基于链比较判断的相对权重确定方法

两两比较判断技术是层次分析法(AHP)以及分析网络法(ANP)的基本构建之一,已经被广泛地应用在多目标决策分析中.两两比较判断技术要求决策者对比较对象作出两两比较,假定比较对象有n个的话,那么决策者要进行n(n-1)/2次偏好价值比较.本文提出一种链比较判断技术,对比较对象有n个的决策问题,只要进行n次偏好价值比较,就可以确定出决策者对比较对象(目标、准则、方案等)的相对权重向量.用一个数值例示对链比较方法进行了说明,最后给出了与该方法相关的、值得进一步研究的有关问题.     

决策评价系统数学模型设计及实现

本文运用层次分析法(AHP)、调整判断矩阵、建立模糊关系矩阵等给出了通用多层次、多目标综合决策评价系统数学模型。主要步骤是建立系统层次结构模型,构建群组决策两两判断矩阵,计算单层次排序权重和针对评价目标的层次总排序权重,最终得到评价结果。为决策评价系统设计提出完整、高效和可行的解决方案。     

基于方案占优和排序稳健性的多属性决策方法

在多属性决策问题中,不同的属性权重会产生不同的评价结果。由于实际问题的复杂性与不确定性,决策者对于属性权重的确定也存在不确定性。这些不确定既来自现实问题的复杂性和可变性,也来自决策者选择的模糊性与随机性。目前已有的研究主要是将不确定的权重信息转化为相对确定的信息（如转化为区间数等）,硬性地消除了不确定,从而给决策结果带来较大风险。本文从方案排序的视角出发,研究在权重空间下,方案的占优关系和排序的稳健性。首先,定义了占优矩阵用于刻画不确定权重信息下方案两两比较的占优关系;其次,分析了方案的排序区间,即在所有可能存在的权重组合下,方案的最好排序和最差排序。然后,定义了方案的全排序排序概率,并且给出了排序概率的计算方法。进而,我们给出了方法的决策步骤和实施过程。最后,本文将该方法应用到某远洋集团的港口评估当中。     

两层群决策的双平台学习与协调模型

为解决现有分层决策方法无法反映决策者真实风险态度、难以保证学习与协调效率或效果的问题,构建了决策信息双平台提取模式和双平台学习协调结构,在此基础上提出了决策信息单平台学习修正模型、基元前景价值双平台系统协调模型以及双平台学习协调分析方法。该新模型方法不仅能够就上下两层在知识结构上的分布性认知优势应用学习修正定理有效地消除两层决策者在单平台上的认知偏差,而且还能系统协调双平台上差异性的决策信息,从而保证所做出的是科学有效决策。基于蒙特卡洛模拟的验证结果表明,新模型方法具有科学有效性和实际应用可行性。     

基于前景理论和隶属度的混合型多属性决策方法

针对带有决策者期望的混合型多属性决策问题,提出了一种基于前景理论和隶属度的决策分析方法。首先依据决策者对各个属性的期望,将具有清晰数、区间数和语义短语三种形式的决策矩阵转化成为前景决策矩阵。然后,根据各个方案与决策期望之间的广义加权欧氏距离,建立了可变模糊模式识别模型,并通过构造拉格朗日松弛函数,进行交叉迭代计算,得到各个方案的最优隶属度以及对应的属性权重,在此基础上,通过合成各个方案的累计前景值与隶属度,得到方案的综合前景值,并依据综合前景值的大小进行方案排序。最后通过一个原油管道路线优选实例,表明了该方法的可行性与有效性。     

基于证据推理和前景理论的交叉效率排序方法研究

针对由交叉效率评价策略和交叉效率集结方法的多样性而造成评价结果不一致的问题,提出利用证据推理方法和前景理论,综合各个交叉效率评价策略的评价结果,实现对决策单元的统一评价。首先,分别将选用的交叉效率评价策略以及各个评价策略中的他评效率设置成一级指标和二级指标,依据算数平均和前景理论分别确定一、二级指标的权重;其次,依据他评效率确定二级指标置信度,利用证据推理方法将各个交叉效率评价策略的他评效率综合转换成决策单元被评价为有效的置信度。决策者可通过比较决策单元被识别为有效的置信度的大小来判断决策单元交叉效率的大小,进而实现对决策单元的排序;最后,通过案例验证和说明本文提出方法的有效性和实用性。     

