An AHP/DEA methodology for ranking decision making units

This paper presents a two-stage model for fully ranking organizational units where each unit has multiple inputs and outputs. In the first stage, the Data Envelopment Analysis (DEA) is run for each pair of units separately. In the second stage, the pairwise evaluation matrix generated in the first stage is utilized to rank scale the units via the Analytical Hierarchical Process (AHP). The consistency of this AHP/DEA evaluation can be tested statistically. Its goodness of fit with the DEA classification (to efficient/inefficient) can also be tested using non-parametric tests. Both DEA and AHP are commonly used in practice. Both have limitations. The hybrid model AHP/DEA takes the best of both models, by avoiding the pitfalls of each. The nonaxiomatic utility theory limitations of AHP are irrelevant here: since we are working with given inputs and outputs of units, no subjective assessment of a decision maker evaluation is involved. AHP/DEA ranking does not replace the DEA classification model, rather it furthers the analysis by providing full ranking in the DEA context for all units, efficient and inefficient.     

New methods for ranking decision making units based on the dispersion of weights and Norm 1 in Data Envelopment Analysis

One of the drawbacks of Data Envelopment Analysis (DEA) is the problem of lack of discrimination among efficient Decision Making Units (DMUs) and hence, yielding large number of DMUs as efficient ones. The main purpose of this paper is to overcome this inability. One of the methods for ranking efficient DMUs is minimizing the Coefficient of Variation (CV) for inputs-outputs weights, which, was suggested by Bal et al. (2008). In this paper, we modify the model and introduce two new models for ranking efficient DMUs based on Norm 1 and using means of inputs-outputs weights. To illustrate purpose, numerical examples are given.     

A new data envelopment analysis method for ranking decision making units: an application in industrial parks

Relative efficiency of decision‐making units (DMUs) is assessed by classical data envelopment analysis (DEA) models. DEA is a popular technique for efficiency evaluation. There might be a couple of efficient DMUs. Classical DEA models cannot fully rank efficient DMUs. In this paper, a novel technique for fully ranking all DMUs based on changing reference set using a single virtual inefficient DMU is proposed. To this end, the first concept of virtual DMU is defined as average of all inefficient DMUs. Virtual DMU is a proxy of all inefficient DMUs. This new method proposes a new ranking method that takes into account impact of efficient DMUs on virtual DMU and impact of efficient DMUs on influences of other efficient DMUs. A case study is given to show applicability of the proposed approach.     

支持共识决策过程的群排序集结

为了支持共识决策过程,引入最大共识排序概念,设计了基于共识排序树的群排序集结算法。该算法能够从排序数据中发现最大共识排序和需要进一步协商的冲突项目。应用模拟数据进行实验,结果表明了这种计算方法的有效性。     

A new DEA‐based method for fully ranking all decision‐making units

Abstract: Decision makers always lay great emphasis on performance evaluation upon a group of peer business units to pick out the best performer. Standard data envelopment analysis models can evaluate the relative efficiency of decision‐making units (DMUs) and distinguish efficient ones from inefficient ones. However, when there are more than one efficient DMU, it is impossible to rank all of them solely according to standard efficiency scores. In this paper, a new method for fully ranking all DMUs is proposed, which is based on the combination of each efficient DMU's influence on all the other DMUs and the standard efficiency scores. This method is effective in helping decision makers differentiate all units' performance thoroughly and select the best performer.     

A full ranking methodology in data envelopment analysis based on a set of dummy decision making units

In this paper, we propose a new methodology for ranking decision making units in data envelopment analysis (DEA). Our approach is a benchmarking method, seeks a common set of weights using a proposed linear programming model and is based on the TOPSIS approach in multiple attribute decision making (MADM). To this end, five artificial or dummy decision making units (DMUs) are defined, the ideal DMU (IDMU), the anti-ideal DMU (ADMU), the right ideal DMU (RIDMU), the left anti-ideal DMU (LADMU) and the average DMU (AVDMU). We form two comprehensive indexes for the AVDMU called the Left Relative Closeness (LRC) and the Right Relative Closeness (RRC) with respect to the RIDMU and LADMU. The LRC and RRC indexes will be used in the new proposed linear programming model to estimate the common set of weights, the new efficiency of DMUs and finally an overall ranking for all the DMUs. The change of the ratio between LRC and RRC indexes is capable to be provoked alternative rankings. One of the best advantages of this model is that we can make a rationale ranking which is demonstrated by the realized correlation analysis. Also, the new proposed efficiency score of the DMUs is close to the efficiency score of the DEA (CCR) methodology. Three numerical examples are provided to illustrate the applicability of the new approach and the effectiveness of the new approach in DEA ranking in comparison with other conventional ranking methods. Also, an "error" analysis proves the robustness of the proposed methodology.     

