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.     

A Multifactorial Risk Prioritization Framework for Foodborne Pathogens

We develop a prioritization framework for foodborne risks that considers public health impact as well as three other factors (market impact, consumer risk acceptance and perception, and social sensitivity). Canadian case studies are presented for six pathogen‐food combinations: Campylobacter spp. in chicken; Salmonella spp. in chicken and spinach; Escherichia coli O157 in spinach and beef; and Listeria monocytogenes in ready‐to‐eat meats. Public health impact is measured by disability‐adjusted life years and the cost of illness. Market impact is quantified by the economic importance of the domestic market. Likert‐type scales are used to capture consumer perception and acceptance of risk and social sensitivity to impacts on vulnerable consumer groups and industries. Risk ranking is facilitated through the development of a knowledge database presented in the format of info cards and the use of multicriteria decision analysis (MCDA) to aggregate the four factors. Three scenarios representing different stakeholders illustrate the use of MCDA to arrive at rankings of pathogen‐food combinations that reflect different criteria weights. The framework provides a flexible instrument to support policymakers in complex risk prioritization decision making when different stakeholder groups are involved and when multiple pathogen‐food combinations are compared.     

How to support the application of multiple criteria decision analysis? Let us start with a comprehensive taxonomy

Decision making is a complex task that involves a multitude of perspectives, constraints, and variables. Multiple Criteria Decision Analysis (MCDA) is a process that has been used for several decades to support decision making. It includes a series of steps that systematically help Decision Maker(s) (DM(s)) and stakeholders in structuring a decision making problem, identifying their preferences, and building a decision recommendation consistent with those preferences. Over the last decades, many studies have demonstrated the conduct of the MCDA process and how to select an MCDA method. Until now, there has not been a review of these studies, nor a proposal of a unified and comprehensive high-level representation of the MCDA process characteristics (i.e., features), which is the goal of this paper. We introduce a review of the research that defines how to conduct the MCDA process, compares MCDA methods, and presents Decision Support Systems (DSSs) to recommend a relevant MCDA method or a subset of methods. We then synthesize this research into a taxonomy of characteristics of the MCDA process, grouped into three main phases, (i) problem formulation, (ii) construction of the decision recommendation, and (iii) qualitative features and technical support. Each of these phases includes a subset of the 10 characteristics that helps the analyst implementing the MCDA process, while also being aware of the implication of these choices at each step. By showing how decision making can be split into manageable and justifiable steps, we reduce the risk of overwhelming the analyst, as well as the DMs/stakeholders during the MCDA process. A questioning strategy is also proposed to demonstrate how to apply the taxonomy to map MCDA methods and select the most relevant one(s) using real case studies. Additionally, we show how the DSSs for MCDA method recommendation can be grouped into three main clusters. This proposal can enhance a traceable and categorizable development of such systems.     

FAMCDM: A fusion approach of MCDM methods to rank multiclass classification algorithms

Various methods and algorithms have been developed for multiclass classification problems in recent years. How to select an effective algorithm for a multiclass classification task is an important yet difficult issue. Since the multiclass algorithm selection normally involves more than one criterion, such as accuracy and computation time, the selection process can be modeled as a multiple criteria decision making (MCDM) problem. While the evaluations of algorithms provided by different MCDM methods are in agreement sometimes, there are situations where MCDM methods generate very different results. To resolve this disagreement and help decision makers pick the most suitable classifier(s), this paper proposes a fusion approach to produce a weighted compatible MCDM ranking of multiclass classification algorithms. Several multiclass datasets from different domains are used in the experimental study to test the proposed fusion approach. The results prove that MCDM methods are useful tools for evaluating multiclass classification algorithms and the fusion approach is capable of identifying a compromised solution when different MCDM methods generate conflicting rankings.     

