基于模糊熵的加权可变模糊评价方法及其应用

可变模糊评价的实质是多模型组合评价.在分析了可变模糊评价法的基础上,针对方法存在的不足,提出了一种考虑模型权重的可变模糊评价方法.方法首先利用可变模糊评价模型对样本进行计算,得到各样本在不同模型下的综合相对隶属度;然后基于得到的综合相对隶属度数据,利用模糊熵确定四种模型的重要性排序,结合二元比较模糊决策分析法求得四种模型的权重,进而得到最终综合级别特征值,并以此作为评价依据;最后,以煤与瓦斯突出危险性评价为例进行了方法的验证.结果表明:改进方法可行、有效,评价结果更符合客观实际.     

基于模糊熵的加权可变模糊评价方法及其应用北大核心

可变模糊评价的实质是多模型组合评价.在分析了可变模糊评价法的基础上,针对方法存在的不足,提出了一种考虑模型权重的可变模糊评价方法.方法首先利用可变模糊评价模型对样本进行计算,得到各样本在不同模型下的综合相对隶属度;然后基于得到的综合相对隶属度数据,利用模糊熵确定四种模型的重要性排序,结合二元比较模糊决策分析法求得四种模型的权重,进而得到最终综合级别特征值,并以此作为评价依据;最后,以煤与瓦斯突出危险性评价为例进行了方法的验证.结果表明:改进方法可行、有效,评价结果更符合客观实际.     

组合权重优化的企业财务绩效可变模糊综合评价模型

针对目前企业模糊综合评价无法解决模糊识别、动态可变性及单一权重不科学的问题,提出组合权重优化的企业财务绩效可变模糊综合评价新模型.首先,建立企业财务绩效综合评价指标体系;然后,获取指标数据并通过主客观权重融合的方法优化指标权重;最后,基于可变模糊集理论构建企业财务绩效可变模糊综合评价新模型.以B企业为例,应用新模型对B企业财务状况进行评价.结果表明:2012-2015年,B企业财务评价等级分别为Ⅲ-Ⅳ、Ⅱ-Ⅲ、Ⅱ-Ⅲ、Ⅲ-Ⅳ,符合B企业实际运营发展状况,证明了新模型的科学合理性.新模型不仅对企业财务绩效评价新方法进行了考察,而且拓展了可变模糊集理论的应用领域.     

基于区间值模糊粗糙集的研究生教育质量的评价方法研究

首先,采用区间值模糊粗糙集的属性约简方法,以属性重要性作为属性约简的重要启发式信息,剔除重要性不足的指标,得到约简后的研究生教育质量评价指标体系.其次,在此基础上确定了该评估指标体系的权重,给出了研究生教育质量的综合评价方法.     

水电工程应急能力模糊可变评估方法研究

针对水电工程应急能力评估的问题,综合运用可变模糊集理论,提出水电工程应急能力模糊可变评价方法.首先,通过分析水电工程应急能力构成要素,构建应急培训、应急预案与演练、危险源辨识与排查、应急保障体系、监测预警、现场处置等六类评价指标;其次,通过定义应急能力等级评价的模糊可变问题,分别计算样本指标对标准区间的级别相对隶属度和综合相对隶属度,构建应急能力模糊可变评价模型;然后,采用可变模糊迭代方法确定客观权向量,融合决策者的经验和主观偏好,调整评价权重.最后,以溪洛渡工程为例,表明方法综合使用主客观权重,提高了评价的可靠性与科学性.     

基于RS-G1理论的多属性不完备信息系统权重的计算及应用

针对多属性不完备信息系统,提出了一种主客观权重相结合的权重计算方法。在对缺失数据进行修补的基础上,利用粗糙集理论计算各属性的客观权重,利用G1法计算各属性的主观权重。与此同时,通过引入权重因子α构建了属性综合权重的计算公式,有效的避免了属性权重为零和权重分配不合理的现象。最后,利用该方法对边坡系统进行了分析,结果表明边坡角和岩石容重对边坡的稳定性影响最大,进一步验证了该方法的有效性和可行性。     

