基于前景理论和灰色关联的群决策评估模型

构建了基于前景理论和灰色关联的国防科研项目运行阶段群决策评估模型.基于群层次分析法确定评估指标权重,采用前景理论描述专家心理期望行为,以各项目的属性均值序列为参考方案,建立各项目与参考方案间的关联系数,并以此构建基于关联系数的价值函数,根据各项目的综合前景价值对国防科研项目运行阶段的各评估项目进行择优排序.实例表明了方法的客观合理性和有效性.     

基于灰色前景关联的民营企业核心竞争力评价研究——以许昌市民营企业为例

针对我国民营企业缺乏核心竞争力的现象,通过分析发现缺乏核心竞争力是其共性,由此提出了一种基于灰色前景关联的民营企业核心竞争力评价模型.该模型是灰色关联分析与前景理论的结合,首先计算各企业与理想企业间的灰色关联系数;考虑决策者风险态度对多指标决策的影响,由灰色关联系数确定了前景价值函数,并构建了方案综合前景值最大化的多指标优化模型求解最优权向量.以许昌市27家民营企业为例,验证了所提出的方法的合理性.     

灰色面板数据视域下的相似性和接近性关联度模型拓展

灰色面板数据包含研究对象诸多信息,由于数据类型和结构较为复杂,目前还没有测度其相似性和接近性的关联度模型,针对这一问题。首先,通过投影方法将灰色面板数据转化为样本关于指标的时间序列行为矩阵,矩阵每行为指标的时间序列;然后,定义一般灰数的距离测度和运算法则;最后,基于两折线间斜率与面积的视角,测度相似性和接近性关联系数。进而构建灰色面板数据的相似性和接近性关联度模型,并研究了该模型的性质。实例表明该模型在测度面板数据类型为一般灰数时的相似性和接近性方面具有良好的效果。     

Fuzzy-Grey综合评判模型与射击方案的优化

本考虑类别标准已确定的综合评判问题，将灰色理论中的关联分析用于Fuzzy综合评判模型，用灰色关联系数来替代隶属度，提出一种的综合评判的方法，运用于射击方案的优化．     

基于区间灰数多属性群决策建模技术的卫生应急综合评价研究

多属性灰色群决策建模方案设计为立足点,引入区间灰数、相离度、逼近理想点、群决策集结算法知识,在属性权重为实数、区间灰数或优化运算形式下,经属性值规范化后制定理想方案.首先,计算区间灰数相离度、灰色关联系数、灰色关联度,讨论以理想方案贴近度确定排序或择优.然后,改进为群体专家独立决策环境下,由属性矩阵虚构理想方案并计算关联度、贴近度,与专家权重集结为贴近度矩阵,由逼近理想点思路排序及择优.最后,由疾控机构卫生应急能力评价案例验证可行性,区间灰数、属性测度、专家权重以及属性群决策信息利用充分,这套建模方案对于类似问题也有推介意义.     

节能项目经济性评价的灰面积关联模型

为完善节能项目评价及管理的决策支持,建立基于灰面积关联决策的节能项目评价模型.以灰色关联决策理论为基础,分析经典灰色关联决策方法的优缺点,采用被选方案与理想方案间两曲线相邻点间多边形面积作为关联系数,度量曲线的几何形状的相似性,构建了灰色关联度公式.采用某企业计划发展的节能项目数据为实证样本,根据其成本、能耗数据及六项指标对节能项目进行评价,分析节能项目方案间的差异.通过算例验证了灰面积关联决策模型的合理性和算法的有效性,为节能项目评价及管理提供新的决策模型.     

基于灰色关联分析的模糊评判模型与系统分析

本文用灰色关联系数来求解隶属度，提出一种类别标准已确定的综合评判模型与方法，并用于系统的排序分析．     

基于前景理论的多目标灰色关联决策方法

针对决策者风险态度对多目标决策的影响,提出了一种基于前景理论的多目标灰色关联决策方法.通过奖优罚劣的线性变换算子对原始数据进行规范化处理,得到不同目标下的正负理想方案.以各方案与正负理想方案的关联系数为参照点计算各方案的前景矩阵,在此基础上构建方案综合前景值最大化的优化模型,求出不同目标下的最优权向量,进而求出综合效果测度矩阵,对每个局势进行排序.最后通过实例验证了该方法的有效性和实用性.     

基于灰色前景关联的多属性决策模型

针对方案属性值为三参数区间灰数的多属性决策问题,提出了一种基于灰色前景关联的多属性决策方法.定义了三参数区间灰数距离测度和排序方法;定义了靶心和靶界点,由此提出了子因素与最优理想效果向量和临界效果向量的灰色相对关联系数;分别以靶心和靶界点为参考点确定了前景价值函数,由此构建了求解最优权向量的优化模型,再求方案的综合前景值对方案进行排序.通过实例说明了该方法的合理性和有效性.     

基于区间二型模糊数的多属性群体灰色关联决策方法

针对属性值以区间二型模糊数形式给出的多属性决策问题,提出基于灰色关联度的多属性群体决策方法.首先,提出了一种新的计算区间二型模糊数之间距离的测度;然后,结合该距离测度公式构造出一种新的基于距离测度来求权重的方法,运用此方法求出决策者属性的权重;接着,通过主客观综合赋权法求出专家权重;最后,通过各方案与理想方案的灰色关联贴近度对方案进行大小排序.案例分析及对比分析说明该方法的合理有效性.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.