对数函数和指数函数的子程序方案

本文提供了在电子计算机上应用的计算lnx的两个子程序方案和e~x的一个子程序方案,它们所需的运算量较为节省。文章描述了方案选择和计算处理的细节,并对选定的方案给出了相应的误差分析和估计。     

山区高速铁路初步设计阶段方案比选的模糊数学方法

在山区高速铁路建设中,初步设计阶段常遇到多方案比选问题.而方案选择涉及因素众多,难以定量分析.针对此问题,引入模糊综合评价模型对各方案进行比选.以渝万铁路客运专线为例,应用模糊综合评价模型对有关方案进行了比选研究,最终得到了首选方案.     

基于Lagrange插值多项式的接近性关联度决策模型及其应用

针对实数情形的灰色关联决策问题,提出了一种选择最优方案的新方法:首先计算出各个方案和理想方案的Lagrange插值多项式,并利用黎曼积分计算出各个方案和理想方案两曲线之间的面积,进而构造接近性关联度,通过比较接近性关联度来选择最优方案.然后针对区间灰数情形,提出分别计算出各方案的下界序列到理想方案的下界序列的接近性关联度,各方案的上界序列到理想方案的上界序列的接近性关联度后再计算两者的新型综合关联度,并通过比较综合关联度来选择最优方案.最后通过实数和区间灰数两个不同的算例来进一步验证了该方法的可行性、合理性和有效性.     

关于复模态参数的冗余性

生成仿真传递函数是考核模态识别算法和评估模态分析软件的不可缺少的环节．比较可行的3种计算方案表明:若选择将传递函数表示为复模态参数的展开式,则可以自由设定仿真模态的特性,如密频、大阻尼和复模态;然而,即使采用这种格式也不能随意设置一组复模态振型,因为这种格式的表观参数个数大于物理参数个数;故而,若对应的物理参数有意义,那么复模态参数必须满足一组约束关系．通过分析复模态系统的特征值问题,和复模态参数反演物理参数的方程式,给出了复模态参数间的一组非线性冗余约束．讨论了实模态、无阻尼和不完全模态等特殊情形的冗余约束具体形式与独立参数的个数,值得注意的是,对于实模态系统,冗余约束自动满足．给出冗余约束在传递函数矩阵和一列传递函数上的等价形式．这些结果有助于产生仿真传递函数,实施优化型识别算法,以及评估识别结果;还可用来评价残余模态和识别完整性．     

雨污处理方案的数学模型

定量分析了雨污分流与混流收集机制对污水处理效果的影响。从污水排放量、费用等角度,对实施清源建设、截排建设或2种措施同时进行的相关效用进行比较,给出了选择不同雨污处理方案的判定条件。最后进行了数值模拟,给出了目标区域的雨污处理方案。     

基于C2组织的边境地区突发事件应急方案评估问题研究

针对边境地区突发事件应急方案评估概化,缺乏数据的收集、整理和定量分析,方案的实效性差等问题,以C2组织为基础,引入任务、任务图、平台、决策者及组织结构关系等相关概念,绘制任务流程图,逐层分解任务,建立评价指标,以边境武装对峙突发事件为例,通过计算突发事件完成时间、决策者的负载测度、任务的资源满足度、任务的完成质量等,对应急方案进行计算评估,以期达到方案编制过程中资源分配更合理、人员调配更科学、分工协同更高效的目的,不断提高边境地区应急方案编制的时效性.     

D流形及其示性类

本文讨论了D-流形的全纯等价分类,并对每类复结构给出计算其第一陈示性类的一个十分简便的公式,避免了庞杂的计算。     

一种无证书的环签名方案和一个基于身份的多重签名方案

在这篇文章里,我们用双线性对构造了一种无证书的环签名方案,并证明它是无条件匿名的,且在随机预言模型中,计算性Diffie-Hellman问题是难解的,我们方案在适应性选择消息攻击下是存在性不可伪造的,它的安全性比在基于身份的公钥密码体制下高.本文首次用多线性形式构造了一个基于身份的广播多重签名方案,它的安全性是基于计算性Diffie-Hellman困难问题.     

二三重积分优化复化二次式数值算法

本文给出二、三重积分的四个优化复化二次式数值算法,它们在迭代计算过程中免去了函数值重复计算,加速收敛减少迭代计算的次数或时间。     

层次分析法在身份鉴别方案选择中的应用

针对身份鉴别方案比较的问题,采用层次分析法AHP(Analytic HierarchyProcess)建立了身份鉴别方案比较的数学模型,定量分析了指纹识别、人脸识别、语音识别、虹膜识别、静脉红外识别和DNA识别六种生物识别技术在身份鉴别中的综合表现,并做出评价.评价结果对重要场合安全检查中人员身份鉴别方法的选择有一定的指导意义.     

部分权重信息下对方案有互补偏好的多属性决策法

研究了只有部分权重信息且对方案的偏好信息以模糊互补判断矩阵形式给出的多属性决策问题.首先,基于模糊互补判断矩阵的主观偏好信息,利用转换函数将客观决策信息一致化,建立一个目标规划模型,通过求解该模型得到属性权重,从而利用加性加权法获得各方案的综合属性值,并以此对方案进行排序或择优.提出了一种基于目标规划的多属性决策方法.该方法具有操作简便和易于上机实现的特点.最后,通过实例说明模型及方法的可行性和有效性.     

