基于差值测度和区间测度的多属性灰靶决策方法

针对决策信息为区间灰数且属性权重未知的多属性决策问题,提出一种基于差值测度和区间测度的区间灰数信息下灰靶决策方法.首先,定义区间灰数的差值测度和区间测度,由此对区间灰数进行排序并确定正、负靶心;然后,给出区间灰数间的距离公式,通过计算正、负靶心距以及正负靶心间距确定综合靶心距,以综合靶心距最小化和灰熵最大化为目标确定属性权重,进而依据综合靶心距对方案进行排序;最后,通过一个实例验证该方法的有效性和可行性.     

基于区间直觉梯形模糊数的改进TOPSIS多属性决策方法

研究了属性权重完全未知的区间直觉梯形模糊数的多属性决策问题,结合TOPSIS方法定义了相对贴近度及总贴近度公式.首先由区间直觉梯形模糊数的Hamming距离给出了每个方案的属性与正负理想解的距离,基于此,给出了相对贴近度矩阵,根据所有决策方案的综合贴近度最小化建立多目标规划模型,从而确定属性的权重值,然后根据区间直觉梯形模糊数的加权算数平均算子求出各决策方案的总贴近度,根据总贴近度的大小对方案进行排序;最后,通过实例分析说明该方法的可行性和有效性.     

区间数互反矩阵几何加权集成多属性群决策方法

研究了属性值以区间数表示的群决策问题,提出了区间数决策向量转化为互反判断矩阵的公式,定义了区间数互反判断矩阵几何加权集成算子.在此基础上,提出了区间数多属性群决策的新方法.方法首先针对每一个属性,将各决策者、各方案对应此属性的区间数向量转换为互反判断矩阵,由新定义的集成算子进行集成.由集成区间数矩阵的上界、下界矩阵计算各方案关于此属性的排序向量.由属性权重、可能度和排序公式对方案进行排序.最后给出一个实例进行分析,结果表明了此方法的实用性和可行性.     

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.     

不确定性多属性决策的新方法

本文研究了属性指标值，属性权重为L—R模糊数的多属性决策问题，首先在不同的α水平下将L—R模糊数转化为区间数，基于优化模型求出方案的区间属性值并利用α-截及区间数序关系的可能度，构造互补判断矩阵。提出一种新的排序公式，得到一族排序向量，然后对不同α水平下的排序向量集结，得出总的排序向量，以此对方案排序，最后通过实例说明了该方法的可行性和有效性。     

基于区间数贴近度的不确定多属性决策模型

针对只有部分权重信息且属性值以区间数形式给出的多属性决策问题,提出了一种基于区间数贴近度的决策方法.首先讨论了区间数贴近度的定义和性质;然后给出了解决不确定多属性决策问题的一般步骤.并依据传统的逼近理想解的基本思路,以实际评价值与理想解之间的贴近度最大化为目标建立优化模型,从而得到指标权重.进而计算出每个方案与正理想解的相对贴近度,即可得到所有方案的排序结果.方法能充分利用规范化评价的先验信息,评价结果客观可靠,不具有主观随意性.最后通过实例分析验证了该方法的有效性和实用性.     

基于新精确函数的区间直觉模糊多属性决策方法

基于区间直觉模糊数隶属度和非隶属度构成的二维几何图形特征给出区间直觉模糊数精确函数的新定义,并将其作为区间直觉模糊数的排序指标,区间直觉模糊数的精确函数值越大,则区间直觉模糊数就越大,进而提出一种权重信息不完全确定的区间直觉模糊多属性决策方法.通过算例分析说明所提出排序指标的有效性和决策方法的可行性.     

一种基于组合不确定型OWA算子的区间数群决策方法

在群决策中,由于决策环境的不确定性,决策者给出区间效信息.基于区间数可能度矩阵公式和互补判断矩阵的排序公式,提出了一种组合不确定型OWA算子,它是不确定型OWA算子的推广.该算子能集结群决策中区间数信息,文中给出了其在应用的具体步骤,最后实例分析说明了该方法的有效性和可行性.     

区间粗糙数序信息系统下的优势关系粗糙集模型

以区间粗糙数为研究对象,提出了基于区间优势度的区间粗糙数比较公式,通过引入参数α调节决策者对区间粗糙数下近似和上近似的重视程度,以充分考虑决策者的风险偏好。在此基础上,引入优势度阈值β并定义了基于优势度的优势关系粗糙集模型,进一步给出了此模型框架下的四种排序方法。对优势度、优势关系及排序方法的相关性质进行了证明,最后通过算例验证模型与排序方法的合理性。     

基于海明距离的区间三角模糊多属性决策问题

针对属性值为区间三角模糊数,权重信息不完全的多属性决策问题,为保证决策的准确性,构建了一种基于信息理论思想的决策方法.首先给出区间三角模糊集(数)的海明距离(Hamming distance)的定义,再利用极大偏差法建立线性规划模型计算属性的权重,最后用TOPSIS方法对方案进行排序,并给出此方法的计算步骤,通过实例验证了该方法的有效性.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].