An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule

The ELECTRE (ELimination Et Choix Traduisant la REalité, in French) is an effective multiple criteria decision making method based on comparative analysis. Among the family of the ELECTRE methods and their extensions, the ELECTRE III is widely used since it can tackle uncertain and imprecise information. The hesitant fuzzy linguistic term set can represent people's perceptions more comprehensively and flexibly than exact numbers especially in cognitive complex decision-making process. In this paper, we develop an integrated method based on the ELECTRE III to handle the cognitive complex multiple experts multiple criteria decision making problems in which the cognitive complex information is represented by hesitant fuzzy linguistic term sets and the outranking relations between alternatives are calculated by a novel score-function-based distance measure between hesitant fuzzy linguistic elements. A combinative weight-determining method involving both subjective and objective opinions of experts is introduced to derive the weights of criteria. After obtaining the ranking of alternatives from each experts’ decision matrix by the distillation algorithm, the weighted Borda rule is implemented to aggregate the rankings of alternatives regarding different experts. Some ordinal consensus measures are introduced to identify the reliability of the final ranking result. An application of hospital ranking in China is provided to validate the efficiency of the proposed method.     

Robust multi-criteria sorting with the outranking preference model and characteristic profiles

We present a new multiple criteria sorting approach that uses characteristic profiles for defining the classes and outranking relation as the preference model, similarly to the Electre Tri-C method. We reformulate the conditions for the worst and best class assignments of Electre Tri-C to increase comprehensibility of the method and interpretability of the results it delivers. Then, we present a disaggregation procedure for inferring the set of outranking models compatible with the given preference information, and use the set in deriving, for each decision alternative, the necessary and possible assignments. Furthermore, we introduce simplified assignment procedures and prove that they maintain a no class jumps-property in the possible assignments. Application of the proposed approach is demonstrated by classifying 40 land zones in 4 classes representing different risk levels.     

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.     

基于Heronian平均算子的Pythagorean模糊不确定语言决策方法

针对评价信息为Pythagorean模糊不确定语言数、属性权重未知且属性间相互影响的多属性决策问题,提出一种基于灰色关联法和Heronian平均算子的决策方法。首先,提出Pythagorean模糊不确定语言Heronian平均（PFULHM）算子和Pythagorean模糊不确定语言几何Heronian平均（PFULGHM）算子,并证明其满足幂等性、单调性、有界性及可交换性。考虑到属性权重之间重要程度的差异,定义了Pythagorean模糊不确定语言加权Heronian平均（PFULWHM）算子和Pythagorean模糊不确定语言加权几何Heronian平均（PFULWGHM）算子。其次,将灰色关联法运用到Pythagorean模糊不确定语言环境中求解属性权重。最后,提出基于PFULWHM算子和PFULWGHM算子的决策方法,并通过算例分析说明本文提出方法的有效性。     

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.     

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).     

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.     

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.     

Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives

Aggregate production planning (APP) addresses matching supply to forecast demand, with varying customer orders over the intermediate planning horizon. In real-world APP problems, input data and related parameters are commonly imprecise because information is incomplete or unavailable, and the decision maker (DM) must simultaneously consider conflicting objectives. This study develops an interactive possibilistic linear programming (i-PLP) approach to solve multi-product and multi-time period APP problems with multiple imprecise objectives and cost coefficients by triangular possibility distributions in uncertain environments. The imprecise multi-objective APP model designed here seeks to minimise total production costs and changes in work-force level with reference to imprecise demand, cost coefficients, available resources and capacity. Additionally, the proposed i-PLP approach provides a systematic framework that helps the decision-making process to solve fuzzy multi-objective APP problems, enabling a DM to interactively modify the imprecise data and parameters until a set of satisfactory solutions is derived. An industrial case demonstrates the feasibility of applying the proposed approach to a practical multi-objective APP problem.     

Evaluation of Multicriteria Decision Analysis Algorithms in Food Safety: A Case Study on Emerging Zoonoses Prioritization

Decision making in food safety is a complex process that involves several criteria of different nature like the expected reduction in the number of illnesses, the potential economic or health-related cost, or even the environmental impact of a given policy or intervention. Several multicriteria decision analysis (MCDA) algorithms are currently used, mostly individually, in food safety to rank different options in a multifactorial environment. However, the selection of the MCDA algorithm is a decision problem on its own because different methods calculate different rankings. The aim of this study was to compare the impact of different uncertainty sources on the rankings of MCDA problems in the context of food safety. For that purpose, a previously published data set on emerging zoonoses in the Netherlands was used to compare different MCDA algorithms: MMOORA, TOPSIS, VIKOR, WASPAS, and ELECTRE III. The rankings were calculated with and without considering uncertainty (using fuzzy sets), to assess the importance of this factor. The rankings obtained differed between algorithms, emphasizing that the selection of the MCDA method had a relevant impact in the rankings. Furthermore, considering uncertainty in the ranking had a high influence on the results. Both factors were more relevant than the weights associated with each criterion in this case study. A hierarchical clustering method was suggested to aggregate results obtained by the different algorithms. This complementary step seems to be a promising way to decrease extreme difference among algorithms and could provide a strong added value in the decision-making process.     

