Ranking grey numbers based on dominance grey degrees

With respect to the decision making problems where a lot of fuzzy and grey information always exists in the real-life decision making information system methods as fuzzy mathematics, it is difficult for such uncertainty probability, and interval numbers to deal with. To this end, based on the thought and method of grey numbers, grey degrees and interval numbers, the concept of dominance grey degree is defined. And then a method of ranking interval grey numbers based on the dominance grey degree is proposed. After discussing the relevant properties, the paper finally uses an example to demonstrate the effectiveness and applicability of the model. The result shows that the proposed model can more accurately describe uncertainty decision making problems, and realize the total ordering process for multiple-attribute decision-making problems.     

Optimization approach of background value and initial item for improving prediction precision of GM（1,1） model

A combination method of optimization of the back-ground value and optimization of the initial item is proposed. The sequences of the unbiased exponential distribution are simulated and predicted through the optimization of the background value in grey differential equations. The principle of the new information priority in the grey system theory and the rationality of the initial item in the original GM（1,1） model are ful y expressed through the improvement of the initial item in the proposed time response function. A numerical example is employed to il ustrate that the proposed method is able to simulate and predict sequences of raw data with the unbiased exponential distribution and has better simulation performance and prediction precision than the original GM（1,1） model relatively.     

Expansion modelling of discrete grey model based on multi-factor information aggregation

This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.     

Response surface method using grey relational analysis for decision making in weapon system selection

A proper weapon system is very important for a na- tional defense system. Generally, it means selecting the optimal weapon system among many alternatives, which is a multiple- attribute decision making （MADM） problem. This paper proposes a new mathematical model based on the response surface method （RSM） and the grey relational analysis （GRA）. RSM is used to obtain the experimental points and analyze the factors that have a significant impact on the selection results. GRA is used to an- alyze the trend relationship between alternatives and reference series. And then an RSM model is obtained, which can be used to calculate all alternatives and obtain ranking results. A real world application is introduced to illustrate the utilization of the model for the weapon selection problem. The results show that this model can be used to help decision-makers to make a quick comparison of alternatives and select a proper weapon system from multiple alternatives, which is an effective and adaptable method for solving the weapon system selection problem.     

基于面积的改进灰关联度算法

灰关联分析是灰色系统理论的重要组成部分,寻找合适的相似性度量方法是提高灰关联分析准确性的关键。通过对现有灰关联模型的研究,提出了一种基于面积的相似性度量方法,以序列相邻采样点间对应面积作为灰关联系数的计算依据,并用灰关联系数的均值作为序列的灰关联度。理论推导证明该方法符合灰关联四公理,体现了灰关联分析中衡量曲线相似性的基本思想。仿真实验表明,在邓氏灰关联度和广义灰关联度算法失效时,该方法仍能得出与定性分析一致的关联序,具有较高的可靠性。     

灰色主成分评价模型的构建及其应用

在梳理和分析主成分分析用于社会科学评价中存在的问题的基础上,将主成分评价拓展到灰色系统领域,构建了灰色主成分评价模型,以灰色相对关联度矩阵代替传统的协方差矩阵或者相关矩阵来进行主成分分析和评价.此外,根据目前主成分评价中权重引起的重复加权问题做一定的讨论,以因子负荷量作为主成分权重合成的重要依据,解决了重要性权对数据的影响问题.最后,构建了两个案例证明所提思想的合理性和有效性.     

Higher-order principal component pursuit via tensor approximation and convex optimization

Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit （HOPCP）, since it is critical in multi-way data analysis. Unlike the convexification （nuclear norm） for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme： the augmented Lagrangian alternating direction method （ALADM） and its truncated higher-order singular value decomposition （ALADM-THOSVD） version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.     

基于动态灰色主成分分析的多时刻威胁评估

针对目标威胁评估问题的高维数、时变性等特点,提出基于动态灰色主成分分析(dynamic grey prin-cipal component analysis,DG-PCA)的多时刻威胁评估方法.首先,以潜艇为分析对象,构建协同作战模式下的威胁评估指标体系.其次,提出扩展灰色相似关联度用于表征指标间动态非线性相关度,构建...     

