多属性隐式变权决策分析方法

为克服多因素变权决策方法的内在缺陷,基于Belton 和Gear提出的B/G-AHP层次分析原理给出了一种隐含式的多属性变权决策建模思想,并运用该思想给出了一种多属性变权决策新方法。它相对于多因素变权决策方法具有三方面的比较优势。其一,依赖的变权偏好信息直接由决策者给出,因而能够克服决策分析者对决策结果的主观武断性影响,更好地反映决策者的真实偏好。其二,不会受到由因素的属性值转化为偏好值所额外引入的主观测度偏差的干扰。其三,对决策者主观判断可能存在的误差予以了旨在弱化其影响的优化控制。数值分析表明新方法拥有较好的变权能力,并且相对于已有方法能够给出更易为决策者所接受的评价结论,因而具有较好的应用有效性。     

Estimating Conditional Probabilities of Terrorist Attacks: Modeling Adversaries with Uncertain Value Tradeoffs

Many analyses conducted to inform security decisions depend on estimates of the conditional probabilities of different attack alternatives. These probabilities are difficult to estimate since analysts have limited access to the adversary and limited knowledge of the adversary’s utility function, so subject matter experts often provide the estimates through direct elicitation. In this article, we describe a method of using uncertainty in utility function value tradeoffs to model the adversary’s decision process and solve for the conditional probabilities of different attacks in closed form. The conditional probabilities are suitable to be used as inputs to probabilistic risk assessments and other decision support techniques. The process we describe is an extension of value‐focused thinking and is broadly applicable, including in general business decision making. We demonstrate the use of this technique with simple examples.     

Assessing Engineering Resilience for Systems with Multiple Performance Measures

Recently, efforts to model and assess a system's resilience to disruptions due to environmental and adversarial threats have increased substantially. Researchers have investigated resilience in many disciplines, including sociology, psychology, computer networks, and engineering systems, to name a few. When assessing engineering system resilience, the resilience assessment typically considers a single performance measure, a disruption, a loss of performance, the time required to recover, or a combination of these elements. We define and use a resilient engineered system definition that separates system resilience into platform and mission resilience. Most complex systems have multiple performance measures; this research proposes using multiple objective decision analysis to assess system resilience for systems with multiple performance measures using two distinct methods. The first method quantifies platform resilience and includes resilience and other “ilities” directly in the value hierarchy, while the second method quantifies mission resilience and uses the “ilities” in the calculation of the expected mission performance for every performance measure in the value hierarchy. We illustrate the mission resilience method using a transportation systems‐of‐systems network with varying levels of resilience due to the level of connectivity and autonomy of the vehicles and platform resilience by using a notional military example. Our analysis found that it is necessary to quantify performance in context with specific mission(s) and scenario(s) under specific threat(s) and then use modeling and simulation to help determine the resilience of a system for a given set of conditions. The example demonstrates how incorporating system mission resilience can improve performance for some performance measures while negatively affecting others.     

Assessing Trade‐offs among Multiple Objectives for Humanitarian Aid Delivery Using Expert Preferences

Humanitarian aid agencies deliver emergency supplies and services to people affected by disasters. Scholars and practitioners have developed modeling approaches to support aid delivery planning, but they have used objective functions with little validation as to the trade‐offs among the multiple goals of aid delivery. We develop a method to value the performance of aid delivery plans based on expert preferences over five key attributes: the amount of cargo delivered, the prioritization of aid by commodity type, the prioritization of aid by delivery location, the speed of delivery, and the operational cost. Through a conjoint analysis survey, we measure the preferences of 18 experienced humanitarian logisticians. The survey results quantify the importance of each attribute and enable the development of a piecewise linear utility function that can be used as an objective function in optimization models. The results show that the amount of cargo delivered is the most valued objective and cost the least important. In addition, experts prioritize more vulnerable communities and more critical commodities, but not to the exclusion of others. With these insights and the experts’ utility functions, better humanitarian objective functions can be developed to enable better aid delivery in emergency response.     

