A two-phase algorithm for consensus building in AHP-group decision making

Group decision making through the AHP has received significant attention in contemporary research, the primary focus of which has been on the issues of consistency and consensus building. In this paper, we concentrate on the latter and present a two-phase algorithm based on the optimal clustering of decision makers (members of a group) into sub groups followed by consensus building both within sub groups and between sub groups. Two-dimensional Sammon’s mapping is proposed as a tool for generating an approximate visualization of sub groups identified in multidimensional vector space, while the consensus convergence model is suggested for reaching agreement amongst individuals in and between sub groups. As a given, all decision makers evaluate the same decision elements within the AHP framework and produce individual scores of these decision elements. The consensual scores are obtained through the iterative procedure and the final scores are declared as the group decision. The results of two selected numerical examples are compared with two sets of results: the results obtained by the commonly used geometric mean aggregation method and also the results obtained if the consensus convergence model is applied directly without the prior clustering of the decision makers. The comparisons indicated the expected differences among the aggregation schemes and the final group scores. The matrices of respect values in the consensus convergence model, obtained for cases when the decision makers are optimally clustered and when they are not, show that in the latter case the decision makers receive lower weights of respect from other members in the group. Various tests showed that our approach is efficient in cases when no clusters can be visually and undoubtedly identified, especially if the number of group members is high.     

解决一类群决策问题的改进德尔菲法

专家综合评价属于委员会形式的群决策问题,提出了基于一致性分析的群决策机制和基于OWA算子的群决策机制,用来弥补常用机制的缺陷;介绍了判断群体意见分歧特征和定量判断标准;提出了基于一致性分析的改进德尔菲法,介绍了这种方法的思想、特点和应用步骤;分析了这类群决策的人员组成和工作程序图.     

The OWA-based consensus operator under linguistic representation models using position indexes

When using linguistic approaches to solve decision problems, we need linguistic representation models. The symbolic model, the 2-tuple fuzzy linguistic representation model and the continuous linguistic model are three existing linguistic representation models based on position indexes. Together with these three linguistic models, the corresponding ordered weighted averaging operators, such as the linguistic ordered weighted averaging operator, the 2-tuple ordered weighted averaging operator and the extended ordered weighted averaging operator, have been developed, respectively. In this paper, we analyze the internal relationship among these operators, and propose a consensus operator under the continuous linguistic model (or the 2-tuple fuzzy linguistic representation model). The proposed consensus operator is based on the use of the ordered weighted averaging operator and the deviation measures. Some desired properties of the consensus operator are also presented. In particular, the consensus operator provides an alternative consensus model for group decision making. This consensus model preserves the original preference information given by the decision makers as much as possible, and supports consensus process automatically, without moderator.     

International portfolio management with affine policies

While dynamic decision making has traditionally been represented as scenario trees, these may become severely intractable and difficult to compute with an increasing number of time periods. We present an alternative tractable approach to multiperiod international portfolio optimization based on an affine dependence between the decision variables and the past returns. Because local asset and currency returns are modeled separately, the original model is non-linear and non-convex. With the aid of robust optimization techniques, however, we develop a tractable semidefinite programming formulation of our model, where the uncertain returns are contained in an ellipsoidal uncertainty set. We add to our formulation the minimization of the worst case value-at-risk and show the close relationship with robust optimization. Numerical results demonstrate the potential gains from considering a dynamic multiperiod setting relative to a single stage approach.     

模糊多属性群决策一致性分析研究

群决策过程中各成员可能以不同的方式给出决策信息,讨论了四种不同决策信息的统一方法,设置了模糊环境下进行一致性判断的准则,介绍了梯形模糊数在群决策过程中的运算方法,举例说明了这种方法的应用步骤.     

知识共享/转移背景下的动态群体决策绩效研究

现有的动态群体决策实践经常存在决策速度慢、观点不收敛的问题。本研究融入知识共享/转移的因素,从决策动态交互的过程视角,探讨决策绩效(一致性及决策时间)的改善机理、影响因素,从而提高相应绩效指标。研究通过构建决策过程模型,证明了知识共享/转移考虑下一致性序列在交互过程中的收敛性。同时,通过定性模拟判断知识共享/转移对决策时间的影响,以最小化决策时间为优化目标,搜索知识共享/转移水平,给出了个体知识差异构成的多维空间下最优的行动方案。     

An intelligent-agent-based fuzzy group decision making model for financial multicriteria decision support: The case of credit scoring

Credit risk analysis is an active research area in financial risk management and credit scoring is one of the key analytical techniques in credit risk evaluation. In this study, a novel intelligent-agent-based fuzzy group decision making (GDM) model is proposed as an effective multicriteria decision analysis (MCDA) tool for credit risk evaluation. In this proposed model, some artificial intelligent techniques, which are used as intelligent agents, are first used to analyze and evaluate the risk levels of credit applicants over a set of pre-defined criteria. Then these evaluation results, generated by different intelligent agents, are fuzzified into some fuzzy opinions on credit risk level of applicants. Finally, these fuzzification opinions are aggregated into a group consensus and meantime the fuzzy aggregated consensus is defuzzified into a crisp aggregated value to support final decision for decision-makers of credit-granting institutions. For illustration and verification purposes, a simple numerical example and three real-world credit application approval datasets are presented.     

