基于改进的T型关联度和AHP的一种新评价模型

首先,对灰色T型关联度进行改进,弥补了其中的不足,通过实例验证,得到了较好的结果,同时展现了改进T型关联度模型的可信度,充分说明其具有广泛的应用价值.其次,将其改进的T型关联度与AHP相结合,构造了一种新的综合评价得分模型,可以反映事物的动态优劣变化,通过具体实例,说明了综合评价得分模型的可行性.     

灰色绝对关联度的改进模型

基于刘思峰教授提出的灰色绝对关联度模型,提出了一点改进,给出了新的灰色绝对关联度模型,并讨论了新模型的性质及其算法.一方面保持了原绝对关联度模型的优点,另一方面改正了原模型在某些方面的不足.     

角度化灰色T型关联度模型及应用研究

通过对现有灰色关联度模型及算法的分析,首次提出了角度化灰色T型关联度模型。在分段线性表示的基础上,使用相邻线段间的夹角构成的角度序列近似表示时间序列,并给出了相关灰色关联系数和灰色关联度的计算方法。角度化灰色T型关联度模型不仅能够反映序列的正负相关关系,并且满足对称性、唯一性、可比性和规范性等性质。最后,通过实证分析证明了该模型的实用性和有效性。     

基于改进灰色斜率关联度的评价研究

提出了一种对灰色斜率关联度的改进模型,并分析了它的性质,改进后的关联度模型能够反映序列的正、负相关关系,具有对称性、唯一性、可比性和无量纲化后的保序性.改进的灰色斜率关联度能够更充分地利用数据所包含的信息,所得关联分析结果较为客观可靠,最后以实例验证了评价方法的有效性与实用性.     

矩阵型灰色关联度的特征检验方法及其应用

针对现有灰色关联理论的不足, 本文提出灰色关联的特征检验思路, 构建了矩阵型灰色关联度的特征检验方法。首先优化矩阵型灰色关联模型, 利用行为矩阵差值定义特征差异矩阵, 采用矩阵2范数构建关联度公式。而后分析特征差异矩阵的稳定性与趋势性, 利用变异系数形式构建稳定性系数, 利用最小二乘法估计趋势性系数, 两者共同组成矩阵型灰色关联度的特征检验方法。最后, 本文模型被应用于湖北省恩施州的长期多维贫困分析, 在与现有模型的比较中, 发现关联度评估结果有效区分了恩施州8个市县的贫困情况, 特征检验方法从贫困不确定性和趋势性两方面对结果进行补充, 验证了模型的可行性与实用性。     

基于改进熵和灰关联分析的模糊物元分析模型及应用

借助改进熵权法对评价指标进行赋权,在灰关联分析和模糊物元分析理论的基础上,建立了改进熵和灰关联分析的模糊物元分析模型,根据灰色关联度的大小对评价对象进行排序,并将其应用到综合评价中,通过实例,说明此模型的合理性.     

关于灰色绝对关联计算模型的探讨

本文通过对现有灰色关联度计算模型的分析,指出了现有灰色关联度计算模型的缺陷,针对不同类型问题构造了不同灰色关联度计算模型,并将其应用于解决实际问题,取得较好的效果．     

基于AHP及灰色关联分析法的发动机健康评估研究

综合运用灰色关联分析及层次分析法,提出了一个航空发动机健康状态评估模型.模型采用层次分析法确定评价指标的权值,并对层次分析法进行了合理改进,用灰色关联分析计算评估对象的灰色关联系数,进而计算加权灰色关联度作为判断航空发动机健康状态的指标.基于航空发动机的QAR(Quick access recorder)数据,将模型应用于实例分析,对多台发动机健康状态进行了评估,结果验证了方法的有效性.     

基于改进的T型关联度在音乐分类中的应用

在音乐分类问题中,绝大多数的算法需要提取多个特征值进行分析,工作量和复杂程度也随之增加,并且分类太绝对化.为了降低工作量和复杂程度,采用新的方式对音乐进行分类,即引进灰色关联度分析方法.现有的灰色T型关联度模型均存在不足,对序列采用绝对初值化处理,并且对关联系数计算公式进行改进,增强了结果的准确性和可信度.将提取出的短时能量、短时平均过零率和短时平均幅度作为音乐分类的三大特征值,对大部分音乐进行了较为准确的分类,排除率达到90.1%.而且此方法能够体现出各音乐之间的关联程度,使得分类更加人性化,这点具有现实意义.并且避免了复杂的计算过程和巨大的工作量,简化了解决问题的方式,也减少了对特征值的依赖,仅采用三种特征就达到了很好的效果.这充分反映了思路的正确性、实用性和可行性.     

基于改进灰色关联度的IOWA算子最优组合预测模型

通过引进诱导有序加权平均(IOWA)算子和改进灰色关联度的计算式,提出了新的基于改进灰色关联度的IOWA算子的组合预测模型.方法可以克服传统的组合预测方法赋予不变的加权平均系数和以单一误差指标作为预测精度衡量的缺陷.定义基于改进灰色关联度的IOWA算子的优性组合预测的概念,最后给出实例分析表明了新模型能有效地提高组合预测精度.     

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.     

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 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

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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].