Improvement of Highway Safety I: Identification of Causal Factors Through Fault-Tree Modeling1

As the first article of a two-part series, the purpose of this paper is to examine the functional factors that contribute to automobile accident occurrence and to model the causation structure in the form of a fault-tree. The fault-tree model provides an intuitive framework for qualitatively decomposing possible pathways to accident occurrence. Fault-tree analysis also provides a statistical representation of how interacting driver, vehicle, and environmental factors contribute to the likelihood of automobile accident occurrence. The application of this model facilitates pinpointing those factors that most contribute to accident causation and subsequently enables the identification and comparison of potential crash avoidance technologies.     

Identifying and Structuring the Objectives of Terrorists

The risk of terrorism is of great concern to many countries and significant resources are spent to counter this threat. A better understanding of the motivation of terrorists and their reasons for selecting certain modes and targets of attack can help improve the decisions to allocate resources in the fight against terrorism. The fundamental question addressed in this article is: “What do terrorists want?” We take the view that terrorists’ preferences for actions are based on their values and beliefs. An important missing piece in our knowledge of terrorists’ preferences is an understanding of their values. This article uses a novel approach to determine these values and state them as objectives, using principles from decision analysis and value‐focused thinking. Instead of interviewing decisionmakers and stakeholders, as would be normal in decision analysis, we extract the values of terrorists by examining their own writings and verbal statements. To illustrate the approach, we extract the values of Al‐Qaeda and structure them in terms of strategic, fundamental, and means objectives. These objectives are interrelated through a means‐ends network. This information is useful for understanding terrorists’ motivations, intent, and likely actions, as well as for developing policies to counter terrorism at its root causes.     

Modeling Correlated Discrete Uncertainties in Event Trees with Copulas

Modeling the dependence between uncertainties in decision and risk analyses is an important part of the problem structuring process. We focus on situations where correlated uncertainties are discrete, and extend the concept of the copula‐based approach for modeling correlated continuous uncertainties to the representation of correlated discrete uncertainties. This approach reduces the required number of probability assessments significantly compared to approaches requiring direct estimates of conditional probabilities. It also allows the use of multiple dependence measures, including product moment correlation, rank order correlation and tail dependence, and parametric families of copulas such as normal copulas, t‐copulas, and Archimedean copulas. This approach can be extended to model the dependence between discrete and continuous uncertainties in the same event tree.     

区间数多指标决策中确定指标权重的一种客观赋权法

研究了指标值以区间数形式给出的不确定性多指标决策中确定指标权重的问题。依据传统的客观赋权法—离差最大化方法,给出了一种确定区间数指标权重的误差分析方法。该方法具有概念清晰、实用的特点,得出的指标权重能够较好地反映各指标信息的差异程度。最后通过一个算例说明了该方法的实用性和有效性。     

A MADM justification of a budget reduction decision

In 1988, a significant budget reduction at the University of Wyoming left the Athletic Department nearly $700,000 short on operating funds compared to the previous biennium. In order to make the necessary monetary cuts, the Athletic Department eliminated the men's and women's varsity ski teams from University sponsorship, thus removing one of the most successful and popular programs from the athletic family. A protest of this action quickly spread throughout the state and the Athletic Department received harsh criticism. However, through the cardinal preference techniques of Multiple Attribute Decision Making, it was determined that the criticism of the Athletic Department for dropping the ski programs was unfounded. But in light of the politics of the situation, after several months of deliberation, the ski programs were eventually reinstated with a greatly reduced budget and the team committed to raise a certain percentage of their monetary requirements through their own fund raising efforts.     