基于综合权重的理想模糊物元多属性决策法及应用

研究了属性指标具有不相容性和模糊性及其指标的权重完全未知的模糊多属性决策问题.分析了目前广泛采用的模糊物元分析法以及仅有主观赋权法或客观赋权法确定其指标权重的缺点.根据物元可拓理论和理想解法的思想,定义了理想模糊物元和负理想模糊物元的概念.利用兼顾主观偏好和客观信息的综合权重赋值法,提出了基于综合权重的理想模糊物元多属性决策方法.该法既能充分利用指标本身所包含的客观信息,又能充分发挥决策者的主观能动性.实例研究结果表明该法能反映出决策方案间的细微差别,能对决策方案的优劣做出更准确有效的评价.     

一种有方案偏好的直觉模糊多属性决策方法

研究了方案属性值和偏好值均为直觉模糊数的多属性决策问题.首先,通过分析部分文献中利用方案属性值与偏好值之间的偏差建立并求解规划模型,从而得到属性权重的不合理性.其次,在最小化方案综合评价值与偏好值偏差的基础上,建立并求解一个规划模型计算出属性权重.然后,利用方案综合评价值的得分函数和准确度函数对方案进行排序,从而得到了一种有方案偏好的直觉模糊数多属性决策方法.最后,通过一个实例说明了该方法的合理性与有效性.     

基于熵权的可变模糊集方法在水质污染评价中的应用

水质污染评价是水环境污染防治的重要基础,针对评价过程中评价指标的不确定性,将可变模糊集理论应用于水质污染评价中,首先,建立合理的指标体系与等级标准,然后,将熵值原理引入该方法中,利用指标实测数据的波动性来计算指标权重,最后,利用模糊可变评价模型对水质污染进行组合评价,并将均值作为最终评价结果,将此方法应用于泰州市新通扬运河水质污染评价中,结果表明,与模糊综合评价相比,基于熵权的可变模糊集方法评价结果合理、客观,具有更好的可靠性与稳定性,为水质污染评价工作提供了一种新的研究方法与思路.     

基于VIKOR和关联系数的犹豫三角模糊语言多属性决策方法

针对属性评价值为犹豫三角模糊语言集的多属性决策问题,提出一种基于VIKOR方法的犹豫三角模糊语言多属性决策方法.首先定义了犹豫三角模糊语言集的相关概念.然后运用VIKOR和关联系数方法,在可接受优势和决策过程稳定的条件下对方案进行择优,在理论分析的基础上,提出了这种新方法的计算步骤.并构建了确定最优属性权重的非线性规划模型,研究了当专家权重和属性权重未知情况下的犹豫三角模糊语言多属性决策方法.最后通过实例说明了该方法的有效性和可行性.     

Long-step primal-dual target-following algorithms for linear programming

In this paper we propose a long-step target-following methodology for linear programming. This is a general framework, that enables us to analyze various long-step primal-dual algorithms in the literature in a short and uniform way. Among these are long-step central and weighted path-following methods and algorithms to compute a central point or a weighted center. Moreover, we use it to analyze a method with the property that starting from an initial noncentral point, generates iterates that simultaneously get closer to optimality and closer to centrality.This work is completed with the support of a research grant from SHELL.The first author is supported by the Dutch Organization for Scientific Research (NWO), grant 611-304-028.The fourth author is supported by the Swiss National Foundation for Scientific Research, grant 12-34002.92.     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Volume preserving RK methods for linear systems

1. IntroductionIn recent yearss there has been a great interest in constructing numerical integrationschemes for ODEs in such a way that some qualitative geometrical properties of the solutionof the ODEs are exactly preserved. R.th[ll and Feng Kang[2'31 has proposed symplectic algorithms for Hamiltollian systems, and since then st ruct ure s- preserving me t ho ds fordynamical systems have been systematically developed[4--7]. The symplectic algorithms forHamiltonian systems, the volume-pre…     

求解离散不适定问题的正则化GMERR方法

迭代极小残差方法是求解大型线性方程组的常用方法, 通常用残差范数控制迭代过程.但对于不适定问题, 即使残差范数下降, 误差范数未必下降. 对大型离散不适定问题,组合广义最小误差(GMERR)方法和截断奇异值分解(TSVD)正则化方法, 并利用广义交叉校验准则(GCV)确定正则化参数,提出了求解大型不适定问题的正则化GMERR方法.数值结果表明, 正则化GMERR方法优于正则化GMRES方法.     

