态与对象描述之间的条件概率。将决策损失与直觉模糊数相结合计算对象分类的预期损失,进而由贝叶斯决策理论引导的最小风险决策规则推导出相应的正域、负域、边界域的决策规则。当决策损失满足一定大小关系时将决策规则进行化简,计算出简化决策规则中的阈值与决策损失之间的关系,并且由简化决策规则定义了直觉模糊决策粗糙集的上、下近似。最后将构造的直觉模糊决策粗糙集的三支决策模型应用到直觉模糊概率决策系统,在已知的决策损失下得到相应的决策规则。     

基于三支决策的灰色可能度聚类方法及应用

针对经典的灰色可能度聚类评估模型难以判定决策对象的灰类归属和过度聚类等问题,利用三支决策的思想和方法,通过引入三支灰类的概念描述决策对象和灰类之间的不确定聚类关系;将其代替灰色定权聚类中的灰类和严格的聚类关系,构建基于三支决策的灰色可能度聚类方法,并采用决策粗糙集中的贝叶斯推理确定聚类阈值;最后,以案例验证所提方法的有效性和合理性。结果表明：本文所构建的模型是经典灰色可能度聚类评估模型的拓展和泛化,可以有效避免过度聚类,降低决策风险,提高聚类可靠性。     

基于三层粒结构的三支邻域熵

邻域粗糙集在实际应用中具有灵活性,相关的邻域信息度量在不确定性分析和知识发现中具有重要作用.经典的条件邻域熵具有相交不完备性和非层次性.对条件邻域熵进行扩展改进,建立了基于三层粒结构的三支邻域熵.首先,提出三支概率,研究三支概率的系统性和单调性;然后,利用三支概率函数及层次构建思想,提出基于三层粒结构的三支邻域熵,并获得系统性、单调性/非单调性;最后,利用实例和实验对以上相关度量的关系、性质进行验证.结果表明提出的三支邻域熵扩展和丰富了条件邻域熵.     

基于可调多粒度对偶犹豫模糊概率粗糙集的三支多属性群决策

本文为减少三支决策中主观性因素对决策结果的影响,并克服经典多粒度粗糙集模型在信息融合方面存在极端性的局限,在对偶犹豫模糊信息系统中探索了基于可调多粒度概率粗糙集的三支决策模型与方法,用于求解多属性群决策问题.首先,本文将对偶犹豫模糊的概念引入三支决策中,提出了可调多粒度对偶犹豫模糊概率粗糙集模型.然后,本文依据离差最大...     

三层粒结构区间集信息系统上变精度粗糙集

区间集信息系统作为传统信息系统的扩张,对不确定性信息具有更强表现力,区间集信息系统上面的变精度粗糙集理论值得被探讨.挖掘区间集信息系统上的三层粒结构(相似粒向量,相似粒覆盖和相似等价类),基于这三种粒结构研究了区间集信息系统上的变精度粗糙集理论.定义了区间集信息系统上变精度粗糙集上和下近似算子,由上和下近似算子得到变粗...     

考虑权重信息未知的区间直觉模糊三支群决策方法

本文提出优化视角下专家权重信息未知的区间直觉模糊三支群决策方法。首先利用区间直觉模糊加权平均算子集结不同专家提供的区间直觉模糊损失评价,获得群体综合损失评价结果。以专家个体与群体综合评价相似度越髙,越能反映群体综合评价意见且赋予髙的专家权重为原则,分别构建专家权重信息完全未知和部分已知的权重确定模型。进而建立确定区间直觉模糊三支决策概率阈值对的优化模型,并提出基于专家权重信息未知的区间直觉模糊三支群决策方法。最后,算例分析及比较结果表明所提出方法的有效性。     

区间值毕达哥拉斯犹豫模糊粗糙集

区间值毕达哥拉斯犹豫模糊集是毕达哥拉斯犹豫模糊集的扩展,增强了不确定信息处理的鲁棒性.将区间值毕迭哥拉斯犹豫模糊信息融入粗糙集分析,进行相应不确定性建模,实现不确定性信息融合.基于区间值毕达哥拉斯犹豫模糊关系,构建区间值毕这哥拉斯犹豫模糊粗糙集模型,研究下上近似关于集合并交补运算的基本性质,得到近似集的知识粒化单调性质...     

基于最小描述的覆盖粒计算模型

在覆盖近似空间(U,C)中,基于最小描述定义了一种新的Zoom-in算子,并讨论了其性质。在论域U上,通过复合Zoom-in和Zoom-out算子,得到了具有对偶性的两对近似算子。同样在粒化论域C上,通过复合Zoom-out和Zoom-in算子,也得到了具有对偶性的两对近似算子。     

One-mode three-way overlapping cluster analysis

The present paper introduces an overlapping cluster analysis model and an associated algorithm that can analyze one-mode three-way similarities. The present model is an extension of ADCLUS model, and the present algorithm is based on the MAPCLUS algorithm. In the present model, one-mode three-way similarities are represented by the sum of the numerical weights of clusters to which any triplet of objects belongs. The present model and algorithm were applied to joint purchase data, and compared the result with that of MAPCLUS to show that the present model is effective in representing one-mode three-way similarities.     

