COMPARISON OF CONSENSUS METHODS FOR PRIORITY RANKING PROBLEMS

Various consensus methods proposed for ranking problems yield controversial rankings and/or tied rankings which are vulnerable to considerable dispute. These include Borda-Kendall (BK) and minimum-variance (MV) methods. This paper compares three continuous (ratio-scale) consensus scoring methods with BK and MV ranking methods. One method, termed GM, is an eigenvector scaling of the geometric-mean consensus matrix. GM allows for (1) paired-comparison voting inputs (as opposed to all-at-once ranking), (2) pick-the-winner preference voting, and (3) ratio-scale preference voting. GM is relatively simple to calculate on small computers or calculators, and merging of “close” candidates into tied rankings can be achieved by using an e-threshold tie rule discussed in this paper. The GM method thus can be used for paired-comparison voting to calculate both a ratio-scaled consensus index (based on a consensus eigenvector) and a ranking of candidates that allows for ties between “close” candidates. Eigenvalue analysis is used as a means of evaluating voter inconsistencies.     

Ranking efficient units in DEA

Super-efficiency data envelopment analysis (DEA) model can be used in ranking the performance of efficient decision making units (DMUs). Because of the infeasibility problem associated with the super-efficiency DEA model, ranking has been restricted to the model where constant returns to scale and proportional changes in all inputs or all outputs are assumed. In fact, when super-efficiency is used as an efficiency stability measure, infeasibility means the highest super-efficiency. However, if super-efficiency is interpreted as input saving or output surplus achieved by a specific efficient DMU, infeasibility does not necessarily mean the highest super-efficiency. In order to obtain a complete ranking of efficient DMUs when the two assumptions are relaxed, a modified super-efficiency DEA model is proposed to overcome the infeasibility problem and to correctly capture the super-efficiency represented by the input saving or the output surplus. The current paper suggests using both input- and output-oriented super-efficiency models to characterize the super-efficiency when infeasibility occurs. As a result, we can rank the efficient DMUs if infeasibility occurs. The approach is applied to 20 largest Japanese companies and 15 US cities, respectively.     

The nearest neighbor Spearman footrule distance for bucket, interval, and partial orders

Comparing and ranking information is an important topic in social and information sciences, and in particular on the web. Its objective is to measure the difference of the preferences of voters on a set of candidates and to compute a consensus ranking. Commonly, each voter provides a total order of all candidates. Recently, this approach was generalized to bucket orders, which allow ties. In this work we further generalize and consider total, bucket, interval and partial orders. The disagreement between two orders is measured by the nearest neighbor Spearman footrule distance, which has not been studied so far. For two bucket orders and for a total and an interval order the nearest neighbor Spearman footrule distance is shown to be computable in linear time, whereas for a total and a partial order the computation is NP-hard, 4-approximable and fixed-parameter tractable. Moreover, in contrast to the well-known efficient solution of the rank aggregation problem for total orders, we prove the NP-completeness for bucket orders and establish a 4-approximation.     

两种改进的超效DEA模型

对DEA有效决策单元不能排序是传统DEA模型的一大缺点。该问题也成为DEA领域研究的热点。AP模型是最常用的区分DEA有效决策单元效率值大小的超效模型,但在实际应用中却出现了无解或解不稳定的情况。国外学者新近提出的MAJ模型、LJK模型则有效解决了这两个问题,但却存在模型区分能力不强的缺点。本文分析了这两种模型缺点产生的原因、予以改进并给出理论证明。标准数据集的实验显示改进效果显著,尤其是改进后的LJK模型表现优异。     

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.     