基于灰色关联度求解指标权重的改进方法

针对决策过程中指标权重的确定问题,在分析现有权重确定方法不足的基础上,提出了一种基于灰色关联度求解指标权重的改进方法,并对其性质进行了研究。该方法是对决策者给出的主观权重经验判断矩阵进行充分挖掘,提取出一个公共比较权重数列,并建立一个简易的数学模型,使确定的权重同时反映主观程度和客观程度。算例分析说明了该改进方法的简单性与实用性。     

考虑决策者损失规避的异质信息多属性变权决策方法

现实中存在大量异质信息（或数据）和需要考虑权重随属性值变化的多属性决策问题。针对这类异质信息多属性决策问题，本文提出了一种基于前景理论的变权综合求解方法。首先，构建了异质信息的统一距离计算公式，进而计算各个决策方案的相对贴近度；然后，提出基于不同类型效用函数的变权向量构造方法；其次，以初始权重为参考点，计算变权向量相对于参考点的益损决策矩阵，进而计算考虑决策者权重损失和收益的风险态度的各个决策方案的前景综合值，据此确定方案优劣排序和最优方案。通过数值例子的计算分析说明，文中所提决策模型与方法具有较好的有效性和合理性，可为解决复杂情景的决策问题提供理论依据与方法支持。     

基于累积前景理论的报酬契约模型设计与分析

传统报酬契约的机制设计以委托代理模型为依据,并基于期望效用理论加以分析、讨论。实证研究认为,委托代理模型中决策者的行为偏好更符合累积前景理论假设,即委托人与代理人均会依据不同预期收益呈现相应的风险偏好,并对收益的概率估计赋以非线性的决策权重。本文引入累积前景理论重构报酬契约模型,通过构建价值函数、决策权重函数,设置参照点,研究委托人、代理人均无明显风险偏好表征下的决策行为。模型结果表明,在参照点为0的情况下,代理人的最优努力水平与自身风险态度系数或决策权重系数无关;在信息透明情形下,委托人制定的最优利润分享系数,完全由自身的风险态度系数与决策权重系数决定。据此,本文提出系列激励机制优化对策。     

基于前景理论的多阶段随机多准则决策方法

研究一种基于动态参考点的多阶段随机多准则决策方法。考虑多阶段决策过程中决策者的风险偏好,建立了基于前景理论的多阶段随机多准则决策分析框架,提出了一种基于阶段发展特征的动态参考点设置方法;构建准则权重的目标规划模型,结合阶段参考点动态变化的特征测算各阶段备选方案的综合前景值;设计方案综合前景值的范围估算模型,以反映决策风险对评价结果的影响;案例研究验证了上述方法的可行性和实际效果。     

Combining Experts’ Judgments: Comparison of Algorithmic Methods Using Synthetic Data

Expert judgment (or expert elicitation) is a formal process for eliciting judgments from subject‐matter experts about the value of a decision‐relevant quantity. Judgments in the form of subjective probability distributions are obtained from several experts, raising the question how best to combine information from multiple experts. A number of algorithmic approaches have been proposed, of which the most commonly employed is the equal‐weight combination (the average of the experts’ distributions). We evaluate the properties of five combination methods (equal‐weight, best‐expert, performance, frequentist, and copula) using simulated expert‐judgment data for which we know the process generating the experts’ distributions. We examine cases in which two well‐calibrated experts are of equal or unequal quality and their judgments are independent, positively or negatively dependent. In this setting, the copula, frequentist, and best‐expert approaches perform better and the equal‐weight combination method performs worse than the alternative approaches.     

Predicting the Validity of Expert Judgments in Assessing the Impact of Risk Mitigation Through Failure Prevention and Correction

Operational risk management of autonomous vehicles in extreme environments is heavily dependent on expert judgments and, in particular, judgments of the likelihood that a failure mitigation action, via correction and prevention, will annul the consequences of a specific fault. However, extant research has not examined the reliability of experts in estimating the probability of failure mitigation. For systems operations in extreme environments, the probability of failure mitigation is taken as a proxy of the probability of a fault not reoccurring. Using a priori expert judgments for an autonomous underwater vehicle mission in the Arctic and a posteriori mission field data, we subsequently developed a generalized linear model that enabled us to investigate this relationship. We found that the probability of failure mitigation alone cannot be used as a proxy for the probability of fault not reoccurring. We conclude that it is also essential to include the effort to implement the failure mitigation when estimating the probability of fault not reoccurring. The effort is the time taken by a person (measured in person-months) to execute the task required to implement the fault correction action. We show that once a modicum of operational data is obtained, it is possible to define a generalized linear logistic model to estimate the probability a fault not reoccurring. We discuss how our findings are important to all autonomous vehicle operations and how similar operations can benefit from revising expert judgments of risk mitigation to take account of the effort required to reduce key risks.     