Can Carbon Nanomaterials Improve CZTS Photovoltaic Devices? Evaluation of Performance and Impacts Using Integrated Life‐Cycle Assessment and Decision Analysis

In emergent photovoltaics, nanoscale materials hold promise for optimizing device characteristics; however, the related impacts remain uncertain, resulting in challenges to decisions on strategic investment in technology innovation. We integrate multi‐criteria decision analysis (MCDA) and life‐cycle assessment (LCA) results (LCA‐MCDA) as a method of incorporating values of a hypothetical federal acquisition manager into the assessment of risks and benefits of emerging photovoltaic materials. Specifically, we compare adoption of copper zinc tin sulfide (CZTS) devices with molybdenum back contacts to alternative devices employing graphite or graphene instead of molybdenum. LCA impact results are interpreted alongside benefits of substitution including cost reductions and performance improvements through application of multi‐attribute utility theory. To assess the role of uncertainty we apply Monte Carlo simulation and sensitivity analysis. We find that graphene or graphite back contacts outperform molybdenum under most scenarios and assumptions. The use of decision analysis clarifies potential advantages of adopting graphite as a back contact while emphasizing the importance of mitigating conventional impacts of graphene production processes if graphene is used in emerging CZTS devices. Our research further demonstrates that a combination of LCA and MCDA increases the usability of LCA in assessing product sustainability. In particular, this approach identifies the most influential assumptions and data gaps in the analysis and the areas in which either engineering controls or further data collection may be necessary.     

考虑多种安全库存策略的选址-库存问题研究

考虑多种安全设置策略的物流网络的选址-库存问题,不仅是选址、订货、运输和库存的集成优化,还需要考虑多种不同的安全库存设置和转运策略。因此,本文深入讨论了二级物流网络中的六种安全库存设置策略,构建了六种考虑不同安全库存设置的选址-库存模型。在考虑集中设置安全库存时,集中安全库存需要通过转载运输实现,因此需要将转载运输成本引入选址-库存模型之中,使新的选址-库存模型更加科学合理。另外,针对六种新的选址-库存模型,提出了基于个体成本差异分配的遗传算法,迭代搜索选址、分配、库存设置策略的优化组合。最后,通过数据实验验证了模型的有效性：（1）安全库存与转载运输之间存在此消彼长的背反关系;（2）安全库存设置和转载运输策略对总成本的影响取决于两种费率权重情况。本文的研究可以为二级物流网络的选址、订货和安全库存策略集成优化决策提供参考依据。     

A robust ranking method extending ELECTRE III to hierarchy of interacting criteria,imprecise weights and stochastic analysis

A great majority of methods designed for Multiple Criteria Decision Aiding (MCDA) assume that all assessment criteria are considered at the same level, however, decision problems encountered in practice often impose a hierarchical structure of criteria. The hierarchy helps to decompose complex decision problems into smaller and manageable subtasks, and thus, it is very attractive for computational efficiency and explanatory purposes. To handle the hierarchy of criteria in MCDA, a methodology called Multiple Criteria Hierarchy Process (MCHP), has been recently proposed. MCHP permits to consider preference relations with respect to a subset of criteria at any level of the hierarchy. Here, we propose to apply MCHP to the ELECTRE III ranking method adapted to handle three types of interaction effects between criteria: mutual-weakening, mutual-strengthening and antagonistic effect. We also involve in MCHP an imprecise elicitation of criteria weights, generalizing a technique called the SRF method. In order to explore the plurality of rankings obtained by the ELECTRE III method for possible sets of criteria weights, we apply the Stochastic Multiobjective Acceptability Analysis (SMAA) that permits to draw robust conclusions in terms of rankings and preference relations at each level of the hierarchy of criteria. The novelty of the whole methodology consists of a joint consideration of hierarchical assessments of alternatives performances on interacting criteria, imprecise criteria weights, and robust analysis of ranking recommendations resulting from ELECTRE III. An example regarding the multiple criteria ranking of some European universities will show how to apply the proposed methodology on a decision problem.     

A case-based distance method for screening in multiple-criteria decision aid

Screening is a process of multiple-criteria decision aid (MCDA) in which a large set of alternatives is reduced to a smaller set that most likely contains the best choice. We propose screening using a distance model calibrated on the basis of the decision-maker's own judgement. Viewing MCDA as preference aggregation based on consequence data, we define consequence and preference expressions (values and weights) and describe how they are aggregated. Then we define screening and explain some of its properties. Using an appropriate definition of distance, our case-based distance method screens a set of alternatives using criterion weights and a distance threshold obtained by quadratic optimization using the decision-maker's selection of alternatives from a test set. This case-based method can elicit the decision maker's preferences more expeditiously and accurately than direct inquiry. An application in water supply planning is used to demonstrate the procedure.     

