Post-consensus analysis of group decision making processes by means of a graph theoretic and an association rules mining approach

It is assumed that a group of experts is tasked to evaluate (rank) a finite set of alternatives during a group decision making (GDM) session. The GDM session may go through a number of iterations (stages) to reach a consensus. At each iteration at least one of the experts changes his/her ranking of some of the alternatives. The session terminates when a consensus has been reached or no expert is willing to alter his/her ranking. In the latter case a compromised consensus is somehow determined. It is also assumed that a data recording mechanism exists that keeps log files with information on each session and the iterations involved at each session. Such logs describe how each individual expert has ranked the alternatives at each iteration of each session. It is also assumed that there is a supervisory authority of this GDM process. This authority wishes to analyze the log files to extract any actionable insights. An approach based on some graph theoretic and the mining of association rules is proposed to identify any dynamics that may exist in the way the experts make ranking decisions. Such analysis may reveal unknown, but potentially useful information, on the way the experts make decisions and also on the way the experts may interact with each other. Knowing such relationships may be pivotal on the way the groups of experts need to be formed and operate during the GDM sessions. Some experimental results based on synthetic data are described and analyzed in terms of the proposed approaches.     

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.     

The Selection of Computer-Aided Software Engineering Tools: A Multi-Criteria Decision Making Approach

The selection of the appropriate computer-aided software engineering (CASE) tools to suit the needs of an organization requires the systematic application of the multi-criteria decision methodology (MCDM). In order to make a case for the use of MCDM, the application of the ELECTRE I method to the selection of CASE tools from a possible set of six alternatives is demonstrated. The demonstration helps in gaining a grasp of the MCDM approach and the ELECTRE I method. There is potential for the application of the MCDM approach in other software engineering decisions, especially in the feasibility analysis of the systems life cycle.     

A New Approach to the Group Ranking Problem: Finding Consensus Ordered Segments from Users’ Preference Data

The group ranking problem involves constructing coherent aggregated results from users’ preference data. The goal of most group ranking problems is to generate an ordered list of all items that represents the user consensus. There are, however, two weaknesses to this approach. First, a complete list of ranked items is always output even when there is no consensus or only a slight consensus. Second, due to similarity of performance, in many practical situations, it is very difficult to differentiate whether one item is really better than another within a set. These weaknesses have motivated us to apply the clustering concept to the group ranking problem, to output an ordered list of segments containing a set of similarly preferred items, called consensus ordered segments. The advantages of our approach are that (i) the list of segments is based on the users’ consensuses, (ii) the items with similar preferences are grouped together in the same segment, and (iii) the relationships between items can be easily seen. An algorithm is developed to construct the consensus of the ordered segments from the users’ total ranking data. Finally, the experimental results indicate that the proposed method is computationally efficient, and can effectively identify consensus ordered segments.     

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。     

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.     

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。     

基于犹豫直觉模糊语言集均值-标准差偏好距离的多属性决策研究

在犹豫直觉模糊语言集和语言尺度函数的基础上定义了均值-标准差偏好的Hamming距离，并提出了基于犹豫直觉模糊语言集距离TOPSIS和TODIM的多属性决策方法，进一步利用这两种方法对实例问题建筑商的招标方案进行排序，并讨论了偏好参数对排序结果的灵敏度分析。为验证上述方法的有效性，与已有方法对同一实例的排序结果进行了比较分析。     

Multicriteria Decision Framework for Cybersecurity Risk Assessment and Management

Risk assessors and managers face many difficult challenges related to novel cyber systems. Among these challenges are the constantly changing nature of cyber systems caused by technical advances, their distribution across the physical, information, and sociocognitive domains, and the complex network structures often including thousands of nodes. Here, we review probabilistic and risk-based decision-making techniques applied to cyber systems and conclude that existing approaches typically do not address all components of the risk assessment triplet (threat, vulnerability, consequence) and lack the ability to integrate across multiple domains of cyber systems to provide guidance for enhancing cybersecurity. We present a decision-analysis-based approach that quantifies threat, vulnerability, and consequences through a set of criteria designed to assess the overall utility of cybersecurity management alternatives. The proposed framework bridges the gap between risk assessment and risk management, allowing an analyst to ensure a structured and transparent process of selecting risk management alternatives. The use of this technique is illustrated for a hypothetical, but realistic, case study exemplifying the process of evaluating and ranking five cybersecurity enhancement strategies. The approach presented does not necessarily eliminate biases and subjectivity necessary for selecting countermeasures, but provides justifiable methods for selecting risk management actions consistent with stakeholder and decisionmaker values and technical data.     

