Weight of Evidence: A Review of Concept and Methods

"Weight of evidence" (WOE) is a common term in the published scientific and policy-making literature, most often seen in the context of risk assessment (RA). Its definition, however, is unclear. A systematic review of the scientific literature was undertaken to characterize the concept. For the years 1994 through 2004, PubMed was searched for publications in which "weight of evidence" appeared in the abstract and/or title. Of the 276 papers that met these criteria, 92 were selected for review: 71 papers published in 2003 and 2004 (WOE appeared in abstract/title) and 21 from 1994 through 2002 (WOE appeared in title). WOE has three characteristic uses in this literature: (1) metaphorical, where WOE refers to a collection of studies or to an unspecified methodological approach; (2) methodological, where WOE points to established interpretative methodologies (e.g., systematic narrative review, meta-analysis, causal criteria, and/or quality criteria for toxicological studies) or where WOE means that "all" rather than some subset of the evidence is examined, or rarely, where WOE points to methods using quantitative weights for evidence; and (3) theoretical, where WOE serves as a label for a conceptual framework. Several problems are identified: the frequent lack of definition of the term "weight of evidence," multiple uses of the term and a lack of consensus about its meaning, and the many different kinds of weights, both qualitative and quantitative, which can be used in RA. A practical recommendation emerges: the WOE concept and its associated methods should be fully described when used. A research agenda should examine the advantages of quantitative versus qualitative weighting schemes, how best to improve existing methods, and how best to combine those methods (e.g., epidemiology's causal criteria with toxicology's quality criteria).     

Developing a supplier selection system through integrating fuzzy AHP and fuzzy DEA: a case study on an auto lighting system company in Taiwan

Supplier selection plays a very important role in supply chain management. This study intends to develop a novel performance evaluation method, which integrates both fuzzy analytical hierarchy process (AHP) method and fuzzy data envelopment analysis (DEA) for assisting organisations to make the supplier selection decision. Fuzzy AHP method is first applied to find the indicators’ weights through expert questionnaire survey. Then, these weights are integrated with fuzzy DEA. We use α -cut set and extension principle of fuzzy set theory to simplify the fuzzy DEA as a pair of traditional DEA model. Finally, fuzzy ranking using maximising and minimising set method is able to rank the evaluation samples. A case study on an internationally well-known auto lighting OEM company shows that the proposed method is very suitable for practical applications.     

A modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.     

Pitfalls of decomposition weights in the additive multi-stage DEA model

This paper examines limitations of the multi-stage DEA (data envelopment analysis) model in the literature. We focus on the DEA model with additive efficiency decomposition. We create taxonomy for the multi-stage DEA models and show when the decomposition weights can be non-increasing. When the decomposition weight for a stage is deemed reflective of the stage׳s relative importance, this property then implies that upstream stages (regardless the stage efficiency scores) in the model will obtain higher priority in efficiency decomposition. We also find that the non-increasing weights can affect the evaluation of overall and stage efficiency scores. We illustrate our findings through an empirical data set.     

Research fronts in data envelopment analysis

Research activities relating to data envelopment analysis (DEA) have grown at a fast rate recently. Exactly what activities have been carrying the research momentum forward is a question of particular interest to the research community. The purpose of this study is to find these research activities, or research fronts, in DEA. A research front refers to a coherent topic or issue addressed by a group of research articles in recent years. The large amount of DEA literature makes it difficult to use any traditional qualitative methodology to sort out the matter. Thus, this study applies a network clustering method to group the literature through a citation network established from the DEA literature over the period 2000 to 2014. The keywords of the articles in each discovered group help pinpoint its research focus. The four research fronts identified are “bootstrapping and two-stage analysis”, “undesirable factors”, “cross-efficiency and ranking”, and “network DEA, dynamic DEA, and SBM”. Each research front is then examined with key-route main path analysis to uncover the elements in its core. In addition to presenting the research fronts, this study also updates the main paths and author statistics of DEA development since its inception and compares them with those reported in a previous study.     

Ambiguous Criteria Weights in AHP: Consequences and Solutions*

Two related streams of criticism of the analytic hierarchy process (AHP) have not yet been satisfactorily resolved, although both date from the early 1980s. The first relates to ambiguity in the meaning of the relative importance of one criterion as compared to another. The second is concerned with reversals of rank alleged to be possible when new options are introduced in an AHP problem. Both proponents and critics of AHP agree that rank reversals occur, but disagree on the legitimacy of such reversals. This paper shows that there is a necessary correspondence between the manner in which criteria importances are interpreted and computed and the manner in which the weights of the options under each criterion are normalized. In general, if this relationship is ignored, incorrect weights are generated for options under consideration regardless of whether new options are added or deleted. A rank reversal on the addition of an option is merely symptomatic of this fact, and such reversals do not occur when the correspondence condition is met.     