Application of a novel PROMETHEE-based method for construction of a group compromise ranking to prioritization of green suppliers in food supply chain

The food sector has a prodigious focus and is constantly gaining in importance in today’s global economic marketplace. Due to an increasing global population, society faces a greater challenge for sustainable food production, quality, distribution, and food safety in the food supply chain. Adopting green supply chain management (GSCM) elements is essential for utilizing the food supply chain in an environmentally benign way. As a solution to the above challenge, the economic and green characteristics for supplier selection in green purchasing are studied in this paper. For an organization, the evaluation and selection of the green supplier is a vital issue due to several tangible and intangible criteria involved. Accordingly, we apply multiple criteria decision aiding techniques.We propose a hybrid approach that combines the revised Simos procedure, PROMETHEE methods, algorithms for constructing a group compromise ranking, and robustness analysis. At first, the revised Simos procedure is used to derive the criteria weights. Next, the PROMETHEE method is applied to rank the suppliers according to each Decision Maker׳s (DM׳s) preferences. Then, the compromise ranking is constructed to minimize the distance of the individual׳s rankings from the solution adopted by the whole group. For this purpose, we introduce and apply some original procedures based on Binary Linear Programming. Finally, the results are validated against the outcomes of robustness analysis. The applicability and efficiency of the proposed approach is endorsed with a case study in an Indian food industry.     

考虑决策者后悔规避的风险投资项目选择方法

在风险投资项目选择过程中,决策者通常是有限理性的,会尽量避免选择可能会令其感到后悔的风险投资项目,而在涉及多个行业的风险投资项目选择过程中如何考虑决策者后悔规避的心理行为因素,这方面的研究特别需要关注。本文提出了一种涉及多个行业的考虑决策者后悔规避的风险投资项目选择方法。在该方法中,首先计算各风险投资项目在不同市场状态下的项目价值;然后,计算各组合市场状态发生的概率;进一步地,构建后悔函数刻画决策者后悔的心理感知,并通过计算不同行业的各风险投资项目的综合效用值得到风险投资项目的排序结果。最后,通过一个算例说明了本文提出方法的可行性与有效性。     

Beyond Markowitz with multiple criteria decision aiding

The paper is about portfolio selection in a non-Markowitz way, involving uncertainty modeling in terms of a series of meaningful quantiles of probabilistic distributions. Considering the quantiles as evaluation criteria of the portfolios leads to a multiobjective optimization problem which needs to be solved using a Multiple Criteria Decision Aiding (MCDA) method. The primary method we propose for solving this problem is an Interactive Multiobjective Optimization (IMO) method based on so-called Dominance-based Rough Set Approach (DRSA). IMO-DRSA is composed of two phases: computation phase, and dialogue phase. In the computation phase, a sample of feasible portfolio solutions is calculated and presented to the Decision Maker (DM). In the dialogue phase, the DM indicates portfolio solutions which are relatively attractive in a given sample; this binary classification of sample portfolios into ‘good’ and ‘others’ is an input preference information to be analyzed using DRSA; DRSA is producing decision rules relating conditions on particular quantiles with the qualification of supporting portfolios as ‘good’; a rule that best fits the current DM’s preferences is chosen to constrain the previous multiobjective optimization in order to compute a new sample in the next computation phase; in this way, the computation phase yields a new sample including better portfolios, and the procedure loops a necessary number of times to end with the most preferred portfolio. We compare IMO-DRSA with two representative MCDA methods based on traditional preference models: value function (UTA method) and outranking relation (ELECTRE IS method). The comparison, which is of methodological nature, is illustrated by a didactic example.     

Responsive contingency planning in supply risk management by considering congestion effects

Contingency rerouting is known as a cost-effective risk management strategy for major disruptions such as earthquakes and natural disasters. The objective of this paper is to develop a decision-making tool to determine the appropriate response speed of a volume-flexible backup supplier to improve the supply chain responsiveness. We propose a mixed integer programming (MIP)-based capacity planning tool which generates the contingency plan of the supply chain subject to random disruptions. In order to make an accurate decision, the impact of critical operational characteristics such as response time and congestion are considered in a disruption scenario. The appropriate response speed is selected through a decision tree analysis by minimizing the expected supply chain costs. The selection is made with respect to three different attitudes of the decision maker towards risk. In order to evaluate the impact of the different failure and recovery probabilities over the selection process, a sensitivity analysis is presented. The results show that considering congestion is especially critical for risk-neutral decision makers in mitigating against disruptions.     

