基于证据推理的不确定多属性决策方法

针对基本属性权重的不确定性,以及基本属性与广义属性评价集的不一致性等问题,提出一种基于证据推理的不确定多属性决策方法,将证据推理算法推广到更一般的决策环境中.根据决策矩阵的信息熵客观地获得属性的权系数;而对于基本属性与广义属性评价集不一致的情况,则通过对基本属性分布评价的模糊化及模糊变换,合理地实现到广义分布评价的统一形式;最后应用证据推理算法得到整个方案集的排序.实例结果表明,该方法是可行的、有效的.     

多属性隐式变权决策分析方法

为克服多因素变权决策方法的内在缺陷,基于Belton 和Gear提出的B/G-AHP层次分析原理给出了一种隐含式的多属性变权决策建模思想,并运用该思想给出了一种多属性变权决策新方法。它相对于多因素变权决策方法具有三方面的比较优势。其一,依赖的变权偏好信息直接由决策者给出,因而能够克服决策分析者对决策结果的主观武断性影响,更好地反映决策者的真实偏好。其二,不会受到由因素的属性值转化为偏好值所额外引入的主观测度偏差的干扰。其三,对决策者主观判断可能存在的误差予以了旨在弱化其影响的优化控制。数值分析表明新方法拥有较好的变权能力,并且相对于已有方法能够给出更易为决策者所接受的评价结论,因而具有较好的应用有效性。     

基于灰色关联度求解指标权重的改进方法

针对决策过程中指标权重的确定问题,在分析现有权重确定方法不足的基础上,提出了一种基于灰色关联度求解指标权重的改进方法,并对其性质进行了研究。该方法是对决策者给出的主观权重经验判断矩阵进行充分挖掘,提取出一个公共比较权重数列,并建立一个简易的数学模型,使确定的权重同时反映主观程度和客观程度。算例分析说明了该改进方法的简单性与实用性。     

The use of OWA operator weights for cross-efficiency aggregation

Cross-efficiency evaluation is an effective way of ranking decision making units (DMUs) in data envelopment analysis (DEA). Existing approaches for cross-efficiency evaluation are mainly focused on the calculation of cross-efficiency matrix, but pay little attention to the aggregation of the efficiencies in the cross-efficiency matrix. The most widely used approach is to aggregate the efficiencies in each row or column in the cross-efficiency matrix with equal weights into an average cross-efficiency score for each DMU and view it as the overall performance measurement of the DMU. This paper focuses on the aggregation process of the efficiencies in the cross-efficiency matrix and proposes the use of ordered weighted averaging (OWA) operator weights for cross-efficiency aggregation. The use of OWA operator weights for cross-efficiency aggregation allows the decision maker (DM)’s optimism level towards the best relative efficiencies, characterized by an orness degree, to be taken into consideration in the final overall efficiency assessment and particularly in the selection of the best DMU.     

多属性相对变权决策模型及方法

为克服多因素变权决策方法以及多属性决策Choquet积分模型没有科学反映多属性决策过程中决策者点依赖偏好关联行为的技术缺陷,在借鉴摆幅置权方法和网络分析法技术要点的基础上,运用数据包络分析的相对评价思维,提出一种全新的评价与决策方法即多属性相对变权决策方法。相对于多因素变权决策方法,新方法可以直接反映决策者的点依赖偏好结构,从而可以克服前者在反映点依赖偏好关联行为上所存在的源于决策分析者的武断随意性;相对于多属性决策Choquet积分模型,新方法可以反映决策者的点依赖偏好关联行为,并且在多数实际决策场合可以较有效地规避Choquet积分模型在决策参数判断上的指数复杂性难题。案例应用验证表明：新方法可以给出与决策者关于偏好依赖关联定性看法及客观事实非常相符的选择结论,可以更好地反映决策者的具体偏好。     

基于κ-可加模糊测度的多属性决策分析

基于κ-可加模糊测度和 Choquet 积分理论,讨论基于关联的多属性决策分析问题的建模和求解.首先通过构建属性间的直接关联矩阵确定κ值;然后依据 Marichal 熵理论求解属性和属性集的权重;利用 Choquet 积分计算方案的综合评价值并以此对方案进行排序;最后给出算例验证上述理论和方法的合理性.     