Spatial Optimization of Future Urban Development with Regards to Climate Risk and Sustainability Objectives

Future development in cities needs to manage increasing populations, climate‐related risks, and sustainable development objectives such as reducing greenhouse gas emissions. Planners therefore face a challenge of multidimensional, spatial optimization in order to balance potential tradeoffs and maximize synergies between risks and other objectives. To address this, a spatial optimization framework has been developed. This uses a spatially implemented genetic algorithm to generate a set of Pareto‐optimal results that provide planners with the best set of trade‐off spatial plans for six risk and sustainability objectives: (i) minimize heat risks, (ii) minimize flooding risks, (iii) minimize transport travel costs to minimize associated emissions, (iv) maximize brownfield development, (v) minimize urban sprawl, and (vi) prevent development of greenspace. The framework is applied to Greater London (U.K.) and shown to generate spatial development strategies that are optimal for specific objectives and differ significantly from the existing development strategies. In addition, the analysis reveals tradeoffs between different risks as well as between risk and sustainability objectives. While increases in heat or flood risk can be avoided, there are no strategies that do not increase at least one of these. Tradeoffs between risk and other sustainability objectives can be more severe, for example, minimizing heat risk is only possible if future development is allowed to sprawl significantly. The results highlight the importance of spatial structure in modulating risks and other sustainability objectives. However, not all planning objectives are suited to quantified optimization and so the results should form part of an evidence base to improve the delivery of risk and sustainability management in future urban development.     

混合多属性群决策中的群体一致性分析方法

本文针对一类属性值为精确实数、区间数和语言值的混合型多属性群决策问题,提出了一种群体一致性分析方法。在该方法中,计算群体一致度时,首先根据专家提供的评价信息在属性层面上计算专家之间的差异度,再由此得到群体一致度,计算过程中不需进行数据类型转换,避免了数据类型转换造成的信息损失;当群体不一致时,在属性层面上给出相应的调整策略,可以使专家有针对性地修改相应属性上的评价信息,使群体尽快达成一致,同时避免了专家评价信息的过度修改。最后通过一个实例分析验证了该方法的可行性和有效性。     

对方案有偏好的不确定语言多属性决策方法

研究了属性权重完全未知、属性值和对方案的偏好值以不确定语言变量形式给出的不确定语言多属性决策问题。首先,引入不确定语言变量的运算法则,以及不确定语言变量之间比较的可能度公式,给出了不确定语言变量间的距离的概念。针对属性权重完全未知的情形,给出了求解权重的公式。然后,利用不确定语言加权平均算子,对不确定语言决策信息进行加权集成,并利用可能度公式构造可能度矩阵(互补判断矩阵),继而利用互补判断矩阵排序公式对决策方案进行排序和择优。最后进行了实例分析。     

权重信息未知情况下的多属性群决策方法及其拓展

本文针对群决策中专家权重及指标权重难以确定的问题,提出一种在权重信息完全未知情况下的基于证据距离和模糊熵权变换的多属性群决策方法,其核心在于如何仅通过决策矩阵客观地确定决策者权重及指标权重。通过信息熵和证据距离确定专家权重,并利用模糊变换原理,将专家权重向量与指标熵权矩阵合成,得到统一的群体决策指标权重;最后使用线性加权法集成所有专家对备选方案的评价信息,得到整个方案集的排序。实验结果及相关讨论表明,该方法概念清晰,计算量适中,具有较强的客观性,而且易于机器实现,是一种可行、有效的多属性群决策方法。最后将该方法推广到属性值由精确数、语言值、区间数、直觉模糊数等多种形式构成的混合型多属性群决策中。     

动态多指标决策问题的投影寻踪模型

针对动态多指标决策中指标和时段的权重确定问题,提出了基于投影寻踪(PP)的理想点法新模型(PP-IPM模型)。该模型利用决策矩阵样本的内部信息,把方案的三维决策矩阵综合成一维投影值,投影值越大表示该方案越优,根据投影值的大小就可对各方案进行综合排序决策。建议用实码加速遗传算法进行PP-IPM的建模,简化了PP技术的实现过程,克服了目前PP技术计算过程复杂、编程实现困难的缺点。实例计算的结果说明,直接由决策矩阵样本数据驱动的PP-IPM模型用于动态多指标决策问题简便可行,适用性和可操作性强,具有推广应用价值。     

基于证据推理的不确定多属性决策方法

针对基本属性权重的不确定性,以及基本属性与广义属性评价集的不一致性等问题,提出一种基于证据推理的不确定多属性决策方法,将证据推理算法推广到更一般的决策环境中.根据决策矩阵的信息熵客观地获得属性的权系数;而对于基本属性与广义属性评价集不一致的情况,则通过对基本属性分布评价的模糊化及模糊变换,合理地实现到广义分布评价的统一形式;最后应用证据推理算法得到整个方案集的排序.实例结果表明,该方法是可行的、有效的.     