Categorizing Risks for Risk Ranking

Any practical process of risk ranking must group hazards into a manageable number of categories. Defining such categories requires value choices that can have important implications for the rankings that result. Most risk-management organizations will find it useful to begin defining categories in terms of environmental loadings or initiating events. However, the resulting categories typically need to be modified in light of other considerations. Risk-ranking projects can benefit from considering several alternative categorization strategies and drawing upon elements of each in developing their final categorization of risks. In principle, conducting multiple ranking exercises by using different categorizations could be interesting and useful. In practice, agencies are unlikely to have either the resources or patience to do this, but other groups in society might. Done well, such additional independent rankings could add valuable inputs to democratic risk-management decision making.     

考虑背景风险的项目投资决策

在项目投资过程中不但面临项目风险,同时还面临背景风险,且背景风险与项目风险之间往往存在着一定的相关性。文章在已有研究的基础上,针对考虑背景风险的项目投资决策问题,分析了风险之间的相关性及相关程度对投资决策的影响。首先讨论了加性背景风险和乘性背景风险单独存在时,背景风险与项目风险之间的相关性对投资决策的影响;其次构建了两种背景风险同时存在情形下的投资模型,进而通过蒙特卡罗仿真方法给出不同相关程度下的仿真结果,在此基础上分析两种背景风险与项目风险之间的相关性及相关程度对投资决策的影响并给出相关研究结论。     

Screening alternatives graphically by an extended case-based distance approach

Screening is a helpful process of multiple criteria decision aid (MCDA) to reduce a larger set of alternatives into a smaller one containing the best alternatives; thereby, decision makers are able to concentrate on evaluating alternatives within a smaller set. Therefore, determining how to assist decision makers in screening is an important issue for MCDA. This study proposes an extended case-based distance approach incorporating the advantages of a case-based distance method, a mixed-integer programming approach of discriminant analysis, and a multidimensional scaling technique to help decision makers screen alternatives visually in MCDA. The proposed approach can screen alternatives by evaluating sets of cases selected by decision makers, providing visual aids to observe decision context, reducing the number of misclassifications, and improving multiple solution problems. An interactive screening procedure is also developed to provide flexibility so that decision makers can check and adjust screening results iteratively.     

不确定环境下考虑风险厌恶的生产-分销网络优化模型及试验设计

考虑上游生产和下游需求不确定性，研究了由工厂、分销中心及终端市场构成的生产-分销网络优化设计问题。针对上游生产不确定性，考虑产生故障和无故障两种状态；针对下游市场需求不确定性，考虑其具有低、中和高三种状态。由于生产发生故障可能导致不合格品的产生，进一步考虑了在上游生产环节是否实施产品监测问题。综合网络运作成本和由不确定性导致的绩效风险，建立了由风险厌恶水平和悲观系数刻画的基于均值-条件风险值（CVaR）准则的生产-分销网络两阶段随机规划模型。特别地，针对由网络潜在节点数众多所导致的不确定情景规模过大的问题，采用情景缩减技术进行了情景筛选，降低了所建模型的求解难度。最后，进行了数值计算，分析了相关参数对网络运作绩效的影响，并给出了期望成本和条件风险值两个目标权衡的帕累托有效前沿。进一步，通过回归试验设计检验了决策者风险厌恶水平和悲观系数对所设计的生产-分销网络绩效的影响程度。结果表明，相对于决策者的风险厌恶程度，悲观系数对网络运作绩效的影响更大。     

A Multicriteria Decision Analysis Model and Risk Assessment Framework for Carbon Capture and Storage