基于交叉效率DEA与群体共识的区间乘性语言偏好关系群决策

针对区间乘性语言偏好关系群决策问题,提出了一种基于交叉效率DEA和群体共识的群决策方法。首先,提出乘性语言偏好关系导出函数的定义,并构建产出导向的DEA模型,证明了一致性乘性语言偏好关系的DEA效率得分与排序向量之间存在比例关系。在此基础上,建立基于理想值的交叉效率DEA模型,提出乘性语言偏好关系的通用排序方法。同时,基于群体共识建立目标规划模型来计算各语言偏好关系的权重系数。最后,利用Monte Carlo随机模拟的方法对群体语言偏好空间进行统计分析,得到群决策期望排序向量及其可信度。算例分析表明本文方法能够有效的避免信息损失,具有较强的适用性和较高的可信度。     

Decision Making Under Uncertainty—An Example for Seismic Risk Management

Decision-making techniques are used to select the "best" alternatives under multiple and often conflicting criteria. Multicriteria decision making (MCDM) necessitates to incorporate uncertainties in the decision-making process. The major thrust of this article is to extend the framework proposed by Yager^{( 1 )} for multiple decisionmakers and fuzzy utilities (payoffs). In addition, the concept of expert credibility factor is introduced. The proposed approach is demonstrated for an example of seismic risk management using a heuristic hierarchical structure. A step-by-step formulation of the proposed approach is illustrated using a hypothetical example and a three-story reinforced concrete building.     

Best-worst multi-criteria decision-making method

In this paper, a new method, called best-worst method (BWM) is proposed to solve multi-criteria decision-making (MCDM) problems. In an MCDM problem, a number of alternatives are evaluated with respect to a number of criteria in order to select the best alternative(s). According to BWM, the best (e.g. most desirable, most important) and the worst (e.g. least desirable, least important) criteria are identified first by the decision-maker. Pairwise comparisons are then conducted between each of these two criteria (best and worst) and the other criteria. A maximin problem is then formulated and solved to determine the weights of different criteria. The weights of the alternatives with respect to different criteria are obtained using the same process. The final scores of the alternatives are derived by aggregating the weights from different sets of criteria and alternatives, based on which the best alternative is selected. A consistency ratio is proposed for the BWM to check the reliability of the comparisons. To illustrate the proposed method and evaluate its performance, we used some numerical examples and a real-word decision-making problem (mobile phone selection). For the purpose of comparison, we chose AHP (analytic hierarchy process), which is also a pairwise comparison-based method. Statistical results show that BWM performs significantly better than AHP with respect to the consistency ratio, and the other evaluation criteria: minimum violation, total deviation, and conformity. The salient features of the proposed method, compared to the existing MCDM methods, are: (1) it requires less comparison data; (2) it leads to more consistent comparisons, which means that it produces more reliable results.     

Exploiting value system multiplicity and preference voting for robust ranking

Under a data envelopment analysis (DEA) framework, full ranking of a group of decision making units (DMUs) can be carried out through an adequate amalgamation of the cross-efficiency (CE henceforth) scores produced for each DMU. In this paper, we propose a ranking procedure that is based on amalgamating the weight profiles selected over the cross-evaluation rather than related CE scores. The new approach builds, for each DMU, a collective weight profile (CWP henceforth) by exploiting the preference voting system embedded within the matrix of weights, which views the assessing DMUs as voters and the input/output factors as candidates. The occurrence of zero votes is discussed as a special case and a two-level aggregation procedure is developed. The CWPs that are produced extend the concept of collective appreciation to the input/output factors of each DMU so that group dynamics is truly reflected, mainly in decision making circumstances where factor prioritization is necessary for making choices or allocating resources. The robustness of the proposed ranking approach is evaluated with three examples drawn from the literature.     