Food Safety Objectives Should Integrate the Variability of the Concentration of Pathogen

The World Trade Organization introduced the concept of appropriate level of protection (ALOP) as a public health target. For this public health objective to be interpretable by the actors in the food chain, the concept of food safety objective (FSO) was proposed by the International Commission on Microbiological Specifications for Foods and adopted later by the Codex Alimentarius Food Hygiene Committee. The way to translate an ALOP into a FSO is still in debate. The purpose of this article is to develop a methodological tool to derive a FSO from an ALOP being expressed as a maximal annual marginal risk. We explore the different models relating the annual marginal risk to the parameters of the FSO depending on whether the variability in the survival probability and in the concentration of the pathogen are considered or not. If they are not, determination of the FSO is straightforward. If they are, we propose to use stochastic Monte Carlo simulation models and logistic discriminant analysis in order to determine which sets of parameters are compatible with the ALOP. The logistic discriminant function was chosen such that the kappa coefficient is maximized. We illustrate this method by the example of the risks of listeriosis and salmonellosis in one type of soft cheese. We conclude that the definition of the FSO should integrate three dimensions: the prevalence of contamination, the average concentration per contaminated typical serving, and the dispersion of the concentration among those servings.     

基于投影的直觉模糊数多属性决策方法

针对指标取值以直觉模糊数形式给出的多属性决策问题,提出了一种基于投影的直觉模糊决策方法.该方法依据一般投影分析方法的基本思路,给出了解决属性取值为直觉模糊数的多属性决策问题的计算步骤,其核心是通过构建并求解每个方案在虚拟正、负理想方案上的投影,进而计算出每个方案对虚拟正、负理想方案的相对隶属度,即可得到所有方案的排序结果.最后给出的数值算例表明,该方法简单、有效和易于计算.     

一种具有不确定偏好序信息的多指标群决策方法

针对具有不确定偏好序信息的多指标群决策问题,给出了一种决策分析方法。在本文中,首先对具有不确定偏好序信息的多指标群决策问题进行了描述;然后给出了将不确定偏好序转换为投票数的计算公式;进一步地,依据Bernardo方法的基本思想,根据每个专家给出的不确定偏好序信息,计算相应的投票数并构建群体投票矩阵,并基于群体投票矩阵构建0-1整数规划模型,通过求解模型可得到方案排序结果。最后,通过一个算例以及与已有方法的对比分析说明了本文给出的方法的可行性和有效性。     

Modeling External Risks in Project Management

To ascertain the viability of a project, undertake resource allocation, take part in bidding processes, and other related decisions, modern project management requires forecasting techniques for cost, duration, and performance of a project, not only under normal circumstances, but also under external events that might abruptly change the status quo. We provide a Bayesian framework that provides a global forecast of a project's performance. We aim at predicting the probabilities and impacts of a set of potential scenarios caused by combinations of disruptive events, and using this information to deal with project management issues. To introduce the methodology, we focus on a project's cost, but the ideas equally apply to project duration or performance forecasting. We illustrate our approach with an example based on a real case study involving estimation of the uncertainty in project cost while bidding for a contract.     

多阶段EOQ的合并订购策略

本文研究了多阶段EOQ下多物资的合并订购策略问题,分别给出了多物资在独立订购和合并订购时在计划期内的综合费用函数,以及合并订购策略的最优解.通过阶段内的费用分析,给出了合并订购方案优于独立订购的条件.