Interpretation of criteria weights in multicriteria decision making

Multicriteria decision making models are characterized by the need to evaluate a finite set of alternatives with respect to multiple criteria. The criteria weights in different aggregation rules have different interpretations and implications which have been misunderstood and neglected by many decision makers and researchers. By analyzing the aggregation rules, identifying partial values, specifying explicit measurement units and explicating direct statements of pairwise comparisons of preferences, we identify several plausible interpretations of criteria weights and their appropriate roles in different multicriteria decision making models. The underlying issues of scale validity, commensurability, criteria importance and rank consistency are examined.     

New analytical hierarchical process/data envelopment analysis methodology for ranking decision‐making units

The analytical hierarchical process/data envelopment analysis (AHP/DEA) methodology for ranking decision‐making units (DMUs) has some problems: it illogically compares two DMUs in a DEA model; it is not compatible with DEA ranking in the case of multiple inputs/multiple outputs; and it leads to weak discrimination in cases where the number of inputs and outputs is large. In this paper, we propose a new two‐stage AHP/DEA methodology for ranking DMUs that removes these problems. In the first stage, we create a pairwise comparison matrix different from AHP/DEA methodology; the second stage is the same as AHP/DEA methodology. Numerical examples are presented in the paper to illustrate the advantages of the new AHP/DEA methodology.     

考虑准则依赖的多准则变权决策新方法

为克服Choquet积分、网络分析法以及决策试行与评价实验室方法在处理具有准则依赖特征的多准则决策问题时存在的指数灾难、难以进行有效判断以及忽视因素自我影响强度等内在缺陷,吸纳网络分析法、数据包络分析以及非线性加权影响测度体系的核心思想,提出一种全新的考虑准则依赖的多准则变权决策方法。该方法不仅从超矩阵构造机理上实现了对系统方案的变权评价,而且更易于反映复杂决策问题的非线性、涌现性、复杂性等本质特征以及决策者的偏好判断信息。案例对比验证结果表明,所提方法是科学可行的,对于解决复杂系统多准则决策问题有着较强的实践应用可操作性。     

An effectiveness analysis of information channeling in choice decision making with attribute importance weights

In multi-alternative, multi-attribute choice decision tasks, decision makers use either alternative-based or attribute-based information processing patterns. Evidence suggests that channeling of access patterns may be effective. Restricted search of only key information attributes may be further encouraged when importance weights for attributes are predetermined and provided to the decision makers. This study examines the effectiveness of alternative-based channeling and attribute-based channeling with or without the provision of attribute importance weights. Both alternative-based and attribute-based channeling improves the decision accuracy when attribute weights are provided. In addition, the results indicate statistically significant effects on decision accuracy for the type of information display.     

A method using weight restrictions in data envelopment analysis for ranking and validity issues in decision making

In this article we introduce a comprehensive yet efficient approach based on data envelopment analysis (DEA) with restricted multipliers for accountable and understandable multiple attribute decision making (MADM). Information system (IS) appraisals are motivated and used for illustrating the proposed methodology. Results show that the given DEA based approach can easily and significantly increase the information frame of the decision maker by identifying disparate rankings and by affirming the stability and validity of ranking outcomes. The given validity concept is contrary to the directions given in the main body of research and can also be used to question ranking outcomes of classic MADM methods.     

属性权重完全未知的犹豫模糊双边匹配决策

针对基于犹豫模糊属性（HFV）信息且权重完全未知的双边匹配（TSM）问题,提出一种多属性匹配决策方法。首先,根据双方主体给出的犹豫模糊多属性评价值,通过最大化各属性之间的离差和从而确定属性权重;然后,由犹豫模糊有序加权平均算子集结多属性及权重信息获得双方的匹配度;进而建立一种基于匹配度的多目标优化模型,并使用极大极小法转化为单目标优化模型求解得到匹配方案;最后,进行实例分析和对比,所提方法得到目标函数值分别为1.689和1.575,且匹配解唯一。实验结果表明,所提方法可避免因主观确定目标函数权重而产生不唯一匹配解。     

直觉模糊群决策中专家权重确定的一种精确方法

在直觉模糊群决策中,一般通过赋权法对不同专家或决策者进行有效区分,相关研究多偏重等值赋权与主观赋权,但两者均存在不足.基于此,提出一种仅依靠非犹豫度(专家对属性的非犹豫程度意味着对该属性信息的掌握程度)的精确加权(AWD)方法,并证明了该方法的单调性与尺度不变性.在 AWD 方法基础上,提出FOAWA 和 IFOAWG 算子,证明了新算子的幂等性、有界性与交换性.最后,通过算例展示了所提出方法的可行性和有效性.     

