基于新得分函数的直觉模糊多属性决策方法

通过考虑直觉模糊数的犹豫度对得分函数的影响,提出了直觉模糊数新的得分函数,并讨论了新得分函数具有的性质,在此基础上给出了直觉模糊数的一种新的排序方法。基于新的得分函数和直觉模糊加权平均算子提出了模糊多属性决策方法,并通过算例分析验证了决策方法的有效性和合理性。     

基于区间粗糙直觉模糊数的多属性决策方法

研究了区间粗糙直觉模糊多属性决策。探讨了区间粗糙直觉模糊数的运算法则及其性质;定义了区间粗糙直觉模糊数的得分函数和精确函数,进而给出其排序方法;给出了区间粗糙直觉模糊数的变权算术平均和变权几何平均算子,并且建立了区间粗糙直觉模糊数的多属性决策模型;实例验证了所提出决策方法的有效性。     

区间直觉正态模糊数集成算子及其在决策中的应用

研究了区间直觉正态模糊数(IVINFN)决策信息及其集成算子。首先,定义了区间直觉正态模糊数的概念,提出了运算法则;其次,给出了区间直觉正态模糊数诱导有序加权平均(IVINFN-IOWA)算子和区间直觉正态模糊数诱导有序加权几何(IVINFN-IOWGA)算子的概念,探讨了其性质;在此基础上,分别定义了基于均值和标准差的区间直觉正态模糊数的得分函数和精确函数,给出其排序方法。最后,针对属性值为区间直觉正态模糊数且权重已知的多属性决策问题,给出了其决策方法,并进行了实例分析,结果表明该决策方法是有效的。     

IVIFS环境下基于模糊熵和得分函数的多准则决策方法

在区间直觉模糊环境和各准则的信息完全未知的条件下,本文提出了一个基于模糊熵和得分函数的多准则决策方法.基于区间直觉模糊集的准则形式,本文给出了模糊熵模型,从而可以确定各准则的权重.在决策方法方面,作者提出了区间直觉模糊集的加权记分函数和加权精确函数,解决了记分函数无法解决的加权问题的难题,同时给出了一种新的决策方法.最后,文章通过实例说明了该方法的可行性和有效性.     

基于直觉模糊多属性决策的公路工程评标方法

公路工程评标定标问题的实质是多属性决策问题,专家对参评标书给出了各指标的区间直觉模糊属性值和属性权重的部分信息后,先定义了区间直觉模糊数的得分函数及标准得分差,进而提出了一种基于线性规划模型的区间直觉模糊多属性决策方法,最后通过实例对该决策途径的详细过程及有效性进行了说明.     

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.     

一种新的粗糙集模型及其应用

提出了一种新的基于区间直觉模糊关系和区间直觉模糊数的粗糙集模型.首先,介绍了区间直觉模糊集,区间直觉模糊关系和区间直觉模糊数等概念.然后,利用区间直觉模糊关系和区间直觉模糊数定义了一种新的粗糙集模型,并给出一些基本性质.最后将该模型应用于临床诊断系统中.实例验证了该粗糙集模型的有效性和实用性.     

基于IITFN的模糊矩阵博弈最优策略研究

由于矩阵博弈支付函数具有模糊性,本文依据区间直觉梯形模糊数(IITFN)的基本理论,用区间直觉梯形模糊数来表示模糊矩阵博弈(FMG)支付函数;基于得分函数与精确函数提出了区间直觉梯形模糊矩阵博弈(IITFN-FMG)的策略最优解的求取方法。通过实例仿真,结果表明:以区间直觉梯形模糊数表示支付函数来分析最优策略如何选取,其效果更好,与实际情形的吻合程度亦更为理想。     

基于IGIFS关系与截集的区间灰数直觉模糊粗糙集模型及性质

在论述区间灰数直觉模糊集概念基础上,提出了区间灰数直觉模糊关系(IGIFS关系)与区间灰数直觉模糊等价关系概念,定义了基于区间灰数直觉模糊关系环境下的区间灰数直觉模糊粗糙集模型,并讨论了相关性质.在界定了区间灰数直觉模糊集关于区间灰数直觉模糊数截集概念的基础上,定义了区间灰数直觉模糊粗糙集上、下截集近似,给出了区间灰数直觉模糊粗糙集的截集表现定理.     

基于新模糊熵和得分函数的区间直觉模糊多属性决策

属性权重的确定以及对区间直觉模糊数的排序是多属性决策问题中两个最为关键的点。本文主要针对属性权重完全未知的多属性决策问题进行了研究,分析了现有大多数研究中关于区间直觉模糊熵和得分函数存在的局限性,进而提出了一种将不确定度和犹豫度相结合的新的模糊熵和得分函数。最后,通过对比实验证实了本文所提出的熵和得分函数应用到多属性决策中的有效性和合理性。     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

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.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

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.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.