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。     

Two ways to handle dependent uncertainties in multi-criteria decision problems

We consider multi-criteria group decision-making problems, where the decision makers (DMs) want to identify their most preferred alternative(s) based on uncertain or inaccurate criteria measurements. In many real-life problems the uncertainties may be dependent. In this paper, we focus on multicriteria decision-making (MCDM) problems where the criteria and their uncertainties are computed using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. The simulation model determines for the criteria a joint probability distribution, which quantifies the uncertainties and their dependencies. We present and compare two methods for treating the uncertainty and dependency information within the SMAA-2 multi-criteria decision aid method. The first method applies directly the discrete sample generated by the simulation model. The second method is based on using a multivariate Gaussian distribution. We demonstrate the methods using a decision support model for a retailer operating in the deregulated European electricity market.     

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。     

考虑决策者心理行为的混合型随机多属性决策方法

针对混合型随机多属性决策问题,提出一种考虑决策者心理行为的决策分析方法。在该方法中,首先将具有离散型随机变量、灰色型随机变量和语言型变量形式的属性值规范化到区间内;然后将决策者给出的针对不同时期的属性期望视为参照点,并通过计算方案属性值与参照点的距离构建方案的益损矩阵;进一步地,依据累计前景理论,计算方案在不同属性上的收益和损失价值,并在此基础上,通过集结不同属性和不同时期的方案前景值确定各方案的综合前景值,进而依据得到的综合前景值确定方案排序结果。最后,通过一个算例说明了该方法的有效性和可行性。     

A three-stage hybrid approach for weight assignment in MADM

How to determine weights for attributes is one of the key issues in multiple attribute decision making (MADM). This paper aims to investigate a new approach for determining attribute weights based on a data envelopment analysis (DEA) model without explicit inputs (DEA-WEI) and minimax reference point optimisation. This new approach first considers a set of preliminary weights and the most favourite set of weights for each alternative or decision making unit (DMU) and then aggregates these weight sets to find the best compromise weights for attributes with the interests of all DMUs taken into account fairly and simultaneously. This approach is intended to support the solution of such MADM problems as performance assessment and policy analysis where (a) the preferences of decision makers (DMs) are either unclear and partial or difficult to acquire and (b) there is a need to consider the best "will" of each DMU. Two case studies are conducted to show the property of this new proposed approach and how to use it to determine weights for attributes in practice. The first case is about the assessment of research strengths of EU-28 member countries under certain measures and the second is for analysing the performances of Chinese Project 985 universities, where the weights of the attributes need to be assigned in a fair and unbiased manner.     

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。     

多属性决策决问题的满意度与赋权研究

多属性决策问题的决策中,决策者往往对属性上的数值存在一定的心理预期。首先,通过心理预期与实际数据获得决策对象在每个属性上的满意度,对决策对象进行筛选过滤;其次,提出属性值信息相容关系,利用属性值之间的相容度进行赋权,信息融合对满足决策者心理预期的决策对象排序择优;再次,提出决策对象满意度,并指出传统的排序方法获取的最优决策对象与决策者总体满意度最大的决策对象并不等价。具体算例表明,该方法科学有效且可行。     

Bayesian best-worst method: A probabilistic group decision making model

The best-worst method (BWM) is a multi-criteria decision-making method which finds the optimal weights of a set of criteria based on the preferences of only one decision-maker (DM) (or evaluator). However, it cannot amalgamate the preferences of multiple decision-makers/evaluators in the so-called group decision-making problem. A typical way of aggregating the preferences of multiple DMs is to use the average operator, e.g., arithmetic or geometric mean. However, averages are sensitive to outliers and provide restricted information regarding the overall preferences of all DMs. In this paper, a Bayesian BWM is introduced to find the aggregated final weights of criteria for a group of DMs at once. To this end, the BWM framework is meaningfully viewed from a probabilistic angle, and a Bayesian hierarchical model is tailored to compute the weights in the presence of a group of DMs. We further introduce a new ranking scheme for decision criteria, called credal ranking, where a confidence level is assigned to measure the extent to which a group of DMs prefers one criterion over one another. A weighted directed graph visualizes the credal ranking based on which the interrelation of criteria and confidences are merely understood. The numerical example validates the results obtained by the Bayesian BWM while it yields much more information in comparison to that of the original BWM.     

基于愿景满意度函数的多属性群决策方法

针对定性和定量属性相混合的多属性群决策问题，提出基于愿景满意度函数的多属性群决策方法。该方法从损失和收益的角度考虑问题，通过计算标准化的愿景值和属性值之间的距离，建立考虑专家不同风险态度的愿景满意度函数，求得专家各自的满意度，最后应用简单加权算子集结专家的排序结果。通过案例分析和算法对比说明了该算法可适用于不同风险态度的专家进行决策，而风险态度和愿景值的分析结果表明当属性不确定性较大时，专家看重损失或者收益取决于专家的风险态度和愿景值的高低，该方法可为参与决策的双方提供有价值的参考意见。     

XOR analytic hierarchy process and its application in the renewable energy sector

Uncertainty is a ubiquitous and inherent feature of the decision-making process. This paper proposes a new method called the XOR-analytical hierarchy process (XOR-AHP) to solve multi-criteria decision-making problems in uncertain and imprecise environments. In particular, the method derives a priority vector from an XOR comparison matrix, an XOR weighting (XOR-W) technique based on mathematical programming that allows decision makers (DMs) to set multiple judgments for a particular evaluation using XOR logic. To incorporate DMs’ preferences in this process, three types of XOR matrices are proposed: optimistic, pessimistic, and neutral. How the new model offers an alternative way to support DMs under uncertain conditions and in imprecise environments is illustrated by considering a hypothetical application (ranking and selecting North African countries for RE investments in the case of the Desertec project).     