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.     

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.     

基于证据推理和广义Shapley值的扩展概率语言多属性群决策方法

扩展概率语言词集通过语言变量概率分布的调整能够转化为多种语言信息表示模型,是语言变量、不确定语言信息、扩展犹豫模糊语言词集、分布语言评估信息、概率语言词集等的一般化,具有较强的通用性和实用性,是处理不确定性信息的重要工具。鉴于此,本文针对扩展概率语言环境下的多属性群决策问题,提出基于证据推理和广义Shapley值的多属性群决策方法。首先,提出扩展概率语言词集的定义和相关基础理论。其次,将广义Shapley值和证据推理相结合用于专家信息融合,并将广义Shapley值和TODIM方法相结合用于备选方案排序。再次,提出基于灰色关联法的权重确定模型来处理专家/属性权重部分未知的情况。最后,以绿色供应商选择为例进行分析,通过对比分析验证所提方法的有效性和优越性。     

基于犹豫模糊语言信息的前景决策方法

本文首先回顾了模糊信息下前景理论研究的现状，发现犹豫模糊语言这一决策中常见的信息表达形式在前景理论框架中的研究被忽略，同时犹豫模糊环境下的前景决策方法具有一定的应用背景；基于此，本文考虑到决策者在实际决策过程中惯用的信息表达以及面对收益和损失时不同的风险态度，试图在犹豫模糊语言环境下构造新的前景理论决策框架，建立基于犹豫模糊语言信息的前景决策方法，并给出具体的决策步骤；最后通过算例分析展示了该方法的实际应用过程，并与犹豫模糊语言环境下的期望效用决策结果进行对比，说明了该方法更符合实际决策情景。     

基于区间灰色不确定语言的多准则决策方法

定义了区间灰色不确定语言及其运算法则和距离公式。拓展了连续区间数据的OWA(C-OWA)算子,提出了基于区间灰色不确定语言的有序加权C-OWA(IGULOWC-OWA)算子,并对其性质进行了分析。针对准则权重已知而方案的准则值为区间灰色不确定语言的多准则决策问题,提出了一种基于IGULOWC-OWA算子的多准则决策方法。该方法通过对各方案在各个准则下的评价值进行转换,将区间灰色不确定语言转化为不确定语言,然后,利用集结算子计算出各个方案的综合准则值,进而得出各方案的排序。最后通过算例表明了方法的可行性和有效性。     

基于Mo-RVIKOR的混合多属性决策方法

针对复杂性和不确定性多属性决策问题，考虑定量和定性融合的属性形式，提出了模块化随机多准则妥协解排序法（Modular Random VlseKriterijumska Opti-mizacija I Kompromisno Resenje，Mo-RVIKOR），该方法无需将信息统一，就能处理多种信息形式存在的多属性决策问题。采用精确数、随机变量处理定量评价信息，用概率语义术语集处理定性评价信息；通过改进离差最大化法确定属性权重；根据Mo-RVIKOR对决策对象进行排序；最后以某公司C2B定制化服务质量评测项目为例，验证了所提方法的有效性。     

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.     

基于信任关系和信息测度的概率语义社会网络群决策模型

设计专家权重和属性指标权重的计算模型已成为近年来备受关注的两个重要研究课题。针对评价信息为概率语义信任函数的社会网络群决策问题,提出一种基于信任关系和信息测度的概率语义社会网络群决策模型。首先,构建基于信任关系的概率语义决策空间,探究专家之间的信任传递模型,通过专家之间信任关系计算专家的权重;其次,引入概率语义信任函数的熵和相似度概念,并运用三角函数设计概率语义信任函数信息熵和相似度的衡量方法;最后,构建基于信任关系和信息测度的概率语义社会网络群决策模型,进而得到合理可靠的决策结果,同时将提出的社会网络群决策模型用于电动汽车供应商的选择实例,对比分析实验验证了模型的合理性和有效性。