基于相似性和接近性视角的新型灰色关联分析模型

以笔者1992年提出的灰色绝对关联度模型为基础,构造出分别从相似性和接近性两个不同视角测度序列之间的相互关系和影响的灰色关联分析模型,并研究了灰色相似关联度和灰色接近关联度的计算及性质,最后给出一个算例.新模型克服了原模型存在的问题,更易于实际应用.相似关联度主要用于测度序列折线在几何形状上的相似程度;接近关联度用于测度序列折线在空间中的接近程度.需要说明的是,接近关联度仅适用于序列的意义、量纲完全相同的情形,当序列的意义、量纲不同时,研究其接近关联度没有意义.     

动态多响应系统的稳健参数设计

针对动态多响应之间的相关性及试验设计的信息不确定性, 提出了一种动态多响应系统的稳健参数设计方法. 首先, 利用满意度函数对动态系统的敏感度和波动分别进行了度量, 在此基础上进行了主成分分析; 其次, 采用灰色关联分析得到主成分序列与其理想序列的灰色关联度, 然后通过TOPSIS方法转换得到综合灰色关联度, 并根据综合灰色关联度确定可控因子的最优水平组合; 最后, 通过两个实例说明了该方法的有效性与优越性.     

基于灰主成分的空战目标威胁评估

由于影响空战目标威胁评估的因素复杂多样,且具有矛盾性、相关性、耦合性等特点,因此利用传统的评估方法无法得到准确客观的评估结果。对此,提出一种基于灰色主成分的目标威胁评估方法。首先,利用主成分分析(principle component analysis, PCA)方法,分析指标之间的相关性,生成指标之间的灰色关联系数矩阵,取代传统的相关矩阵或协方差矩阵,将相互关联的指标转化成相互独立的分量,重构目标威胁评估体系。其次,构建灰色关联深度极大熵模型确定原始评估指标权重。然后,分析以累计贡献率为客观性赋权且没有考虑指标重要性差异的问题,将因子载荷作为主成分权重合成的重要依据。最后,通过仿真案例,对不同的威胁评估方法得出的结果进行对比分析,证明了灰主成分法的有效性和合理性。     

基于灰熵优化的加权灰色关联度

基于灰色系统内各因素关系稳定的基本假设和灰内涵序列熵的分析,首次给出了灰关联分析中关联系数权重的确定方法。通过定义加权灰色关联系数分布密度值,构建了灰内涵序列,建立了关联系数权重的优化模型,并以算例验证了该方法的有效性与实用性。结果表明,该方法能够反映不同时点关联系数的重要性,使关联系数的波动性得到了有效控制,解决了局部点关联系数控制整个灰色关联序的问题。     

基于城市金融竞争力评价的我国多层次金融中心体系

为了对我国的多层级金融中心体系进行研究, 论文设计了一套系统的评价方法. 在评价过程中, 首先建立了评价各城市金融竞争力的指标体系, 接着采用熵权法、灰色关联分析法、主成分分析法等对我国21个大中城市的金融竞争力进行了评价, 再运用Kendall协同系数检验法对三种方法评价结果的一致性进行了检验并进行组合评价, 给出了各城市金融竞争力的排名, 最后还运用K-均值聚类分析法将21个城市划分了层级. 根据评价的结果以及区域经济发展的特点和各城市的优势和差异, 对我国多层次金融中心体系格局的构建给出了政策建议.     

基于改进调节变量主成分权重的广义灰靶决策模型研究

在现实生活中，由于信息的不完全性和认知的不充分性，多数决策对象具有强烈的多源不确定性特点，存在多种不确定性因素共存的现象.针对目前灰靶决策模型未充分考虑决策对象多种不确定性因素共存的局限，以及确定决策指标权重时未深入探讨指标间相关性的问题，首先引入广义灰数的表征形式对指标属性值进行统一表征，并提出广义灰数的一致效果测度模型，然后根据传统主成分分析法确定权重时所存在的二次加权放大问题，揭示指标差异性与相关性对二次加权的影响，通过改进调节变量对原始主成分权重进行修正，接着将传统的灰靶决策模型扩展为广义灰数形式，构建基于加权欧式距离的广义灰靶靶心距模型，并据此建立基于改进调节变量主成分权重的广义灰靶决策模型.最后通过案例研究，验证本文模型的合理性和可行性.     