基于前景理论的新产品开发方案选择方法

为了解决新产品开发中考虑竞争产品方案评价信息的方案选择问题,提出了一种基于前景理论的决策分析方法。在该方法中,依据新产品开发方案与竞争产品方案相比的绩效确定前景参考点,并给出了前景价值函数和权重函数;通过计算和比较新产品开发方案的前景值和竞争产品方案的前景值,得到新产品开发方案的优选结果;最后给出一个算例,说明该方法的可行性和有效性。     

区间信息下的主客方协作式群体评价方法及其应用

目前关于主客方协作式评价问题的研究相对较少且主要是基于点值评价信息的,考虑到评价环境的复杂性与不确定性,本文将点值信息向区间信息方向拓展,探讨了一种新的区间信息下的主客方协作式群体评价方法。本文首先探讨了一种能够较好融合评价信息"质与量"的区间诱导密度加权合成算子-IIDWA;然后以主方信息完备度及客方信息诚信度为诱导分量分别对主客方评价信息进行聚类分组,并从规模和属性两个角度出发分别确定相应的密度加权向量;最后在主客方协作规则下,利用IIDWA算子对主客方区间信息分别进行二维集结,以得出最终综合评价结果。文章最后给出了一个应用算例,算例表明了方法的可行性与有效性。     

基于语言评价信息的快速集结方法研究

针对具有语言评价信息的多指标群决策问题,研究了基于二元语义的快速集结方法。把各决策者的语言评价信息转化为二元语义矩阵;依据各决策者的判断偏好,提出方案属性权重求解的规划模型;通过集结和比较各决策者偏好和总体偏好的差异,提出决策者权重确定模型;定义决策者判断一致度及决策者偏差的查找算法,快速辨别偏差较大的决策者并对其提供偏好调整建议;文后例子将其应用于某危险品的救险应急方案的选择。     

RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements

In this paper, we present a new preference disaggregation method, called RUTA, which infers a set of additive value functions from the preference information referring to the desired ranks of some reference alternatives. Real-life experience indicates that people willingly refer to the range of allowed ranks that a particular alternative should attain, or to constraints on the final scores of the alternatives. We develop a mathematical model for incorporating such preference information via mixed-integer linear programming (MILP). Then, we discuss how decision making could be supported with the use of the already proposed extreme ranking analysis (ERA), which indicates the best and worst ranks gained by each alternative over the set of compatible preference model instances. We also introduce a new interactive UTA-like technique, which aims at selecting a single value function representing the outcomes of ERA. In the interactive process, the decision maker (DM) is assigning priorities to different pre-defined targets, which are built on results of ERA, and refer to the comparison of the best and/or worst ranks for pairs of alternatives. In particular, the DM may choose to emphasize or neglect the advantage of some alternatives over the others, in terms of results of ERA. In this way, one obtains a synthetic representation of extreme ranking analysis at a higher level of abstraction.     

基于DEA理论的ANP/BOCR方案评价值综合集成新方法

网络分析法(ANP)是一种能够有效处理复杂决策问题的多准则决策方法。然而现有ANP文献在对收益、机会、成本、风险(统称为BOCR)评价值综合集成时会因评价值之间的不匹配而可能得出错误的方案排序结果和绩效表示。为克服上述缺陷,本文基于数据包络分析理论提出一种新的针对ANP/BOCR评价值的综合集成方法,使用摆幅置权区间估计方式反映出了决策者在判断BOCR相对权重时所面临的不精确性和模糊性。实例验证结果表明,所提方法对BOCR评价值的处理更符合实际情况。     

基于区间灰色区间数的多准则决策方法

将灰色模糊数扩展,定义了区间灰色区间数及其距离.针对准则值为区间灰色区间数的信息不完全的多准则决策问题,提出了一种基于目标规划法的灰色模糊多准则决策方法,求得最优权重向量,从而得到各方案的排序.最后给出一个算例说明方法的可行性和有效性.     

Ranking irregularities when evaluating alternatives by using some ELECTRE methods

The ELECTRE II and III methods enjoy a wide acceptance in solving multi-criteria decision-making (MCDM) problems. Research results in this paper reveal that there are some compelling reasons to doubt the correctness of the proposed rankings when the ELECTRE II and III methods are used. In a typical test we first used these methods to determine the best alternative for a given MCDM problem. Next, we randomly replaced a non-optimal alternative by a worse one and repeated the calculations without changing any of the other data. Our computational tests revealed that sometimes the ELECTRE II and III methods might change the indication of the best alternative. We treat such phenomena as rank reversals. Although such ranking irregularities are well known for the additive variants of the AHP method, it is the very first time that they are reported to occur when the ELECTRE methods are used. These two methods are also evaluated in terms of two other ranking tests and they failed them as well. Two real-life cases are described to demonstrate the occurrence of rank reversals with the ELECTRE II and III methods. Based on the three test criteria presented in this paper, some computational experiments on randomly generated decision problems were executed to test the performance of the ELECTRE II and III methods and an examination of some real-life case studies are also discussed. The results of these examinations show that the rates of the three types of ranking irregularities were rather significant in both the simulated decision problems and the real-life cases studied in this paper.