A Model of Consumer Inertia with Applications to Dynamic Pricing

This paper introduces a decision model of consumer inertia. Consumers exhibit inertia when they have an inherent bias to delay purchases. Inertia may induce consumers to wait even when it is optimal to buy immediately. We embed our decision model within a dynamic pricing context. There is a firm that sells a fixed capacity over two time periods to an uncertain number of both rational and inertial consumers. We find that consumer inertia has both positive and negative effects on profits: it decreases demand (in period one) but intensifies competition among consumers for the product (in period two). We show that our model of inertia is consistent with well‐established behavioral regularities, such as loss aversion and probability weighting in the sense of prospect theory, and hyperbolic time preferences. We offer practical recommendations for firms to influence the level of consumer inertia. These include offering returns policies (to mitigate potential consumer losses), providing decision aids (to avoid perception errors), and offering flexible payment options (to lower transaction costs).     

Missing consequences in multiattribute utility theory

This paper addresses how to deal with decision alternatives with missing consequences in multicriteria decision-making problems. We propose disregarding the attributes for which a decision alternative provides no consequence by redistributing their respective weights throughout the objective hierarchy in favor of a straightforward idea: the assignation of the respective attribute range as a default value for missing consequences due to possible uncertainty about the decision alternative consequences. In both cases, decision alternatives are evaluated by means of an additive multi-attribute utility model. An illustrative example of the restoration of radionuclide contaminated aquatic ecosystems is shown.     

Dominance intensity measure within fuzzy weight oriented MAUT: An application

We introduce a dominance intensity measuring method to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision-making problems on the basis of multi-attribute utility theory (MAUT) and fuzzy sets theory. We consider the situation where there is imprecision concerning decision-makers' preferences, and imprecise weights are represented by trapezoidal fuzzy weights. The proposed method is based on the dominance values between pairs of alternatives. These values can be computed by linear programming, as an additive multi-attribute utility model is used to rate the alternatives. Dominance values are then transformed into dominance intensity measures, used to rank the alternatives under consideration. Distances between fuzzy numbers based on the generalization of the left and right fuzzy numbers are utilized to account for fuzzy weights.     

An extension of the Electre I method for group decision-making under a fuzzy environment

Many real-world decision problems involve conflicting systems of criteria, uncertainty and imprecise information. Some also involve a group of decision makers (DMs) where a reduction of different individual preferences on a given set to a single collective preference is required. Multi-criteria decision analysis (MCDA) is a widely used decision methodology that can improve the quality of group multiple criteria decisions by making the process more explicit, rational and efficient. One family of MCDA models uses what is known as “outranking relations” to rank a set of actions. The Electre method and its derivatives are prominent outranking methods in MCDA. In this study, we propose an alternative fuzzy outranking method by extending the Electre I method to take into account the uncertain, imprecise and linguistic assessments provided by a group of DMs. The contribution of this paper is fivefold: (1) we address the gap in the Electre literature for problems involving conflicting systems of criteria, uncertainty and imprecise information; (2) we extend the Electre I method to take into account the uncertain, imprecise and linguistic assessments; (3) we define outranking relations by pairwise comparisons and use decision graphs to determine which action is preferable, incomparable or indifferent in the fuzzy environment; (4) we show that contrary to the TOPSIS rankings, the Electre approach reveals more useful information including the incomparability among the actions; and (5) we provide a numerical example to elucidate the details of the proposed method.     

PAHAP: A Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences

In this paper, we present a Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences (PAHAP), a new method for solving discrete alternative multicriteria decision problems. Following the Analytic Hierarchy Process (AHP), PAHAP uses pairwise preference judgments to assess the relative attractiveness of the alternatives. By first aggregating the pairwise judgment ratios of the alternatives across all criteria, and then synthesizing based on these aggregate measures, PAHAP determines overall ratio scale priorities and rankings of the alternatives which are not subject to rank reversal, provided that certain weak consistency requirements are satisfied. Hence, PAHAP can serve as a useful alternative to the original AHP if rank reversal is undesirable, for instance when the system is open and criterion scarcity does not affect the relative attractiveness of the alternatives. Moreover, the single matrix of pairwise aggregated ratings constructed in PAHAP provides useful insights into the decision maker's preference structure. PAHAP requires the same preference information as the original AHP (or, altematively, the same information as the Referenced AHP, if the criteria are compared based on average (total) value of the alternatives). As it is easier to implement and interpret than previously proposed variants of the conventional AHP which prevent rank reversal, PAHAP also appears attractive from a practitioner's viewpoint.     