Ensemble ranking: Aggregation of rankings produced by different multi-criteria decision-making methods

One of the essential problems in multi-criteria decision-making (MCDM) is ranking a set of alternatives based on a set of criteria. In this regard, there exist several MCDM methods which rank the alternatives in different ways. As such, it would be worthwhile to try and arrive at a consensus on this important subject. In this paper, a new approach is proposed based on the half-quadratic (HQ) theory. The proposed approach determines an optimal weight for each of the MCDM ranking methods, which are used to compute the aggregated final ranking. The weight of each ranking method is obtained via a minimizer function that is inspired by the HQ theory, which automatically fulfills the basic constraints of weights in MCDM. The proposed framework also provides a consensus index and a trust level for the aggregated ranking. To illustrate the proposed approach, the evaluation and comparison of ontology alignment systems are modeled as an MCDM problem and the proposed framework is applied to the ontology alignment evaluation initiative (OAEI) 2018, for which the ranking of participating systems is of the utmost importance.     

超效率DEA模型的模糊扩展

在输入、输出数据为模糊数而效率值为准确值的模糊DEA模型中,会出现有两个以上有效单元,从而无法对所有决策单元进行全排序的情形。本文利用模糊数的基于α-截集的比较规则,建立了模糊条件下的超效率DEA模型,有效地解决了模糊决策单元的全排序问题。文末给出了一个实例。     

A modified DEA cross efficiency method with negative data and its application in supplier selection

Basic Data Envelopment Analysis (DEA) models are designed for non-negative data. However, negative data is inevitably used in many real-world issues. Also, multiple units with a maximum relative performance score (equal to one) can be obtained due to the benevolent view of evaluating Decision Making Units (DMUs) consistent performance. Therefore, the researchers proposed ranking models to differentiate efficient units. Cross efficiency is one of the most useful tools for DMUs ranking in the DEA. There are two major drawbacks to implementing this process. First, it gives different results in the presence of other optimal solutions; second, it does not provide a compelling reason to use the arithmetic mean to aggregate the results of the cross efficiency matrix. In this paper, first a new non-radial model is proposed to evaluate the performance of DMUs in the presence of negative data and then based on this model a new secondary goal model is proposed to eliminate the first drawback in the cross efficiency method. Also, to solve the second drawback in this method, a hybrid Multi-Attribute Decision Making (MADM)-DEA process with the help of fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje method is proposed. Finally, to show the applicability of the proposed methods, the results are used to select the supplier in a real-world problem.

     

基于交叉效率和合作博弈的决策单元排序方法

在数据包络分析中，大量的交叉效率模型已被提出。然而选择不同的目标模型将实现不一样的交叉效率评价。本文基于针对单个决策单元实施的对抗型和仁慈型两个交叉效率模型，用合作博弈方法来研究交叉效率模型的选取，并利用Shapley值对决策单元进行排序。最后通过实例分析显示该排序方法充分利用了最小交叉效率和最大交叉效率的信息完全排序了所有决策单元，具有一定的综合性和合理性。     

A two-phase robot selection procedure

In this paper, a two-phase methodology is proposed for robot selection. In phase 1, data envelopment analysis is used as a means to determine the technically efficient robot alternatives, considering cost and technical performance parameters. Using data envelopment analysis permits us to consider the fact that the performance parameters specified by the vendors are generally unattainable in practice. In the second phase, a fuzzy robot selection algorithm is utilized to rank the technically efficient robots according to both predetermined objective criteria and additional vendor-related subjective criteria. The algorithm is based on calculating fuzzy suitability indices for the technically efficient robot alternatives, and then, ranking the fuzzy indices to select the best robot alternative. A comprehensive example is provided to illustrate the decision procedure. The algorithm proposed in here is also applicable to a broader area of decision problems, e.g. facility site selection, determination of the best CNC machine or flexible manufacturing system among a set of mutually exclusive alternatives.     

