模糊环境下的一种多准则决策方法

本文利用模糊集理论以及层次分析法（AHP）原理，建立了一种在模糊环境下对方案进行择优或排序的多准则决策方法。     

A Hypergame Approach to Crisis Decision-Making: The 1973 Middle East War

The theory of hypergames is used to retrospectively analyse actions taken during the period of crisis immediately prior to the 1973 Arab-Israeli war. The analysis supports the hypothesis that each player behaved rationally within the framework of his own perceptual game, actions corresponding to stable outcomes in the axis of the game. A proposed methodology is put forward for applying the theory to current crisis problems.     

On Man-Computer Interaction in Organisational Decision-Making. A Behavoural Approach

Journal of the Operational Research Society -     

Structural Approach to Subset Sum Problems

We discuss results obtained jointly with Van Vu on the length of arithmetic progressions in \(\ell \)-fold sumsets of the form

$$\begin{aligned} \ell \mathcal {A}=\{a_1+\dots +a_\ell ~|~a_i\in \mathcal {A}\} \end{aligned}$$

and

$$\begin{aligned} \ell \mathcal {A}=\{a_1+\dots +a_\ell ~|~a_i\in \mathcal {A}\text { all distinct}\}, \end{aligned}$$

where \(\mathcal {A}\) is a set of integers. Applications are also discussed.

     

Complex Boosts: A Hermitian Clifford Algebra Approach

The aim of this paper is to study complex boosts in complex Minkowski space-time that preserves the Hermitian norm. Starting from the spin group Spin ${^+(2n, 2m, \mathbb{R})}$ in the real Minkowski space ${\mathbb{R}^{2n,2m}}$ we construct a Clifford realization of the pseudo-unitary group U(n,m) using the space-time Witt basis in the framework of Hermitian Clifford algebra. Restricting to the case of one complex time direction we derive a general formula for a complex boost in an arbitrary complex direction and its KAK-decomposition, generalizing the well-known formula of a real boost in an arbitrary real direction. In the end we derive the complex Einstein velocity addition law for complex relativistic velocities, by the projective model of hyperbolic n-space.     

区间数的多目标格序决策方法改进研究

格序决策方法在对区间数进行优劣排序方面尚有改进完善的余地,通过研究发现,改进后的格序决策方法在不可比较区间数的优劣排序上不必求出拟上、下确界,也没必要绘制偏好结构图和海赛图来进行整个过程的优劣程度排序.通过算例比较验证了改进后的方法更加简洁有效,更加有利于提高决策的效率.     

基于证据推理的混合型多指标群组决策方法

针对决策方案的属性值为语言评价等级和区间灰数的灰色多指标群组决策问题,提出一种基于证据推理的灰色多指标群组决策方法.首先,根据语言评价信息的概率分布和效用值等价原理确定定性指标和定量指标的信用结构,进而得到群体等级信用结构决策矩阵,然后,依据证据推理方法,对群组评价信息进行合成,求出各方案在各等级的信任度,最后,利用期望方差排序方法确定整个方案集的排序.具体算例表明方法合理有效.     

基于前景理论的多目标灰色关联决策方法

针对决策者风险态度对多目标决策的影响,提出了一种基于前景理论的多目标灰色关联决策方法.通过奖优罚劣的线性变换算子对原始数据进行规范化处理,得到不同目标下的正负理想方案.以各方案与正负理想方案的关联系数为参照点计算各方案的前景矩阵,在此基础上构建方案综合前景值最大化的优化模型,求出不同目标下的最优权向量,进而求出综合效果测度矩阵,对每个局势进行排序.最后通过实例验证了该方法的有效性和实用性.     

技术创新项目投资决策方法研究

利用科学实用的多目标决策方法对企业不同技术创新投资项目进行决策评估,可为企业提供重要的决策支持,具有重要的现实意义.结合多目标决策理论和模糊数学的方法,在分析技术创新项目特点的基础上,提出了一种基于模糊数学的多目标决策方法.应用算例表明该方法用于技术创新项目投资决策是合理可行的.     