An Integrated Framework for Environmental Multi‐Impact Spatial Risk Analysis

Quantitative risk analysis is being extensively employed to support policymakers and provides a strong conceptual framework for evaluating decision alternatives under uncertainty. Many problems involving environmental risks are, however, of a spatial nature, i.e., containing spatial impacts, spatial vulnerabilities, and spatial risk‐mitigation alternatives. Recent developments in multicriteria spatial analysis have enabled the assessment and aggregation of multiple impacts, supporting policymakers in spatial evaluation problems. However, recent attempts to conduct spatial multicriteria risk analysis have generally been weakly conceptualized, without adequate roots in quantitative risk analysis. Moreover, assessments of spatial risk often neglect the multidimensional nature of spatial impacts (e.g., social, economic, human) that are typically occurring in such decision problems. The aim of this article is therefore to suggest a conceptual quantitative framework for environmental multicriteria spatial risk analysis based on expected multi‐attribute utility theory. The framework proposes: (i) the formal assessment of multiple spatial impacts; (ii) the aggregation of these multiple spatial impacts; (iii) the assessment of spatial vulnerabilities and probabilities of occurrence of adverse events; (iv) the computation of spatial risks; (v) the assessment of spatial risk mitigation alternatives; and (vi) the design and comparison of spatial risk mitigation alternatives (e.g., reductions of vulnerabilities and/or impacts). We illustrate the use of the framework in practice with a case study based on a flood‐prone area in northern Italy.     

基于双平台协调的两层群决策方法

为解决现有研究未考虑决策者的认知判断参考点与风险偏好态度对现实决策选择行为影响的问题,首先基于前景理论和T -JM矩阵构建了用于提取主观决策信息的价值平台与风险平台,然后针对上下两层知识在两个平台上的分布性特征给出并分析了两层双平台协调决策结构及运行机理,最后从上下两层满意协调度最优化的视角提出了能够有效提取两层决策信...     

Robust Climate Policies Under Uncertainty: A Comparison of Robust Decision Making and Info‐Gap Methods

This study compares two widely used approaches for robustness analysis of decision problems: the info‐gap method originally developed by Ben‐Haim and the robust decision making (RDM) approach originally developed by Lempert, Popper, and Bankes. The study uses each approach to evaluate alternative paths for climate‐altering greenhouse gas emissions given the potential for nonlinear threshold responses in the climate system, significant uncertainty about such a threshold response and a variety of other key parameters, as well as the ability to learn about any threshold responses over time. Info‐gap and RDM share many similarities. Both represent uncertainty as sets of multiple plausible futures, and both seek to identify robust strategies whose performance is insensitive to uncertainties. Yet they also exhibit important differences, as they arrange their analyses in different orders, treat losses and gains in different ways, and take different approaches to imprecise probabilistic information. The study finds that the two approaches reach similar but not identical policy recommendations and that their differing attributes raise important questions about their appropriate roles in decision support applications. The comparison not only improves understanding of these specific methods, it also suggests some broader insights into robustness approaches and a framework for comparing them.     

移情关系影响下的群体共识决策模型研究

群体成员之间的社会关系及其网络结构特征是影响群决策的重要因素。移情关系是客观存在于一些现实群决策问题中的一种社会关系，但目前考虑移情关系的群决策研究尚不多见。为拓展群决策模型的应用范围，面向移情网络环境提出一种群体共识决策方法，并揭示移情关系对群体共识决策的影响规律。首先，从偏好交互影响的角度出发，构建局部移情模型和全局移情模型，并由此确定移情关系影响下决策者偏好演化的结果。其次，利用个体偏好分解为内在偏好和移情偏好的结构特点，为群体共识达成过程设计一种有效的移情关系引导的反馈机制，该机制可以通过内在偏好层面的偏好调整实现个体偏好层面的共识收敛。最后，数值仿真分析表明：群体成员之间的移情关系提升了群体共识水平，而且全局移情关系比局部移情关系更有利于群体共识的达成；移情网络结构和群体规模是影响移情网络环境下群体共识达成的重要因素。相关决策模型和研究结论可为移情网络环境下的群体共识决策提供理论和方法支持。     

Sequential Search and Selection Problem Under Uncertainty

This paper formulates and discusses a series of sequential decision problems of the following common structure: A decision alternative of multiple attributes‐that is, a job, an employee, or an investment alternative‐is to be selected within a certain fixed length of time. An unknown number of alternatives are presented sequentially, either deterministically or in a random manner. The decision maker can rank all the alternatives from best to worst without ties, and the decision to accept or reject an alternative is based solely on the relative ranks of those alternatives evaluated so far. The nonparametric sequential decision problem is first studied for a model involving a discrete time period and then generalized in terms of continuous time. Also considered is a variant of this problem involving a Bayesian estimation of (1) the uncertain probability of having an alternative at a given stage in the discrete‐time model and (2) the arrival rate of alternatives in the continuous‐time model. The optimal selection strategy that maximizes the probability of selecting the absolute best alternative is illustrated with the job search problem and the single‐machine job assignment problem.