Multicriteria decision analysis (MCDA) has been applied to various energy problems to incorporate a variety of qualitative and quantitative criteria, usually spanning environmental, social, engineering, and economic fields. MCDA and associated methods such as life‐cycle assessments and cost‐benefit analysis can also include risk analysis to address uncertainties in criteria estimates. One technology now being assessed to help mitigate climate change is carbon capture and storage (CCS). CCS is a new process that captures CO₂ emissions from fossil‐fueled power plants and injects them into geological reservoirs for storage. It presents a unique challenge to decisionmakers (DMs) due to its technical complexity, range of environmental, social, and economic impacts, variety of stakeholders, and long time spans. The authors have developed a risk assessment model using a MCDA approach for CCS decisions such as selecting between CO₂ storage locations and choosing among different mitigation actions for reducing risks. The model includes uncertainty measures for several factors, utility curve representations of all variables, Monte Carlo simulation, and sensitivity analysis. This article uses a CCS scenario example to demonstrate the development and application of the model based on data derived from published articles and publicly available sources. The model allows high‐level DMs to better understand project risks and the tradeoffs inherent in modern, complex energy decisions.     

Bayesian Modeling of Measurement Errors and Pesticide Concentration in Dietary Risk Assessments

We propose new models for dealing with various sources of variability and uncertainty that influence risk assessments for dietary exposure. The uncertain or random variables involved can interact in complex ways, and the focus is on methodology for integrating their effects and on assessing the relative importance of including different uncertainty model components in the calculation of dietary exposures to contaminants, such as pesticide residues. The combined effect is reflected in the final inferences about the population of residues and subsequent exposure assessments. In particular, we show how measurement uncertainty can have a significant impact on results and discuss novel statistical options for modeling this uncertainty. The effect of measurement error is often ignored, perhaps due to the laboratory process conforming to the relevant international standards, for example, or is treated in an  ad hoc  way. These issues are common to many dietary risk analysis problems, and the methods could be applied to any food and chemical of interest. An example is presented using data on carbendazim in apples and consumption surveys of toddlers.     

Integrating multicriteria decision analysis and scenario planning—Review and extension

Scenario planning and multiple criteria decision analysis (MCDA) are two key management science tools used in strategic planning. In this paper, we explore the integration of these two approaches in a coherent manner, recognizing that each adds value to the implementation of the other. Various approaches that have been adopted for such integration are reviewed, with a primary focus on the process of constructing preferences both within and between scenarios. Biases that may be introduced by inappropriate assumptions during such processes are identified, and used to motivate a framework for integrating MCDA and scenario thinking, based on applying MCDA concepts across a range of “metacriteria” (combinations of scenarios and primary criteria). Within this framework, preferences according to each primary criterion can be expressed in the context of different scenarios. The paper concludes with a hypothetical but non-trivial example of agricultural policy planning in a developing country.     

Multicriteria Decision Analysis: A Comprehensive Decision Approach for Management of Contaminated Sediments

Contaminated sediments and other sites present a difficult challenge for environmental decisionmakers. They are typically slow to recover or attenuate naturally, may involve multiple regulatory agencies and stakeholder groups, and engender multiple toxicological and ecotoxicological risks. While environmental decision-making strategies over the last several decades have evolved into increasingly more sophisticated, information-intensive, and complex approaches, there remains considerable dissatisfaction among business, industry, and the public with existing management strategies. Consequently, contaminated sediments and materials are the subject of intense technology development, such as beneficial reuse or in situ treatment. However, current decision analysis approaches, such as comparative risk assessment, benefit-cost analysis, and life cycle assessment, do not offer a comprehensive approach for incorporating the varied types of information and multiple stakeholder and public views that must typically be brought to bear when new technologies are under consideration. Alternatively, multicriteria decision analysis (MCDA) offers a scientifically sound decision framework for management of contaminated materials or sites where stakeholder participation is of crucial concern and criteria such as economics, environmental impacts, safety, and risk cannot be easily condensed into simple monetary expressions. This article brings together a multidisciplinary review of existing decision-making approaches at regulatory agencies in the United States and Europe and synthesizes state-of-the-art research in MCDA methods applicable to the assessment of contaminated sediment management technologies. Additionally, it tests an MCDA approach for coupling expert judgment and stakeholder values in a hypothetical contaminated sediments management case study wherein MCDA is used as a tool for testing stakeholder responses to and improving expert assessment of innovative contaminated sediments technologies.