复方向导数与保角映射

定义了复方向导数,并用复方向导数分别给出了与C-R条件和共轭解析条件等价的条件;得到了解析与共轭解析新的充要条件.复方向导数的刻画使得保角映射的几何意义更加直观明了.     

基于类Pearson综合相关系数的概率语言TOPSIS多属性决策方法

概率语言术语集(PLTS)包含了语言术语信息及其相应的概率信息,使得原始决策信息得到充分利用,大大提高了语言术语多属性决策的科学性.文章研究了一种基于概率语言术语集类Pearson综合相关系数的TOPSIS多属性决策方法.首先考虑了PLTSs的3个特征因素:均值、方差和长度,然后基于传统Pearson相关系数的思想,提出了一种新的概率语言术语集类Pearson综合相关系数,其特征是可从完整性、分布情况和犹豫性3个方面描述PLTSs,且取值大小介于区间[-1,1],从而可度量变量之间的正负相关关系,改进了现有方法存在的缺陷.为融合属性指标的不同权重,提出了概率语言术语集加权类Pearson综合相关系数,其考虑了属性权重的重要性,拓宽了适用范围.进一步地,构建了基于类Pearson综合相关系数的概率语言术语相对贴近度指标,并在此基础上提出了一种基于类Pearson综合相关系数的概率语言术语TOPSIS多属性方法.最后,通过数值算例和比较分析,说明该方法的有效性和适用性.     

Structural Time Approach to Cleavage Fracture by Submicrosecond Pulses

The feasibility of using a structural time criterion to describe microfracture is demonstrated on the basis of previously acquired experimental data on cleavage fracture by pulses of submicrosecond duration.     

属性具有线性优先级的区间数多属性决策方法

针对属性具有线性优先级、属性值为区间数的多属性决策问题进行了决策方法的研究.在属性权重的确定上,采用低级属性的权重值由所有比其高级属性效用值的乘积,并引入决策者的风险态度因子将区间数映射成点值,再经过规范化后得到.接着,给出了属性具有线性优先级的、属性值为区间数的加权算术平均算子,讨论了该算子的相关性质.最后,利用算子对具有线性优先级的区间数多属性决策问题进行算例分析,结果说明方法是有效的.     

Evaluating Suppliers of Complex Systems: A Multiple Criteria Approach

Organizations are frequently required to make long-term strategic choices regarding the design and manufacture of innovative process equipment and systems which address future needs. An important consideration in such choices is the evaluation of the unique capabilities of available suppliers. Typically, such evaluations must be made relative to multiple attributes or criteria. This paper examines one such supplier evaluation process in the context of a major international manufacturer of telecommunication equipment. The ad hoc method used by the organization to evaluate the multiple factors involved is presented, and an alternative, structured approach to deal with the multiple factors is then discussed.     

Operational Research for Complex Conflicts: A Gaming Methodology for the Development of a Decision-Making Monitor

A methodology for providing assistance to decision-makers in conflicts is demonstrated. It is shown that in simple "Chicken" games, conflict-like situations arise only when players have radically different aims and that players experiencing crisis-like situations in such games typically exhibit behaviours which would exacerbate real conflicts. It is argued that explicit knowledge of such behavioural tendencies. the conditions in which they arise, and the possible underlying mechanisms, would be of assistance to decision-makers, both for them to monitor their own behaviour, and to assess that of other parties.     

Guaranteed Deterministic Approach to Superhedging: Structural Stability and Approximation

Computational Mathematics and Modeling - The discrete-time superreplication problem is considered in the guaranteed deterministic setting: the problem requires a guaranteed coverage of contingent...     

一个非解析复映射的广义Julia集

推广了Michelitsch和Rossler所提出的由一个简单非解析映射所构造Julia集的方法,并由推广的复映射,构造出一系列实数阶的广义Julia集(简称广义J集)． 利用复变函数理论和计算机制图相结合的实验数学的方法,对广义J集的结构和演化进行了研究,结果表明： ①广义J集的几何结构依赖于参数α、R和c; ②广义J集具有对称性和分形特征; ③小数阶广义J集出现了错动和断裂,且其演化过程依赖于相角主值范围的选取.