决策偏好不确定条件下群体决策收敛一致性研究

决策个体之间交互影响是达成群体一致意见的重要因素。本文引入决策个体决策偏好的不确定性以及个体间不对称的影响权重,以此为基础建立群体决策动态观点演化模型,并进行matlab仿真。文中取决策个体的偏好不确定性为常数,作为决策个体对自身观点确定性的大致考量,并把群体中所有决策者的决策偏好不确定性分为相同和不相同两种情况来讨论。仿真实例证明:决策个体观点的不确定性是最终影响群体决策一致性的重要因素,当决策个体偏好不确定性较大时,决策群体更容易得到一致意见;当偏好不确定性较小时,决策群体难以达成一致意见,最终形成几个观点簇;在初始观点分布均匀的情况下,群体观点最终会演化出怎样的观点形态,是由群体中观点不确定性较小的群体所持有的观点决定的。研究内容有助于理解群体决策中一致观点的演化规律,能够为群体决策的引导策略提供参考和借鉴。     

A modified procedure for synthesising ratio judgements in the analytic hierarchy process

The analytic hierarchy process (AHP) has been widely applied to solve problems arising in group decision making, by synthesising different or conflicting judgements. However, directly synthesising conflicting judgements by calculating the geometric mean of preference weights (ratios) in AHP may not reach consensus from all members in a decision making group, especially, when those members represent the stakeholders of the decision making problem. This study proposes a new method that uses the genetic algorithm and utility function to synthesise preference weights to prevent this fallacy occurring when implementing the classical AHP approach. Using the proposed method, the final decision can be achieved with only minimally-adjusted preference weights.     

MCDA and preference disaggregation in group decision support systems

Within the frame of decision aid literature, group decision making has drawn the attention of researchers from a wide spectrum of disciplines. Group Decision Support Systems (GDSS) can play a critical role, in decision situations with multiple individuals, each having his/her own private point of view on the handling of the decision problem. In such an environment, the conflict between the members of the group is not a seldom situation. Multiple criteria decision aid (MCDA) methods can be proven as invaluable tools in handling such interpersonal conflicts where the aim is to achieve consensus between the group members or at least reduce the amount of conflict among participating individuals. This paper reviews some of the past approaches in the multiple criteria–multiple decision makers context.     

多属性群决策算法及一致性分析研究

在多属性群决策中 ,集结群体意见之前必须先对群体的决策数据进行一致性分析 ,以确保群体作出的决策符合客观实际 .提出了群决策的三种三维层次模型 ;用欧几里得距离 ( Euclidean Distance)表示个人决策中方案的评价值 ;然后设置一致性指标值α,作为群体数据一致性的判断依据 ;提出了满足一致性基础上的一种群决策方法 ;最后用实例说明了算法的使用步骤 .     

A multiple attribute group decision making framework for the evaluation of lean practices at logistics distribution centers

In recent years, to adapt rapidly to changing market environments and outdo the competition more companies and organizations have adopted lean management practices. One problem that has arisen in these companies and organizations is the need to develop methods to accurately evaluate the lean practices performance. This study proposes a multiple attribute group decision making (MAGDM) framework to facilitate such evaluations. It deals with the consensus process and selection process for MAGDM problems based on the 2-tuple linguistic computation model. The similarity degree and consensus for the linguistic decision matrix are defined using an Euclidian distance function. An algorithm describing the consensus reaching process is presented and its properties analyzed. The entropy method is generalized to a linguistic setting to derive the importance weights for the attributes. One of the main ideas behind the entropy method is that attributes with quite different values are considered more important and therefore have higher weights. Finally, the developed MAGDM framework is applied to a lean practices evaluation problem for a commercial tobacco company’s logistics distribution centers in China.     

改进的多属性群决策共识方法及其在图书供应商选择中的应用

针对多属性群决策问题,提出了一种改进的加型集结共识方法.在每轮决策中,共识一致性指标较小的决策个体都修改其偏差较大的偏好,能快速使参与决策的个体对各属性形成满意的一致性意见.数值实验也表明该共识方法是合理有效的.     

