基于相对优势类差量的序信息系统属性约简算法

针对序信息系统,定义了优势类差量和相对优势类差量,讨论了一种刻画属性重要度的新指标.在此基础上,提出一种基于相对优势类差量的启发式约简算法,它能从搜索空间中删除不重要属性,降低了约简的时间复杂度.与现有启发式约简算法相比,该算法具有较高的搜索效率.实例与实验表明了该算法的可行性与有效性.     

基于粗糙集与层次分析法的组合预测方法

本文在改进的属性约简启发式算法 ,即应用加权平均的属性重要度对属性进行约简的基础上 ,将粗糙集理论和层次分析相结合 ,给出了一种全新的组合预测方法 .     

基于粒关系包含度矩阵的属性约简算法研究

针对信息系统属性约简问题,通过借助粒关系包含度矩阵这一中间工具,给出一种决策表属性启发式约简算法.首先,计算决策表中条件属性与决策属性之间的粒关系包含度矩阵;然后,将粒关系包含度矩阵中隐含的信息L_B作为启发式算子对决策表进行属性约简;最后,删除冗余属性并设置终止条件,实现决策表的属性约简.通过实例验证了该算法的有效性.     

基于可辨识矩阵的模糊目标系统决策约简算法

在模糊目标信息系统决策约简和可辨识矩阵定义的基础上,讨论了可辨识矩阵的性质以及与决策约简集之间的关系.同时定义一种新的属性重要度,并将此作为启发式信息,设计了一种模糊目标决策信息系统最小决策约简算法,通过实例验证该算法简捷、有效.     

基于可辨识矩阵的属性约简算法及应用

针对决策信息系统最大分布约简问题,从代数角度给出了一种启发式属性约简算法.该算法在最大分布可辨识属性矩阵基础上,首先以最大分布核属性集为起点,然后对其余属性按其在可辨识属性矩阵中出现的频数大小逐次添加到核属性集中,再根据启发式算子对新的属性集给出最大分布约简的判断.重复以上步骤,直到找到最大分布约简.算例分析表明该算法的有效性和可行性.     

区间值优势关系系统中属性约简及规则提取方法北大核心

本文以包含偏序关系的区间值决策系统为研究对象,对连续属性值进行模糊化处理,构造一种模糊优势关系粗糙集模型,并讨论了其相关性质。基于新模型提出一种不确定性度量-模糊粗糙熵,并以此为启发信息构造一种启发式约简算法,同时给出了该算法的时间复杂度分析结果。由该算法所得到的决策规则集具备较高的准确度和覆盖度,从而保证了数据预测、分类的准确性和合理性。通过实例分析,证明该算法是区间值优势关系系统中规则获取的有效方法。     

变精度粗糙集的约简算法

文中研究了变精度粗糙集的属性约简问题,通过设置参数β,简化决策表,定义其上β的限制正域,进而给出其约简算法,并结合实例分析,验证该算法的有效性.     

求解资源约束项目调度问题的启发式算法综述

本文综述了求解RCPSP的启发式算法.首先在对各种优先权规则进行归纳的基础上,概述基于优先权规则的RCPSP启发式算法研究现状;其次,综述项目进度的表述方式及常用超启发式策略,汇总求解RCPSP的超启发式算法的研究成果.此外,简要介绍除上述两大类启发式算法之外的其他几种启发式算法;最后,对全文进行总结,并指出该领域几个有希望的研究方向.     

基于粗糙集的突发事件属性约简方法

针对突发事件不完备信息系统中的原始数据存在大量属性冗余的问题,提出一种基于粗糙集的不完备信息系统属性约简方法,以剔除冗余属性,提高知识清晰度。首先对缺失、冗余、噪声以及连续型数据进行预处理;然后进行属性分类,将属性分为条件属性与决策属性,进而建立决策表;最后根据决策表的特征,结合有序加权平均算子的思想,提出一种基于属性重要度的启发式属性约简算法。文末,通过实例验证了方法的正确性与有效性,并利用该方法实现了火灾数据的属性约简。     

基于优先度搜索的基站规划解决方案

基站规划问题通常为大型的组合优化问题.在规划过程中既要保证成本最低,同时也要降低站点之间连接的路径损耗.针对此类问题,传统的解决方案主要为使用退火、遗传等启发式算法,算法效率较低,运行结果无法保证.具体到Relay无线回传中基站的拓扑规则,本文提出了一种有效解决问题的启发式算法,引入"优先度"的概念,并将其作为判据函数进行一种类贪婪的"选取-连接-剔除"的搜索过程,并进一步对算法进行了理论完善,构建抽象函数Γ,引入参数搜索,将算法推广为一种系统的优化问题启发式算法的范式.对于路径损耗,该解决方案借鉴了A*算法,在保持成本不变的前提下,提出若干种高效的"变换"方法,优化各站点之间的拓扑关系来降低总体路径损耗.算法在随机生成的样本和真实测试数据上均能取得良好的结果,且在区域总面积、区域形状发生变化时,能保持良好的稳定性.该算法在运算速度和运算结果上均优于传统的启发式算法.     

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.