A note on the biasing of Newton's direction

This note deals with the geometric interpretation of the Levenberg-Marquardt search direction when the augmented Hessian is not positive definite.     

Diagonalized multiplier methods and quasi-Newton methods for constrained optimization

Two approaches to quasi-Newton methods for constrained optimization problems inR ⁿ are presented. These approaches are based on a class of Lagrange multiplier approximation formulas used by the author in his previous work on Newton's method for constrained problems. The first approach is set in the framework of a diagonalized multiplier method. From this point of view, a new update rule for the Lagrange multipliers which depends on the particular quasi-Newton method employed is given. This update rule, in contrast to most other update rules, does not require exact minimization of the intermediate unconstrained problem. In fact, the optimal convergence rate is attained in the extreme case when only one step of a quasi-Newton method is taken on this intermediate problem. The second approach transforms the constrained optimization problem into an unconstrained problem of the same dimension.The author would like to thank J. Moré and M. J. D. Powell for comments related to the material in Section 13. He also thanks J. Nocedal for the computer results in Tables 1–3 and M. Wright for the results in Table 4, which were obtained via one of her general programs. Discussions with M. R. Hestenes and A. Miele regarding their contributions to this area were very helpful. Many individuals, including J. E. Dennis, made useful general comments at various stages of this paper. Finally, the author is particularly thankful to R. Byrd, M. Heath, and R. McCord for reading the paper in detail and suggesting many improvements.This work was supported by the Energy Research and Development Administration, Contract No. E-(40-1)-5046, and was performed in part while the author was visiting the Department of Operations Research, Stanford University, Stanford, California.     

s个几乎相等的素数的k次方和(Ⅰ)

假定pθ‖k,当p=2,2|k时，γ=θ 2；其它情况时，γ=θ 1。而R＝П(p-1)|kp^γ。本文在GRH（广义Riemann假设下），证明了当s=2^k 1,1≤k≤11时，任何足够大的整N≡s(modR)都可以表示为s个几乎相等的素数的k次方程。     

投入产出技术在计划平衡中的理论与应用

在用投入产出技术作计划平衡时，目前一般采用最终产品法、总产品法及国民收入法等．本文从理论上研究了这些方法的可行性问题，并在此基础上提出一个较理想的综合法．最后附有实例并说明综合法的现实意义．     

Stabilization of algebraic multilevel iteration methods; additive methods

There exist two main versions of preconditioners of algebraic multilevel type, the additive and the multiplicative methods. They correspond to preconditioners in block diagonal and block matrix factorized form, respectively. Both can be defined and analysed as recursive two-by-two block methods. Although the analytical framework for such methods is simple, for many finite element approximations it still permits the derivation of the strongest results, such as optimal, or nearly optimal, rate of convergence and optimal, or nearly optimal order of computational complexity, when proper recursive global orderings of node points have been used or when they are applied for hierarchical basis function finite element methods for elliptic self-adjoint equations and stabilized in a certain way. This holds for general elliptic problems of second order, independent of the regularity of the problem, including independence of discontinuities of coefficients between elements and of anisotropy. Important ingredients in the methods are a proper balance of the size of the coarse mesh to the finest mesh and a proper solver on the coarse mesh. This paper presents in a survey form the basic results of such methods and considers in particular additive methods. This method has excellent parallelization properties. This revised version was published online in June 2006 with corrections to the Cover Date.     

一种求解鞍点问题的广义对称超松弛迭代法

本文研究了鞍点问题的迭代算法.利用新的待定参数加速迭代格式并结合SSOR分裂的方法,获得了有两个参数的广义对称超松弛迭代法及其收敛性条件.数值例子表明选择适当的参数值可以提高算法的收敛效率,推广和改进了SOR-like迭代法.