目标导向层次分析方法

对含有抽象属性的多属性层次结构而言，层次分析法即AHP（包括DIS-AHP、ABS-AHP、IDE-AHP和SUP-AHP四种具体方法）会因比率比较基准缺失、权重内涵模糊不清或方案评价不保序而缺乏科学理性。为发展AHP，基于摆幅置权（SW）判断模式和多属性决策属性价值公度方法，首先给出了能为层次结构抽象属性上的SW判断提供支持的规约性多属性决策属性价值公度方法，然后由此并结合多属性价值理论给出了能够克服现有层次分析法内在缺陷的目标导向层次分析方法即ToAHP。相对于AHP，ToAHP在判断模式与权重内涵、方法建构的理论基础和相关假设检验、方案评价保序与其内在数理依据上具有明显的相对科学合理性。应用分析表明：在输入信息可比的条件下，ToAHP明显优于AHP的四种分析方法之中最具可信性的SUP-AHP方法。     

基于Mo-RVIKOR的混合多属性决策方法

针对复杂性和不确定性多属性决策问题，考虑定量和定性融合的属性形式，提出了模块化随机多准则妥协解排序法（Modular Random VlseKriterijumska Opti-mizacija I Kompromisno Resenje，Mo-RVIKOR），该方法无需将信息统一，就能处理多种信息形式存在的多属性决策问题。采用精确数、随机变量处理定量评价信息，用概率语义术语集处理定性评价信息；通过改进离差最大化法确定属性权重；根据Mo-RVIKOR对决策对象进行排序；最后以某公司C2B定制化服务质量评测项目为例，验证了所提方法的有效性。     

DEA game cross-efficiency approach to Olympic rankings

A number of studies have used data envelopment analysis (DEA) to evaluate the performance of the countries in Olympic games. While competition exists among the countries in Olympic games/rankings, all these DEA studies do not model competition among peer decision making units (DMUs) or countries. These DEA studies find a set of weights/multipliers that keep the efficiency scores of all DMUs at or below unity. Although cross efficiency goes a further step by providing an efficiency measure in terms of the best multiplier bundle for the unit and all the other DMUs, it is not always unique. This paper presents a new and modified DEA game cross-efficiency model where each DMU is viewed as a competitor via non-cooperative game. For each competing DMU, a multiplier bundle is determined that optimizes the efficiency score for that DMU, with the additional constraint that the resulting score should be at or above that DMU 's estimated best performance. The problem, of course, arises that we will not know this best performance score for the DMU under evaluation until the best performances of all other DMUs are known. To combat this “chicken and egg” phenomenon, an iterative approach leading to the Nash equilibrium is presented. The current paper provides a modified variable returns to scale (VRS) model that yields non-negative cross-efficiency scores. The approach is applied to the last six Summer Olympic Games. Our results may indicate that our game cross-efficiency model implicitly incorporates the relative importance of gold, silver and bronze medals without the need for specifying the exact assurance regions.     

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.     

交互式多属性群决策评价方法研究

针对多属性群决策中属性指标权重的确定,将群体看作由多个被评价且参与权重决策的独立成员组成,提出一种交互式迭代算法,以均等属性权重为起点进入迭代过程,每一次迭代在当前给定的权重参数下求解含参规划模型并计算得到新的权重参数。迭代过程终止于任一群成员在相邻两次迭代的参数权重下加权综合属性值的绝对差异控制在非阿基米德无穷小量以内,此时使用的参数权重即为各属性的最优权重。实际迭代计算过程以及属性指标权重由所有群体成员共同参与和决定,故可以认为最终优化和选择结果为绝大部分成员所接受并满意。通过一个算例以及一个关于研发项目选择的实例,说明该交互式群决策评价方法的可行性和有效性。     

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.     

Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.     

Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.     

基于Heronian平均算子的Pythagorean模糊不确定语言决策方法

针对评价信息为Pythagorean模糊不确定语言数、属性权重未知且属性间相互影响的多属性决策问题,提出一种基于灰色关联法和Heronian平均算子的决策方法。首先,提出Pythagorean模糊不确定语言Heronian平均（PFULHM）算子和Pythagorean模糊不确定语言几何Heronian平均（PFULGHM）算子,并证明其满足幂等性、单调性、有界性及可交换性。考虑到属性权重之间重要程度的差异,定义了Pythagorean模糊不确定语言加权Heronian平均（PFULWHM）算子和Pythagorean模糊不确定语言加权几何Heronian平均（PFULWGHM）算子。其次,将灰色关联法运用到Pythagorean模糊不确定语言环境中求解属性权重。最后,提出基于PFULWHM算子和PFULWGHM算子的决策方法,并通过算例分析说明本文提出方法的有效性。     