Supplier Rationalization: A Sourcing Decision Model

We draw on extant literature on strategic sourcing and supply base rationalization to anchor our argument that measuring supplier performance diversity is germane to executing an effective supply base rationalization strategy. We explicate how a novel approach to data envelopment analysis (DEA) efficiency assessment can be utilized to measure this performance diversity. More specifically, our methods are anchored in cross efficiency analysis in DEA that allows for evaluating the efficiency of a supplier with respect to the optimal weights (strengths) of its peers. This methodology is applied to an actual supplier dataset of a large multinational telecommunications company in categorizing their supply base into groups for effective supplier rationalization. We conclude that measuring and analyzing the performance diversity within the framework of DEA provides a mechanism for firms to better balance a rationalized and diversified supply base with unique skills.     

Assessing the performance of business colleges in Taiwan using data envelopment analysis and student based value-added performance indicators

The purpose of this study is to construct a student-based performance evaluation model for business schools in Taiwan. College graduates’ starting wage and their multiple abilities cultivated in school are used as performance indicators. The value-added forms of these indicators are employed to assess the pure impact of school on graduate's performance. To prevent impractical indicator weights, we incorporate job market recruiters’ weights from an AHP survey into the assurance region data envelopment analysis (AR-DEA) for empirical analysis. Empirical results show that the public schools on average outperform the private schools. However, there are still some private schools that perform better than the public ones. Besides, in regard to the discriminatory power and the distribution of output weights, the proposed AR-DEA is better than DEA in measuring the performance of the business colleges in Taiwan.     

Application of hybrid framework to facilitate lean six sigma implementation: a manufacturing company case experience

This study aims to propose a hybrid framework for lean six sigma (LSS) based on the prioritisation of barriers and solution approaches, to facilitate hassles free applications for handling the challenges of wastes reduction and quality improvement. The study identifies 27 LSS barriers and 22 solution approaches through literature review and utilises feedback from industry experts. For framework, study uses fuzzy AHP-PROMETHEE to prioritise LSS barriers and solution approaches. Incorporating fuzzy sets in analytical hierarchy process (AHP) ensures the optimality of barrier weights. Whereas, preference ranking organisation method for enrichment of evaluations (PROMETHEE) helps in pairwise comparisons of solution approaches with respect to each LSS barrier, facilitating fair judgements. This research guides regarding the development of framework and checks its suitability and robustness through case application of an Indian manufacturing organisation. Authors expect that researchers and practitioners will find study useful for LSS and multi criteria decision making(MCDM) domains.     

An application of the integrated AHP-PGP model for performance measurement of supply chain management

The performance measurement problem has gained great attention in business and operations management literature. The first objective of this study is to determine the required performance measures and to develop a model for performance evaluation, based on these selected measures using analytical hierarchy process (AHP) methodology. The second objective is to explain how an integrated AHP-PGP (pre-emptive goal programming) model can be used in performance measurement while optimising the overall performance. An integration of AHP and multi-objective PGP is used to consider both quantitative and qualitative performance measures in optimising the overall performance of the system. The integrated model is presented with a real-world application using source data provided by a survey conducted in India. Findings demonstrate that the integrated AHP-PGP model can be useful to all supply chain industries in their day-to-day performance measurement decisions.     

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.     

基于层次分析法在价值链分析中的应用研究

竞争者价值链之间的差异是竞争优势的一个关键来源,但是竞争价值链分析大多停留在定性分析阶段,只是提出了分析思路和模式,在定量化分析方面尚未有较为深入的进展。层次分析法是解决这类问题的行之有效的方法,本文尝试将层次分析法引入价值链分析中,通过对不同企业价值链活动的分析,得出竞争优势的优先排序,作为企业并购的决策依据。研究表明,本方法对企业并购的决策分析是比较有意义的。     

Incorporating cost and environmental factors in quality function deployment using data envelopment analysis

Quality function deployment (QFD) is an important tool available to organizations for efficient product design and development. Traditionally, QFD rates the design requirements (DRs) with respect to customer needs, and aggregates the ratings to get relative importance scores of DRs. An increasing number of studies stress on the need to incorporate additional factors, such as cost and environmental impact, while calculating the relative importance of DRs. However, there is a paucity of methodologies for deriving the relative importance of DRs when several additional factors are considered. In this paper, data envelopment analysis (DEA) is suggested for the purpose. It is proved that the relative importance values computed by DEA coincide with traditional QFD calculations when only the ratings of DRs with respect to customer needs are considered, and when only one additional factor, namely cost, is considered. DEA provides a general framework facilitating QFD computations when more factors need to be considered. The calculations are explained using a step-by-step procedure and illustrations. The proposed QFD–DEA methodology is applied to the design of security fasteners for a Chinese company. Though traditional QFD calculations consider the ratings as cardinal numbers, DEA has the flexibility to treat the ratings as qualitative variables. This aspect is illustrated in a separate section.     