The Measurement of Subjective Probability: Evaluating the Sensitivity and Accuracy of Various Scales

The RISK of an event generally relates to its expected severity and the perceived probability of its occurrence. In RISK research, however, there is no standard measure for subjective probability estimates. In this study, we compared five commonly used measurement formats—two rating scales, a visual analog scale, and two numeric measures—in terms of their ability to assess subjective probability judgments when objective probabilities are available. We varied the probabilities (low vs. moderate) and severity (low vs. high) of the events to be judged as well as the presentation mode of objective probabilities (sequential presentation of singular events vs. graphical presentation of aggregated information). We employed two complementary goodness‐of‐fit criteria: the correlation between objective and subjective probabilities (sensitivity), and the root mean square deviations of subjective probabilities from objective values (accuracy). The numeric formats generally outperformed all other measures. The severity of events had no effect on the performance. Generally, a rise in probability led to decreases in performance. This effect, however, depended on how the objective probabilities were encoded: pictographs ensured perfect information, which improved goodness of fit for all formats and diminished this negative effect on the performance. Differences in performance between scales are thus caused only in part by characteristics of the scales themselves—they also depend on the process of encoding. Consequently, researchers should take the source of probability information into account before selecting a measure.     

Representation,Propagation, and Decision Issues in Risk Analysis Under Incomplete Probabilistic Information

This article tries to clarify the potential role to be played by uncertainty theories such as imprecise probabilities, random sets, and possibility theory in the risk analysis process. Instead of opposing an objective bounding analysis, where only statistically founded probability distributions are taken into account, to the full‐fledged probabilistic approach, exploiting expert subjective judgment, we advocate the idea that both analyses are useful and should be articulated with one another. Moreover, the idea that risk analysis under incomplete information is purely objective is misconceived. The use of uncertainty theories cannot be reduced to a choice between probability distributions and intervals. Indeed, they offer representation tools that are more expressive than each of the latter approaches and can capture expert judgments while being faithful to their limited precision. Consequences of this thesis are examined for uncertainty elicitation, propagation, and at the decision‐making step.     

Combining Probability Distributions From Experts in Risk Analysis

This paper concerns the combination of experts' probability distributions in risk analysis, discussing a variety of combination methods and attempting to highlight the important conceptual and practical issues to be considered in designing a combination process in practice. The role of experts is important because their judgments can provide valuable information, particularly in view of the limited availability of hard data regarding many important uncertainties in risk analysis. Because uncertainties are represented in terms of probability distributions in probabilistic risk analysis (PRA), we consider expert information in terms of probability distributions. The motivation for the use of multiple experts is simply the desire to obtain as much information as possible. Combining experts' probability distributions summarizes the accumulated information for risk analysts and decision-makers. Procedures for combining probability distributions are often compartmentalized as mathematical aggregation methods or behavioral approaches, and we discuss both categories. However, an overall aggregation process could involve both mathematical and behavioral aspects, and no single process is best in all circumstances. An understanding of the pros and cons of different methods and the key issues to consider is valuable in the design of a combination process for a specific PRA. The output, a combined probability distribution, can ideally be viewed as representing a summary of the current state of expert opinion regarding the uncertainty of interest.     

A Methodology for Assessing the Probability of Occurrence of Undesired Events in the Tietê–Paraná Inland Waterway Based on Expert Opinion

The market share of Tietê–Paraná inland waterway (TPIW) in the transport matrix of the São Paulo state, Brazil, is currently only 0.6%, but it is expected to increase to 6% over the next 20 years. In this scenario, to identify and explore potential undesired events a risk assessment is necessary. Part of this involves assigning the probability of occurrence of events, which usually is accomplished by a frequentist approach. However, in many cases, this approach is not possible due to unavailable or nonrepresentative data. This is the case of the TPIW that even though an expressive accident history is available, a frequentist approach is not suitable due to differences between current operational conditions and those met in the past. Therefore, a subjective assessment is an option as allows for working independently of the historical data, thus delivering more reliable results. In this context, this article proposes a methodology for assessing the probability of occurrence of undesired events based on expert opinion combined with fuzzy analysis. This methodology defines a criterion to weighting the experts and, using the fuzzy logic, evaluates the similarities among the experts’ beliefs to be used in the aggregation process before the defuzzification that quantifies the probability of occurrence of the events based on the experts’ opinion. Moreover, the proposed methodology is applied to the real case of the TPIW and the results obtained from the elicited experts are compared with a frequentist approach evidencing the impact on the results when considering different interpretations of the probability.     