考虑群体一致性的动态群体决策方法

为了求解一类包含多轮群体评价过程的动态群体决策问题，定义了个体效用波动和群体一致度的概念并分别建立了相应的计算指标，利用决策个体的效用波动指标提出了决策个体权重的修正方法，然后提出了一种基于群体一致度指标的加权算法，得到了各决策方案的群体效用评价。最后给出了计算实例。     

Measuring super-efficiency in DEA in the presence of infeasibility

Super-efficiency data envelopment analysis (DEA) model is obtained when a decision making unit (DMU) under evaluation is excluded from the reference set. Because of the possible infeasibility of super-efficiency DEA model, the use of super-efficiency DEA model has been restricted to the situations where constant returns to scale (CRS) are assumed. It is shown that one of the input-oriented and output-oriented super-efficiency DEA models must be feasible for a any efficient DMU under evaluation if the variable returns to scale (VRS) frontier consists of increasing, constant, and decreasing returns to scale DMUs. We use both input- and output-oriented super-efficiency models to fully characterize the super-efficiency. When super-efficiency is used as an efficiency stability measure, infeasibility means the highest super-efficiency (stability). If super-efficiency is interpreted as input saving or output surplus achieved by a specific efficient DMU, infeasibility does not necessary mean the highest super-efficiency.     

Linguistic fuzzy consensus model for collaborative development of fuzzy cognitive maps: a case study in software development risks

Fuzzy cognitive maps (FCMs) have been widely used in several domains for information processing, such as, data fusion, decision making. Although several methods to automatically learn FCMs are recognized from the scientific literature, the most used approach to build an FCM relies on a collaborative task involving single person or, more suitably, group of experts. Collaborative development increases reliability and robustness of the resulting FCM, but rises some problems in terms of group decision making to aggregate different perspectives of the problem representation. This paper proposes to support collaborative development of FCMs introducing knowledge engineering process that relies on Linguistic Fuzzy Consensus Model. In the proposed approach, each expert builds the own version of the FCM. When all different versions are available, a Group Decision Making process is activated in order to reach the consensus on conflictual modeling opinions. The result is a unique final version of the FCM that is not a simple aggregation of the versions provided by the experts but is the result of a well-suited mathematical model. In addition, this work adopts consensus model with incomplete preference relations scheme to address knowledge harmonization issues. Finally, advantages and the limitations of the proposed framework are argued.     

A consistency and consensus-based method to group decision making with interval linguistic preference relations

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.     

The effects of mental model formation on group decision making: An agent‐based simulation

We investigated dynamics of group decision making on complex problems when agents can form mental models of others from discussion history. Results indicated that as the agents' memory capacity increases, the group reaches superficial consensus more easily. Surprisingly, however, the shared mental model of the problem develops only within a limited area of the problem space, because incorporating knowledge from others into one's own knowledge quickly creates local agreement on where relevant solutions are, leaving other potentially useful solutions beyond the scope of discussion. The mechanisms stifling group‐level exploration and their implications for decision making research are discussed. © 2010 Wiley Periodicals, Inc. Complexity 16: 49–57, 2011     

群决策中成员意见的分歧特征及判断准则研究

群决策过程中各成员的评价在决策初始存在分歧,对这些分歧进行一致性分析是群决策过程的一个关键步骤,不剔除与群体意见偏离较远的决策者的评价信息就进行群体意见集结,可能会得出不符合客观实际的结论;讨论了群决策中成员意见的分歧特征,提出了成员评价的集中性和相似性概念;定义了群决策过程中判断个人意见是否与群体意见一致的判断准则,即集中性指标和相似性指标.     

A multiattribute GDSS for aiding problem-solving

This study proposes a group decision support system (GDSS) with multiattribute to help solve problems in the real world. The problems are usually characterized as a multiattribute decision making (MADM) for selections, and shall be the responsibility of an expert group. On a regular basis, experts within that group will meet and conduct discussions on the web. After each individual make efforts of judgments, comparisons, and rankings, they shall determine, collectively as a group, the final rankings of all possible alternatives. Furthermore, aimed at insuring the decision quality of the collective decisions, an integrated procedure will be applied to make any modifications as necessary. Based on the geometric aspects of decision quality, the disparity of each individual member's preferences on attribute can be filtered out by the suggested bounded indicators. And then the outliers related to attributes' weights will be identified through a different set of consensus indicators, thus, further improving the decision quality while maintaining a quantitative level of consensus. Finally, using a car-selection problem herein, the proposed integrated procedure is implemented on a network-based PC system with web interfaces.