不确定性视角下考虑“双预期”的动态多属性决策方法

针对不确定环境下的多阶段、多属性决策问题,文章提出了一种不确定视角下考虑双预期目标的动态多属性决策方法.为全方位评估决策对象,从时间维度研究对象的动态发展特征,综合横向对比和纵向发展两个方面,构建了“差异化”发展状态下针对区间数的双重预期设置方法;结合决策者的心理特征、区间分布状态以及信息不确定度的影响作用,基于前景理论进行信息融合及排序.最后,以应用型高校产教融合绩效评估问题为案例背景,通过分析和方法比较验证所提方法的实用性和合理性.     

TOPSIS-GRA法下的企业动态信用评价方法及其应用

针对传统信用评价方法较少考虑到时间的延续性,且只注重信用基础值而忽视其发展趋势的问题,本文提出了一种具有风险抗性信用奖惩特征的TOPSIS-GRA的动态信用评价方法。首先,利用指标信息量诱导密度算子对静态数据进行综合集成,得到静态综合信用评价值,在此基础上构造动态信用评价加权决策矩阵;其次,在对矩阵进行TOPSIS法验算的过程中嵌入企业风险抗性信用奖惩点,进而得到包含奖惩性质的相对贴近度;再以GRA方法得到各受评企业理想的信用发展趋势关联度,结合两者最终得到融合风险抗性奖惩量、信用基础值和信用发展趋势三项特征的稳定科学的企业动态信用评价结果。最后,给出了一个实证分析,验证了该方法的有效性及合理性。     

基于FCM-GRNN的驾驶倾向性识别方法

为提高对驾驶倾向性的辨识准确率,进行驾驶倾向性问卷表调查、模拟驾驶、人因工程测试,考虑了驾驶员的心理、生理信息,以及环境、车辆和操作信息的基础上,提出用广义神经网络确定聚类中心,优化模糊c均值聚类算法,实现目标识别级信息融合的方法,对驾驶倾向性进行预测.利用实验数据对识别方法进行验证,结果表明,该算法对驾驶倾向性的预测准确率达到了85.83%,为进一步研究驾驶员倾向的动态特性提供了依据.     

二维区间密度加权算子及其应用

针对不确定多属性决策中的属性信息分布不均匀,且评价信息多数为二维信息的情况,本文提出了二维区间密度加权算子(TDIDW算子)的属性信息集结方法.依据密度算子的集结过程特点,文章首先定义了二维区间密度加权算子及其合成算子,然后介绍了基于灰色区间聚类法的评价信息分组方法以及基于非线性模型的密度加权向量确定方法,最后进行了算例验证.验证结果表明,该方法可以有效地解决由于属性信息分布不均匀而导致评价结果不准确的问题.     

一种动态获取簇核心的自动聚类tNN-MEANS算法

K-means算法是一种非常重要的聚类算法,然而算法的聚类效果受簇的个数、初始中心点位置的影响很大.提出基于优化初始中心集合和中心移动算法tNN-MEANS,算法有效解决了以下三个问题:1)准确确定大规模数据集中簇的个数;2)精确确定全局高密度的核心区域;3)克服了簇中存在多个高密度区域的问题.运用UCI数据集分别对X-means算法、DBSCAN算法和tNN-MEANS算法进行对比实验,实验结果验证了tNN-MEANS算法的聚类精度、确定簇的个数、蔟划分的正确率等性能均优于与之对比的其它算法.     

闪电分叉过程算法优化的K-means聚类

K-means聚类算法是在数据挖掘和数据分析中一种常用算法,但是其存在依赖初始值和易陷入局部最优值的缺陷,针对这些不足,本文提出一种闪电分叉过程算法优化的K-means聚类,克服聚类算法在初始值选择困难的问题,提高K-means聚类算法的求解精度,降低陷入局部最优的可能性。从UCI数据集中选取6个真实的数据集进行仿真实验,结果表明本文改进后的聚类算法有更好的求解精度和鲁棒性。     

基于先验信息和一维数据聚类的专家赋权方法

多属性群体评价方法研究中,对专家赋权是一项重要的研究内容。本文结合专家的先验信息和后验信息,提出了一种确定专家权重的方法。首先,利用专家历史评价活动中的序值相关系数,做出本次评价活动的预测值,进而确定专家先验权重;其次,基于群体共识视角,对各专家所给出的指标信息进行一维数据聚类,结合不同分组情况下出现的概率,计算出专家后验权重;最后,将两类权重进行组合确定最终权重,并用一个算例验证了该方法的有效性以及合理性。     

基于一致性排序的动态评价方法研究

主要工作是通过Copealand重排序方法构建动态评价模型,研究动态评价中的一致性排序问题,并通过实证研究验证模型的有效性.首先,利用基尼系数赋权法建立评价模型,确定静态评价结果和排名;然后,通过Copealand法确定出一个综合不同年份排序的一致性排序;最后,根据评价对象不同年份排名的发展趋势对一致性排序进行修正,得到最终的排序.主要特色一是通过Copealand法集合不同年份的排序确定最终的一致性排序,避免了通过引入时间权向量确定动态权重时人为主观因素太强的问题,解决了动态综合评价中的一致性排序问题;二是通过对一致性排序的修正,保证了最终的排序能够体现不同年份的发展趋势.     

基于分层激励控制线的多阶段信息集结方法

针对时序动态综合评价问题,给出了一种具有分层激励特征的多阶段信息集结方法。该方法通过分层实现逐步激励,从而诱导个体或组织的突破式发展。首先,在界定了分层原则的基础上给出了激励控制线的确定方法;然后,提出了一种带有奖惩特征的信息集结模型。最后,通过一个算例对该方法的有效性进行了验证。在实践中长期使用此方法,可促使被评价对象的快速成长,同时也能减弱或避免其出现大幅倒退的情形。     

基于方差与改进群智能算法的K-means聚类优化

利用K-means进行数据聚类时,借用不同处理手段其统计距离和聚类中心等会有所差异,从而影响聚类结果,尤其是当数据维度增高时,这种现象更为明显.对此,文章提出一种基于样本方差的多元统计距离算法,并引入改进人工蜂群算法及评价准则函数确定聚类中心和最佳聚类数,优化K-means算法.理论上,该方法可以克服原算法易陷入局部最优和固定聚类数等缺陷.最后,通过特异值检测,人工数据集以及UCI真实数据集测试验证该优化算法性能.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].