Parallel iterated methods based on variable step‐size multistep Runge—Kutta methods of Radau type for stiff problems

In our previous paper [3], the performance of a variable step‐size implementation of Parallel Iterated Methods based on Multistep Runge–Kutta methods (PIMRK) is far from satisfactory. This is due to the fact that the underlying parameters of the Multistep Runge–Kutta (MRK) method, and the splitting matrices W that are needed to solve the nonlinear system are designed on a fixed step‐size basis. Similar unsatisfactory results based on this method were also noted by Schneider [12], who showed that the method is only suitable when the step‐size does not vary too often. In this paper, we design the Variable step‐size Multistep Runge–Kutta (VMRK) method as the underlying formula for Parallel Iterated methods. The numerical results show that Parallel Iterated Variable step‐size MRK (PIVMRK) methods improve substantially on the PIMRK methods and are usually competitive with Parallel Iterated Runge–Kutta methods (PIRKs). This revised version was published online in June 2006 with corrections to the Cover Date.     

A proof of the basic measure extension theorem of Carathéodory

In this note a direct elementary proof of Carathéodory's measure extension theorem is presented. It is based on an approximation argument for outer measures where elements of the -algebra are approached by elements of the underlying algebra of sets with respect to the symmetric difference. Received: 3 April 2000 / Accepted: 20 September 2000     

Order restricted inference for a multiple step-stress model with long-term survivors for a general family of distributions

In this article, we propose a failure rate based step-stress accelerated life testing (SSALT) model assuming that the time-to-event distribution belongs to a fairly general family of distributions and the underlying population consists of long term survivors. With increase in stress levels, it is expected that the mean time to the event of interest gets shortened leading to an order restriction among the mean times-to-event. We propose here a method of obtaining order restricted maximum likelihood estimators (MLEs) based on expectation maximization (EM) algorithm coupled with the method of generalized isotonic regression technique. Additionally, we address the testing of hypothesis problem for the presence of long term survivors in the underlying population based on both asymptotic and non-asymptotic approaches. To illustrate the effectiveness of the proposed method, extensive simulation experiments are carried out and a real data set is analyzed.     

基于弹性壳的三维群体细胞动力学模型

群体细胞迁移常见于胚胎发育、伤口愈合和肿瘤侵袭等各种生理和病理过程中,关于其动力学的研究对于揭示群体细胞迁移机理、深刻理解有关生物过程十分重要.该文构建了群体细胞的三维可变形壳状模型,提出了一种考虑细胞弹性形变和细胞间接触与黏附相互作用的群体细胞动力学理论,并发展了相应的数值算法.基于所发展的动力学模型与算法,对多细胞在嚢腔里的受限旋转运动进行了模拟,复现了相关实验现象,分析了细胞极性、细胞形变、胞间相互作用等因素对多细胞三维动力学的影响规律.     

Confidence intervals based on interpolated order statistics

Confidence intervals for the population median based on interpolating adjacent order statistics are presented. They are shown to depend only slightly on the underlying distribution. A simple, nonlinear interpolation formula is given which works well for a broad collection of underlying distributions.     

Operator-splitting methods via the Zassenhaus product formula

In this paper, we contribute an operator-splitting method improved by the Zassenhaus product. Zassenhaus products are of fundamental importance for the theory of Lie groups and Lie algebras. While their applications in physics and physical chemistry are important, novel applications in CFD (computational fluid dynamics) arose based on the fact that their sparse matrices can be seen as generators of an underlying Lie algebra. We apply this to classical splitting and the novel Zassenhaus product formula. The underlying analysis for obtaining higher order operator-splitting methods based on the Zassenhaus product is presented. The benefits of dealing with sparse matrices, given by spatial discretization of the underlying partial differential equations, are due to the fact that the higher order commutators are very quickly computable (their matrix structures thin out and become nilpotent). When applying these methods to convection-diffusion-reaction equations, the benefits of balancing time and spatial scales can be used to accelerate these methods and take into account these sparse matrix structures.The verification of the improved splitting methods is done with numerical examples. Finally, we conclude with higher order operator-splitting methods.     

Direct numerical simulation of one type of compressible turbulence interacting with a shock wave

Direct numerical simulations of compressible turbulence interacting with an initially plane shock wave are presented. The underlying model is based on the numerical solution of the Euler equations combined with direct statistical simulation. Steady-state isentropic isotropic turbulence is considered. The amplification factors for fluctuations of the thermodynamic variables, velocity, vorticity, and kinetic energy of fluctuations are analyzed; and the correlation coefficients between flow variables are studied for Mach numbers ranging from 1.2 to 3.