基于广义动态灰关联度窗口的时滞分析模型

基于静态最大关联度准则的经典灰关联时滞分析方法对样本时序的依赖性较强,分析结论的代表性较差、甚至会出现自相矛盾的地方.为此,本文探讨了一种新的全局性动态时滞分析方法.首先,设计了新信息优先加权算子,将其引入广义灰色关联度模型,强调新信息在关联分析中的重要性.其次,针对经典的基于灰关联度的时滞分析方法的不足,提出动态灰关联度窗口的概念,对样本时序中所有潜在时滞取值展开系统化的分析.再者,定义了基于动态灰关联度窗口概念的时滞关联度矩阵以及相应的时滞灰关联度向量,设计出灰栈矩阵这一特殊灰关联数据存储结构,动态对比所有潜在时滞关系,找出代表性时滞值.最后,对宏观经济指标之间的时滞关系展开案例分析,并与经典灰关联时滞分析方法进行对比,结果表明本文设计的时滞分析方法具有更好的说服力.     

模糊灰关联模式识别方法及其应用

首先建立灰关联分析的新的理论模型,然后将其与模糊集理论结合起来,提出了一种模糊灰关联模式识别方法．通过应用于场地土类别的评定,从而说明了本文方法的有效性     

One Kind of Effective Discrete Transformation on Converting the High Growth Series into the Low Growth One

To the transformation F（a（s））=a（s）/d^s,this paper brings out two kinds of ways to ascertain parameter d, one way, we let d be arithmetic average of class ration inverse, namely d1=1/n-1（y^（0）（2）/y^（0）（1）＋y^（0）（3）/y^（0）（2）＋y^（0）（4）/y^（0）（3）＋…＋y^（0）（n-1）/y^（0）（n-1）＋y^（0）（n）/y^（0）（n-1）.The other way, we let d be geometric average of class ration inverse, namely d2=（y^（0）（n）/y^（0）（1））^1/n-1.Through the close theory testifying, we find that the model given by this paper has white exponential law coincidence property, that is to say, if we build the model to the normal index, the result has not model error. At the same time, this paper points out, the request d 〉 1 is not appropriate to monotone decreasing series; even precision of model will decrease.     

A New Grey Model Based on Optimizing the Grey Derivative and the Background Value at the Same Time

Based on both white response and connotation expression are geometric progression in the most primitive grey differential equation of GM（1,1）x（k） （k）＋ ax（1） （k） = b, this paper begins with generation of the time response .function＇s grey derivative at discrete points. Through derivative＇s definition, establishing a new GM（1,1） by optimizing grey derivative and background value. Then, getting the best coefficient c by introducing criterion function and it has proved that the new expression has the whitened exponent law coincident property and the whitened coefficient coincident property in theory. Finally, some examples show the new model has higher prediction precision.     

部分权重信息且对方案有偏好的灰色关联决策法

以灰色系统理论的思想和方法为基础,探讨了决策方案的属性值为区间灰数、属性权重部分已知和决策者对方案有偏好的灰色决策问题,提出了解决这种灰色决策问题的方法与算法。运用分析技巧,构建了基于区间灰数相离度的灰色区间关联系数公式和灰色区间相对关联系数公式。该决策方法既利用了客观信息,又尽可能地满足决策者的主观愿望,也避免了在某些准则下去求出属性权重真值的估计值,并且计算易于在计算机上实现。实例分析说明了所提出的灰色关联决策方法的合理性及其算法的有效性。     

灰色关联分析模型研究进展

本文对灰色关联分析模型的研究进展进行了系统梳理. 从早期基于点关联系数的灰色关联分析模型, 到基于整体或全局视角的广义灰色关联分析模型; 从基于接近性测度相似性的灰色关联分析模型, 到分别基于相似性和接近性视角构造的灰色关联分析模型; 研究对象从曲线之间的关系分析到曲面之间的关系分析, 再到三维空间立体乃至n维空间中超曲面之间的关系分析. 明确了有待进一步研究的问题. 较为清晰地向读者展示出灰色关联分析模型的几条研究脉络.