Public Understanding of Ebola Risks: Mastering an Unfamiliar Threat

Ebola was the most widely followed news story in the United States in October 2014. Here, we ask what members of the U.S. public learned about the disease, given the often chaotic media environment. Early in 2015, we surveyed a representative sample of 3,447 U.S. residents about their Ebola‐related beliefs, attitudes, and behaviors. Where possible, we elicited judgments in terms sufficiently precise to allow comparing them to scientific estimates (e.g., the death toll to date and the probability of dying once ill). Respondents’ judgments were generally consistent with one another, with scientific knowledge, and with their self‐reported behavioral responses and policy preferences. Thus, by the time the threat appeared to have subsided in the United States, members of the public, as a whole, had seemingly mastered its basic contours. Moreover, they could express their beliefs in quantitative terms. Judgments of personal risk were weakly and inconsistently related to reported gender, age, education, income, or political ideology. Better educated and wealthier respondents saw population risks as lower; females saw them as higher. More politically conservative respondents saw Ebola as more transmissible and expressed less support for public health policies. In general, respondents supported providing “honest, accurate information, even if that information worried people.” These results suggest the value of proactive communications designed to inform the lay public's decisions, thoughts, and emotions, and informed by concurrent surveys of their responses and needs.     

A fuzzy AHP application in government-sponsored R&D project selection

Due to the funding scale and complexity of technology, the selection of government sponsored technology development projects can be viewed as a multiple-attribute decision that is normally made by a review committee with experts from academia, industry, and the government. In this paper, we present a fuzzy analytic hierarchy process method and utilize crisp judgment matrix to evaluate subjective expert judgments made by the technical committee of the Industrial Technology Development Program in Taiwan. Our results indicate that the scientific and technological merit is the most important evaluation criterion considered in overall technical committees. We demonstrate how the relative importance of the evaluation criteria changes under various risk environments via simulation.     

An Experimental Study of the Effectiveness of Three Debiasing Techniques*

Subjective probability distributions constitute an important part of the input to decision analysis and other decision aids. The long list of persistent biases associated with human judgments under uncertainy [16] suggests, however, that these biases can be translated into the elicited probabilities which, in turn, may be reflected in the output of the decision aids, potentially leading to biased decisions. This experiment studies the effectiveness of three debiasing techniques in elicitation of subjective probability distributions. It is hypothesized that the Socratic procedure [18] and the devil's advocate approach [6] [7] [31] [32] [33] [34] will increase subjective uncertainty and thus help assessors overcome a persistent bias called “overconfidence.” Mental encoding of the frequency of the observed instances into prespecified intervals, however, is expected to decrease subjective uncertainty and to help assessors better capture, mentally, the location and skewness of the observed distribution. The assessors' ratings of uncertainty confirm these hypotheses related to subjective uncertainty but three other measures based on the dispersion of the elicited subjective probability distributions do not. Possible explanations are discussed. An intriguing explanation is that debiasing may affect what some have called “second order” uncertainty. While uncertainty ratings may include this second component, the measures based on the elicited distributions relate only to “first order” uncertainty.     

Understanding Cumulative Risk Perception from Judgments and Choices: An Application to Flood Risks

Catastrophic events, such as floods, earthquakes, hurricanes, and tsunamis, are rare, yet the cumulative risk of each event occurring at least once over an extended time period can be substantial. In this work, we assess the perception of cumulative flood risks, how those perceptions affect the choice of insurance, and whether perceptions and choices are influenced by cumulative risk information. We find that participants' cumulative risk judgments are well represented by a bimodal distribution, with a group that severely underestimates the risk and a group that moderately overestimates it. Individuals who underestimate cumulative risks make more risk‐seeking choices compared to those who overestimate cumulative risks. Providing explicit cumulative risk information for relevant time periods, as opposed to annual probabilities, is an inexpensive and effective way to improve both the perception of cumulative risk and the choices people make to protect against that risk.