基于前景理论和隶属度的混合型多属性决策方法

针对带有决策者期望的混合型多属性决策问题,提出了一种基于前景理论和隶属度的决策分析方法。首先依据决策者对各个属性的期望,将具有清晰数、区间数和语义短语三种形式的决策矩阵转化成为前景决策矩阵。然后,根据各个方案与决策期望之间的广义加权欧氏距离,建立了可变模糊模式识别模型,并通过构造拉格朗日松弛函数,进行交叉迭代计算,得到各个方案的最优隶属度以及对应的属性权重,在此基础上,通过合成各个方案的累计前景值与隶属度,得到方案的综合前景值,并依据综合前景值的大小进行方案排序。最后通过一个原油管道路线优选实例,表明了该方法的可行性与有效性。     

Cross efficiency measurement and decomposition in two basic network systems

The data envelopment analysis (DEA) technique uses the most favorable weights for each decision making unit (DMU) to calculate efficiency. The resulting efficiency scores are thus incomparable and difficult to discriminate. This phenomenon is more prominent for network systems, which involves the ranking of the component divisions, in addition to the system. This paper applies the idea of cross evaluation, which has been demonstrated to be an effective approach in ranking DMUs for systems considered as a whole-unit, to measure the efficiency of the two basic structures of network systems, series and parallel. The proposed model is able to decompose the cross efficiency measure of the system into the product of those of the divisions for the series structure and a weighted average for the parallel structure. The results from two real-world cases, one for the basic series structure and another for the parallel one, show that the cross efficiency measures proposed in this paper not only increase the discriminating power in ranking systems and divisions, but also identify the relationship between the system and division efficiencies. Which division has stronger effects on the performance of the system is reflected from this relationship.     

A slacks-based measure of super-efficiency in data envelopment analysis: An alternative approach

The current paper proposes a slack-based version of the Super SBM, which is an alternative super-efficiency model for the SBM proposed by Tone. Our two-stage approach provides the same super-efficiency score as that obtained by the Super SBM model when the evaluated DMU is efficient and yields the same efficiency score as that obtained by the SBM model when the evaluated DMU is inefficient. The projection identified by the Super SBM model may not be strongly Pareto efficient; however, the projection identified from our approach is strongly Pareto efficient.     

Common benchmarking and ranking of units with DEA

This paper develops a common framework for benchmarking and ranking units with DEA. In many DEA applications, decision making units (DMUs) experience similar circumstances, so benchmarking analyses in those situations should identify common best practices in their management plans. We propose a DEA-based approach for the benchmarking to be used when there is no need (nor wish) to allow for individual circumstances of the DMUs. This approach identifies a common best practice frontier as the facet of the DEA efficient frontier spanned by the technically efficient DMUs in a common reference group. The common reference group is selected as that which provides the closest targets. A model is developed which allows us to deal not only with the setting of targets but also with the measurement of efficiency, because we can define efficiency scores of the DMUs by using the common set of weights (CSW) it provides. Since these weights are common to all the DMUs, the resulting efficiency scores can be used to derive a ranking of units. We discuss the existence of alternative optimal solutions for the CSW and find the range of possible rankings for each DMU which would result from considering all these alternate optima. These ranking ranges allow us to gain insight into the robustness of the rankings.     

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.     

基于修剪平均的神经网络集成时序预测方法

由于复杂时序存在结构性断点和异常值等问题，往往导致预测模型训练效果不佳，并可能出现极端预测值的情况。为此，本文提出了基于修剪平均的神经网络集成预测方法。该方法首先从训练数据中生成多组训练集，然后分别训练多个神经网络预测模型，最后将多个神经网络的预测结果使用修剪平均策略进行集成。相较于简单平均策略而言，修剪平均策略不容易受到极值的影响，能够使集成模型获得鲁棒性强的预测效果。在实证研究中，本文构造了两种神经网络集成预测模型，分别为基于修剪平均的自举神经网络集成模型(Trimmed Average based Bootstrap Neural Network Ensemble, TA-BNNE)和基于修剪平均的蒙特卡洛神经网络集成模型(Trimmed Average based Monte Carlo Neural Network Ensemble, TA-MCNNE)，并采用这两种模型对NN3竞赛数据集进行预测，结果表明在常规和复杂数据集上，修剪平均策略比简单平均策略具有更好的预测精度。此外，本文将所提出的集成模型与NN3的前十名模型进行比较，发现两种模型在全部数据集上均超过了第6名，在复杂数据集上的表现均超过了第1名，进一步验证本文所提方法的有效性。     

