综合处理专家意见的ZHBM方法

在专家意见的不确定性量化法的基础上,给出了不确定性量化值的运算,进而通过实例创立了综合处理专家意见的ZHBM方法.     

层次分析法中极端专家意见排除研究

层次分析法是通过群决策的方法利用专家的定性判断矩阵研究决策问题.当极端专家意见出现时,会使得群决策的结果存在偏误.提出的极端专家意见排除模型是针对层次分析法中极端专家意见排除的改进方法,利用专家判断矩阵和经层次分析法得到结果的距离,给出排除极端专家意见的规则.利用未被排除的专家意见矩阵,计算新的决策结果,使得结果更为代表性、科学性,有效体现了总体意见,对利用层次分析法进行群决策有一定借鉴意义和实际应用价值.     

群体AHP方法在复杂系统易损性分析中的应用

群体层次分析法(Group AHP)是专家群体评判意见的综合量化方法,本文讨论了该方法在系统易损性分析中的应用,并针对群体层次分析法专家意见合成问题,提出了基于主成分分析方法计算各专家客观权重,并根据该权重合成专家评判意见的方法.应用结果表明,该方法能更好地克服人为主观判断及偏好给决策带来的影响,为复杂系统易损性定量评估提供了有效的技术途径.     

基于直觉模糊距离的群决策专家意见聚合分析

提出了一种基于直觉模糊距离来聚合专家个人意见为一个优化的群体意见一致度的新方法.首先,根据直觉模糊集的几何意义,定义了两个直觉模糊集之间的距离;然后,利用直觉模糊距离来聚合专家两两之间对备选方案意见的一致度,综合考虑每位专家的相对重要权重,得到专家群体对备选方案意见的综合一致度;最后通过一个具体实例来说明这种方法的具体应用及计算过程.     

一类专家意见的不确定性量化法与不确定性决策

以不确定性信息的数学处理理论为基础,建立了一类专家意见的不确定性量化表达式,定义了表达式间的运算与运算律,给出此类专家意见合成的不确定性决策模型.     

基于D-S证据理论的群决策专家意见集结方法

将D-S证据理论应用于群决策，指出其优势在于应用基本可信度分配函数描述专家意见，并能区分对所描述对象不知道和否定的差异。在专家意见集结上，Dempster证据合成规则有一定的局限性，当证据发生冲突时，会得到不合理的结果。定义了证据间的分歧度，提出一种专家意见集结方法，使得专家意见发生冲突时亦可得到合理的集结结果。     

基于TOPSIS的模糊群体多属性决策方法

针对模糊群体多属性决策问题,给出一种基于理想点法(TOPSIS)的多属性决策方法.方法先用三角模糊数的形式表示专家评价值的模糊性和不确定性,而后考虑了专家在不同评价属性中的重要程度和意见的相似度,并将专家意见进行集结得到专家群体关于方案集的模糊决策矩阵,最后定义了三角模糊数形式的正负理想方案,通过计算各方案与正负理想方案的距离以及各方案与理想点的相对接近度,最终确定最优方案.通过实例分析说明了该方法的可行性和有效性.     

群决策中基于判断相似度的专家聚类及群体意见集结方法

针对大规模群决策问题,提出了一种基于专家意见相似度的群体判断信息逐步集结规划的方法。首先利用备选方案序关系向量的灰色关联度和夹角余弦构造两两专家判断信息的组合相似度;其次以判断相似度为标准,采用一种广度邻居搜索算法对专家进行聚类;然后以判断偏差最小为目标,构造非线性的约束规划模型对每一类专家意见进行集结,从而获得类内专家的集结信息;最后从专家数量最多的类别开始,依次对每类专家集结后的判断信息进行再次集结,从而获得最终的评判结果。该方法将大规模的复杂群决 策转化为低复杂度的多阶段专家信息集结问题,并保证了群体结果的一致性。算例分析验证了方法的可行性和有效性。     

一种基于直觉模糊集的群决策方法

利用直觉模糊集理论研究专家意见为{满意,不满意,弃权}三种形式的群决策问题.在构建群决策模型的过程中,分如下两种情形分别将专家意见综合为直觉模糊集:一是首先综合单个专家根据各准则给出的方案评估值;二是首先对单个准则综合所有专家给出的方案评估值.由此建立两个群决策模型.对由直觉模糊集表示的群决策结果,利用推广的TOPSIS方法对它们进行排序选优.最后给出一个应用实例.     

社会网络环境下保护少数意见的风险性大群体应急决策方法

大群体决策过程中,少数意见十分重要,但考虑少数意见又有一定风险性,本文提出了一种社会网络环境下保护少数意见的风险性大群体应急决策方法。首先,利用自然语言处理技术对社交媒体中公众对突发事件的传播信息进行关键词提取,再采用TF-IDF技术提取公众关心的事件属性并确定属性权重;其次,将专家之间的联系考虑到决策当中,构建决策专家之间的社会网络关系;然后,建立少数意见的识别和风险测度机制,并定义了两个风险系数:信任风险系数和偏好风险系数,通过少数意见聚集的信任风险系数调节少数意见聚集的权重,通过偏好风险系数调节群体共识,以得到共识水平较高的大群体决策方案;最后,通过“7.1”宁乡洪灾案例分析,验证了所提方法的可行性和有效性。     

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.