Using data envelopment analysis for the assessment of technical efficiency of units with different specialisations: An application to agriculture

In this paper we consider the use of data envelopment analysis (DEA) for the assessment of efficiency of units whose output profiles exhibit specialisation. An example of this is found in agriculture where a large number of different crops may be produced in a particular region, but only a few farms actually produce each particular crop. Because of the large number of outputs, the use of conventional DEA models in such applications results in a poor efficiency discrimination. We overcome this problem by specifying production trade-offs between different outputs, relying on the methodology of Podinovski (J Oper Res Soc 2004;55:1311–22). The main idea of our approach is to relate various outputs to the production of the main output. We illustrate this methodology by an application of DEA involving agricultural farms in different regions of Turkey. An integral part of this application is the elicitation of expert judgements in order to formulate the required production trade-offs. Their use in DEA models results in a significant improvement of the efficiency discrimination. The proposed methodology should also be of interest to other applications of DEA where units may exhibit specialization, such as applications involving hospitals or bank branches.     

Upper Confidence Limits on Excess Risk for Quantitative Responses

The definition and observation of clear-cut adverse health effects for continuous (quantitative) responses, such as altered body weights or organ weights, are difficult propositions. Thus, methods of risk assessment commonly used for binary (quantal) toxic responses such as cancer are not directly applicable. In this paper, two methods for calculating upper confidence limits on excess risk for quantitative toxic effects are proposed, based on a particular definition of an adverse quantitative response. The methods are illustrated with data from a dose-response study, and their performance is evaluated with a Monte Carlo simulation study.     

基于可变权重的DEA效率评价模型

传统DEA模型将投入、产出权重视为固定变量。为了更合理地对决策单元的效率进行评价,本文研究了如何将有关投入、产出变量的权重的更多信息融入效率评价模型,提出了可变权重的概念,给出了一种基于可变权重的DEA效率评价模型。本文模型是CCR模型的推广。在有关权重信息可得的前提下,本文模型较之CCR模型中效率评价上更为合理。但是,如何准确度量投入、产出权重并将其函数化,是本文方法应用的难点。一个算例分析演示了本文模型。     

DEA博弈模型的分析与发展

数据包络分析(Data Envelopment Analysis,DEA)与博弈论之间关系密切.传统DEA模型忽略了决策单元(Decision Making Units,DMUs)之间的竞合关系,对权重的限制过于宽松,难以合理评价DMU效率值.为此,将博弈论方法引入至DEA模型,开展DEA的博弈研究,既是对DEA理论的重大发展,也将极大拓宽博弈论的应用研究.本文分三个阶段对现有的DEA博弈研究进行述评:(1)DEA的博弈论解释;(2)DEA Game模型及其应用;(3)DEA效率博弈;在深入分析重点模型基础上,总结其发展脉络,促进DEA理论与实践的发展.     

具有双重角色和非期望要素的供应商评价两阶段DEA模型

在基于DEA方法的供应商评价过程中,会出现供应商同时具有双重角色要素和非期望输出要素的情形。文章提出了一个处理双重角色要素的新思路,认为DEA模型中双重角色要素同时扮演了输入和输出两个角色,所有双重角色要素本质上就是网络DEA模型中的中间变量,并同时认为包含双重角色要素的生产系统一定能分解成为多个子系统,其中的双重角色要素既是一个子系统的输入,同时又是另一个子系统的输出。为测度供应商的效率,基于已有关系型两阶段DEA模型,将供应商的生产运营视为两阶段过程,其双重角色要素视为两阶段过程的中间变量,并通过将所有输出以加权和的形式表达,但对非期望输出用负的权重的方式,提出了一个具有双重角色和非期望输出要素的供应商评价两阶段DEA模型,最后用一个实例验证了方法的可行。     

城市商业银行的定量内控评价研究

鉴于目前城市商业银行内控评价方法的缺陷,按照综合评价的思路,本文采用层次分析法进行改进.实证表明改进方法有助于综合评价指标系统化和权重确定合理化.     

Dependence Assessment in Human Reliability Analysis Using Evidence Theory and AHP

Dependence assessment among human errors in human reliability analysis (HRA) is an important issue. Many of the dependence assessment methods in HRA rely heavily on the expert's opinion, thus are subjective and may sometimes cause inconsistency. In this article, we propose a computational model based on the Dempster‐Shafer evidence theory (DSET) and the analytic hierarchy process (AHP) method to handle dependence in HRA. First, dependence influencing factors among human tasks are identified and the weights of the factors are determined by experts using the AHP method. Second, judgment on each factor is given by the analyst referring to anchors and linguistic labels. Third, the judgments are represented as basic belief assignments (BBAs) and are integrated into a fused BBA by weighted average combination in DSET. Finally, the CHEP is calculated based on the fused BBA. The proposed model can deal with ambiguity and the degree of confidence in the judgments, and is able to reduce the subjectivity and improve the consistency in the evaluation process.