An Alternative FMEA Method for Simple and Accurate Ranking of Failure Modes

Failure modes and effects analysis (FMEA) is a methodology for prioritizing actions to mitigate the effects of failures in products and processes. Although originally used by product designers, FMEA is currently more widely used in industry in Six Sigma quality improvement efforts. Two prominent criticisms of the traditional application of FMEA are that the risk priority number (RPN) used to rank failure modes is an invalid measure according to measurement theory, and that the RPN does not weight the three decision criteria used in FMEA. Various methods have been proposed to mitigate these concerns, including many using fuzzy logic. We develop a new ranking method in this article using a data‐elicitation technique. Furthermore, we develop an efficient means of eliciting data to reduce the effort associated with the new method. Subsequently, we conduct an experimental study to evaluate that proposed method against the traditional method using RPN and against an approach using fuzzy logic.     

基于在线评论和随机占优准则的生鲜电商顾客满意度测评

生鲜电商被认为是电子商务领域的下一片蓝海，吸引着各类资本、平台竞相追逐，但目前生鲜电商仍处于发展探索阶段，如何及时准确地把握顾客需求和有效地提升顾客满意度是当前面临的重要问题。本文提出一种基于在线评论和随机占优准则的生鲜电商顾客满意度测评方法：首先，利用生鲜电商存在的大量在线评论数据信息，基于LDA模型提取出在线评论中的主题，作为顾客对生鲜电商满意度的影响因素；其次，构建生鲜电商顾客需求的情感词典，计算在线评论中顾客的情感倾向得分，作为判断顾客满意度的依据；最后，利用随机占优准则，构建不同商品类别中影响因素的随机占优程度矩阵，并应用PROMETHEE-Ⅱ方法给出不同商品类别中影响因素的排序结果。通过爬取天猫网站中不同类别的生鲜商品在线评论信息进行顾客满意度评估的案例分析，验证本文提出的方法的可行性和有效性。结果显示，不同生鲜商品类别中顾客满意度影响因素的重要度排序是不同的。值得注意的是，所提方法也为其他产品或服务的顾客满意度评估问题提供了参考和支撑。     

A Decision Model for the Robot Selection Problem Using Robust Regression*

Industrial robots are increasingly used by many manufacturing firms. The number of robot manufacturers has also increased with many of these firms now offering a wide range of models. A potential user is thus faced with many options in both performance and cost. This paper proposes a decision model for the robot selection problem. The proposed model uses robust regression to identify, based on manufacturers' specifications, the robots that are the better performers for a given cost. Robust regression is used because it identifies and is resistant to the effects of outlying observations, key components in the proposed model. The robots selected by the model become candidates for testing to verify manufacturers' specifications. The model is tested on a real data set and an example is presented.     

THE IMPACT OF LOCAL CONTENT RULES ON GLOBAL SOURCING DECISIONS

Many governments have established, for various reasons, local confent purchasing rules for companies that wish to operate in their country. These requirements force firms to purchase a certain amount of components from suppliers located in that country. This paper describes local content rules and develops models to select suppliers while satisfying local content provisions. The single plant model can be transformed into a knapsack problem that is solved by a ranking procedure, and the solution provides insight as to the manner in which local content rules impact more generalized models. Furthermore, we illustrate possible negative effects to local industry that may result when governments set the local content percentage too high, and we discuss methods for companies to circumvent local content rules. Finally, we address the issue of local content rules in the context of multi-plant global sourcing decisions, and we provide an efficient solution procedure for the classical plant location model extended to include local content rules at each site