How to treat strict preference information in multicriteria decision analysis

This paper addresses the use of incomplete information on both multi-criteria alternative values and importance weights in evaluating decision alternatives. Incomplete information frequently takes the form of strict inequalities, such as strict orders and strict bounds. En route to prioritizing alternatives, the majority of previous studies have replaced these strict inequalities with weak inequalities, by employing a small positive number. As this replacement closes the feasible region of decision parameters, it circumvents certain troubling questions that arise when utilizing a mathematical programming approach to evaluate alternatives. However, there are no hard and fast rules for selecting the factual small value and, even if the choice is possible, the resultant prioritizations depend profoundly on that choice. The method developed herein addresses and overcomes this drawback, and allows for dominance and potential optimality among alternatives, without selecting any small value for the strict preference information. Given strict information on criterion weights alone, we form a linear program and solve it via a two-stage method. When both alternative values and weights are provided in the form of strict inequalities, we first construct a nonlinear program, transform it into a linear programming equivalent, and finally solve this linear program via the same two-stage method. One application of this methodology to a market entry decision, a salient subject in the area of international marketing, is demonstrated in detail herein.     

Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets

This paper proposes the concept of the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets (IVIFSs) with respect to adjustable weight vectors and the Dice similarity measure based on the reduct intuitionistic fuzzy sets to explore the effects of optimism, neutralism, and pessimism in decision making. Then a decision-making method with the pessimistic, optimistic, and neutral schemes desired by the decision maker is established by combining adjustable weight vectors and the Dice similarity measure for IVIFSs. The proposed decision-making method is more flexible and adjustable in practical problems and can determine the ranking order of alternatives and the optimal one(s), so that it can overcome the difficulty of the ranking order and decision making when there exist the same measure values of some alternatives in some cases. This adjustable feature can provide the decision maker with more selecting schemes and actionable results for the decision-making analysis. Finally, two illustrative examples are employed to show the feasibility of the proposed method in practical applications.     

Decision making in stock trading: An application of PROMETHEE

The key issue for decision making in stock trading is selection of the right stock at the right time. In order to select the superior stocks (alternatives) for investment, a finite number of alternatives have to be ranked considering several and sometimes conflicting criteria. Therefore, we are faced with a special multicriteria decision-making problem. The purpose of this paper is to develop a decision-making model for selecting superior stocks in stock exchange and a model is provided in order to structure this problem. The proposed model is structured around two pillars: Industry evaluation and Company evaluation. The preference ranking organization method for enrichment evaluation (PROMETHEE) has been used for solving the problem. The model has been applied at Tehran Stock Exchange (TSE) as a real case and a survey from the experts in order to determine the effective criteria for industry evaluation and company evaluation has been conducted.     

Extended VIKOR method in comparison with outranking methods

The VIKOR method was developed to solve MCDM problems with conflicting and noncommensurable (different units) criteria, assuming that compromising is acceptable for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria, and on proposing compromise solution (one or more). The VIKOR method is extended with a stability analysis determining the weight stability intervals and with trade-offs analysis. The extended VIKOR method is compared with three multicriteria decision making methods: TOPSIS, PROMETHEE, and ELECTRE. A numerical example illustrates an application of the VIKOR method, and the results by all four considered methods are compared.     

Performance of successively complex rules for locational decision-making

The relative performance of five simple rules for selecting facility locations are compared with two heuristic location-allocation algorithms in the context of a real region. It is hypothesized that the performance of a rule is likely to be systematically related to the spatial structure of the region in which it is used. In the Iowa settlement system, known to have predictable structural regularity, some rules performed over 95 percent of the level achieved by the algorithms (the greedy add and the modified vertex exchange algorithms) on a range of commonly used criteria for evaluating locational efficiency. Under certain circumstances, these rules may be recommended as alternatives to more formal algorithms.     

A multiobjective evolutionary algorithm for approximating the efficient set

In this article, a new framework for evolutionary algorithms for approximating the efficient set of a multiobjective optimization (MOO) problem with continuous variables is presented. The algorithm is based on populations of variable size and exploits new elite preserving rules for selecting alternatives generated by mutation and recombination. Together with additional assumptions on the considered MOO problem and further specifications on the algorithm, theoretical results on the approximation quality such as convergence in probability and almost sure convergence are derived.     

一种基于决策者风险态度的区间数多指标决策方法

针对具有区间数的多指标决策问题，提出了一种新的决策分析方法。该方法的思路是：首先通过引入决策的风险态度因子将区间数决策问题映射为传统的点值决策问题。然后给出了基于TOPSIS的方案排序方法，最后通过对风险态度因子的不同取值可进行方案排序的灵敏度分析。     

Optimization models for quality and cost of modular software systems

This study presents two optimization models for selecting the best Commercial Off-The-Shelf (COTS) software product among alternatives for each module in the development of modular software systems. The objective function of the models is to maximize quality within a budgetary constraint. The software system consists of several programs, where a specific function of each program can call upon a series of modules. Several alternative COTS products are available for each module. A weight to the modules is given by utilizing the Analytic Hierarchy Process (AHP) based on the access frequencies of the modules. A simplified example is given to demonstrate each optimization model.     

On the use of information criteria in analytic hierarchy process

In this article, we discuss how the model-selection procedures such as Akaike's information criteria (AIC) can be used for selecting the most appropriate one out of several existing statistical models in the literature for the judgment data used in analytic hierarchy process (AHP). Furthermore, once the appropriate model is selected, a procedure is proposed on the basis of AIC for statistical ranking of the alternatives. This ranking procedure does not suffer from the problem of intransitivity and can be based on non-normal distribution. It enables one to obtain the detailed pattern for the ordered priorities of the alternatives in the decision process involving AHP.