Managing consensus and weights in iterative multiple-attribute group decision making

This study put forwards a novel consensus framework to manage the consensus and weights (i.e., weights of the experts and attributes) in iterative multiple-attribute group decision making (MAGDM) problem. In this consensus framework, an optimization-based consensus model is devised to support the process of preferences-modifying, which seeks to minimize the adjustment amounts (in the sense of Manhattan distance) between the original and adjusted preferences. Then, the other two optimization-based consensus models are constructed to support the weights-updating, in which the consensus level among experts can be further improved. A numerical example is provided to show the application of the proposed consensus framework, and a detailed comparison analysis is presented to verify the effectiveness of the proposed consensus framework.     

Learning decision tree for ranking

Decision tree is one of the most effective and widely used methods for classification. However, many real-world applications require instances to be ranked by the probability of class membership. The area under the receiver operating characteristics curve, simply AUC, has been recently used as a measure for ranking performance of learning algorithms. In this paper, we present two novel class probability estimation algorithms to improve the ranking performance of decision tree. Instead of estimating the probability of class membership using simple voting at the leaf where the test instance falls into, our algorithms use similarity-weighted voting and naive Bayes. We design empirical experiments to verify that our new algorithms significantly outperform the recent decision tree ranking algorithm C4.4 in terms of AUC.

动态环境下的群组专家多准则变权决策方法

为克服经典多准则决策（MCDM）方法不适应动态的决策环境、难以反映方案集对准则集的非线性反馈效应等方面缺陷,通过运用网络分析和数据包络分析技术,提出一种动态环境下的群组专家多准则变权决策方法。较之于经典MCDM方法,新方法主要创新之处在于：给出了MCDM模型的动态演化机理;通过专家对方案所处准则状态予以有偏好（无偏好）判断,提出一种保证信息无损的群组专家信息提取方式;实现了对方案的变权评价,有效反映出蕴含在系统内部的准则集与方案集的非线性交互作用关系。实例验证结果表明,所提方法是科学可行的,能够有效解决救灾方案动态优选、供应商动态评价等实践问题。     

变权决策中变权效果分析与状态变权向量的确定

引入状态变权向量调节度和标准调节度以及调权水平的概念，为分析状态变权向量调节权重的能力提供了可量化的工具．利用标准调节度讨论了选择状态变权向量的一些基本原则和理论依据，并由调权水平给出了一种选择状态变权向量的可操作性方法．     

属性和专家客观权重未知的区间数群决策方法

针对偏好信息为区间数形式、属性和专家客观权重未知的多属性群决策问题,提出通过属性评价值之间偏离程度的熵值分析和建立目标最小化的非线性规划模型确定属性客观权重,并结合属性主观权重获得属性综合权重;通过灰色关联法分析专家综合评价和群体综合评价之间一致性程度确定专家客观权重,并利用自适应迭代法求得稳定的专家权重;构造了一个新的区间数比较的可能度公式,并基于此公式,给出了方案排序问题的解决方法。通过算例分析及与其他方法对比,验证了所提出方法的可行性和有效性。最后,分析了相关参数对决策结果的影响。     

Vague集多指标决策的模糊值线性序法

就Vague集的多指标决策问题,提出了一种新的多指标决策方法。该方法首先将Vague值转化为模糊值,从而建立模糊值矩阵,由模糊值矩阵按各指标对应值的大小对方案进行排序,形成多个线性序,进而由线性序来构造模糊优先矩阵,然后通过对模糊优先矩阵进行截割,得到方案的优劣程度排序,从而选出最优方案。最后通过一个实例说明此方法的具体决策过程。     

Multi-step ranking of alternatives in a multi-criteria and multi-expert decision making environment

In this work we introduce a decision model, in the form of a recursive aggregation algorithm, that attempts to mimic a multi-step ranking process of a set of alternatives in a multi-criteria and multi-expert decision making environment. The main idea is rather intuitive. Each alternative is initially assigned a list of values, representing the group experts’ opinion about the extent to which the alternative satisfies a set of given criteria. Then the values for each alternative are combined with the weighted mean operator according to vectors of weights, one for each decision maker in the group. These weights express the personal judgement of the decision makers about the relative importance of the individual criteria. Consequently, a new vector of values is obtained for each alternative. These new values are combined again with the weighted mean operator taking into account the different degrees of influence each decision maker accepts from the rest of the group. The latter aggregation step is repeated again and again for each alternative until a consensus is attained.