基于证据推理和广义Shapley值的扩展概率语言多属性群决策方法

扩展概率语言词集通过语言变量概率分布的调整能够转化为多种语言信息表示模型,是语言变量、不确定语言信息、扩展犹豫模糊语言词集、分布语言评估信息、概率语言词集等的一般化,具有较强的通用性和实用性,是处理不确定性信息的重要工具。鉴于此,本文针对扩展概率语言环境下的多属性群决策问题,提出基于证据推理和广义Shapley值的多属性群决策方法。首先,提出扩展概率语言词集的定义和相关基础理论。其次,将广义Shapley值和证据推理相结合用于专家信息融合,并将广义Shapley值和TODIM方法相结合用于备选方案排序。再次,提出基于灰色关联法的权重确定模型来处理专家/属性权重部分未知的情况。最后,以绿色供应商选择为例进行分析,通过对比分析验证所提方法的有效性和优越性。     

基于证据推理和前景理论的交叉效率排序方法研究

针对由交叉效率评价策略和交叉效率集结方法的多样性而造成评价结果不一致的问题,提出利用证据推理方法和前景理论,综合各个交叉效率评价策略的评价结果,实现对决策单元的统一评价。首先,分别将选用的交叉效率评价策略以及各个评价策略中的他评效率设置成一级指标和二级指标,依据算数平均和前景理论分别确定一、二级指标的权重;其次,依据他评效率确定二级指标置信度,利用证据推理方法将各个交叉效率评价策略的他评效率综合转换成决策单元被评价为有效的置信度。决策者可通过比较决策单元被识别为有效的置信度的大小来判断决策单元交叉效率的大小,进而实现对决策单元的排序;最后,通过案例验证和说明本文提出方法的有效性和实用性。     

群决策中基于二元语义的主客观权重集成方法

针对一类属性值和属性权重信息均以语言评价信息形式给出的多属性群决策问题,提出了一种基于二元语义信息处理的主客观属性权重集成方法.首先运用二元语义集成算子计算属性的主观权重,然后给出一种基于最小偏差的属性客观权重计算方法,该方法根据决策者给出的语言决策矩阵计算决策群体对属性判断的偏差,偏差越大,表明决策者对该属性评价意见的分歧越大,则应赋给该属性越小的权重值,以提高群体意见的一致性.在此基础上,对属性的主、客观权重信息进行集成,得到属性综合权重.最后通过算例说明了该方法的有效性和实用性.     

Evaluating the administrative efficiency of courts

In addition to being held accountable for judicial decision, courts, like other public agencies, can and should be evaluated in terms of their administrative efficiency. This paper illustrates how courts can be evaluated in terms of their relative administrative efficiency, using a new approach—data envelopment analysis (DEA)—first proposed by Charnes et al. [1]. The DEA is based upon the economic notion of Pareto optimality which states that a given decision making unit (DMU) is inefficient if some other DMU, or some combination of other DMUs, can produce at least the same amounts of all outputs with less of some resource input and not more of any other resource. Conversely a DMU is said to be efficient if the above is not possible. Charnes et al. [1] generalized the usual input/output ratio measure of efficiency for a given unit in terms of a fractional linear program with fractional constraints. In the case of courts, the efficiency of any particular court is calculated by forming the ratio of a weighted sum of outputs to a weighted sum of inputs, where the weights for both outputs and inputs are to be selected in a manner that calculates the Pareto-Koopmans efficiency of the court. This paper reviews the DEA method and illustrates its application to a data base for 100 criminal superior courts in North Carolina.     

一种新的基于双前沿面的交叉效率方法及其应用

本文将双前沿面效率评价的思想引入到传统交叉效率模型中，同时，针对双前沿面交叉效率方法中仁慈型和激进型交叉效率策略无法抉择，以及这两种交叉效率策略的应用范围有限的不足，提出了一种新的基于双前沿面的交叉效率方法。该方法的基本思想是选取一个理想决策单元和负理想决策单元，使用被评价决策单元的权重来计算理想决策单元和负理想决策单元的效率，并使被评价决策单元的效率尽可能接近理想解的效率，同时，尽可能远离负理想解的效率。根据该思想，分别在乐观前沿面和悲观前沿面下求解交叉效率值并进行集结，避免了由于前沿面的选择不同导致的差异以及决策者对仁慈型和激进型交叉效率策略进行抉择的困难。最后，将本文方法与现有方法进行对比分析，并将本文方法应用于我国东部地区10个省(直辖市)的创新效率评价中，以验证方法的有效性。