数据包络分析研究热点综述

数据包络分析是面向多输入多输出决策单元的有效性评估方法。在介绍数据包络分析的基本思想和模型基础之上,总结了近年来国内外的研究热点,包括两阶段DEA、效率排序DEA、随机DEA和相关扩展问题,旨在围绕以上研究热点,对DEA近年来的理论研究及其扩展模型进行梳理和分类。最后对数据包络分析进一步研究提出展望。     

基于模糊综合评判的M&S可信性评估研究*

为保证M&S可信性评估工作有效和成功地完成,构建了由影响因素、校核与验证（verification and validation, V&V）过程和可信性特性组成三维可信性信息空间,并以此为理论基础,以V&V过程模型为基本框架,综合分析可信性在V&V过程中不同阶段的评价标准,建立了M&S可信性评估模型;在分析了模糊综合评估模型的基础上,以某飞行视景仿真系统的设计与开发为例,进行可信性评估。应用实例表明,所建立的评估模型及采用的评估方法合理有效。     

基于T-S 模糊模型的采样数据网络控制系统H∞ 输出跟踪控制

研究具有采样数据的基于T-S (Takagi-Sugeno) 模糊模型网络控制系统H输出跟踪控制问题. 提出将采集器端数据采样周期、数据传输时滞和数据丢包转换为零阶保持器端数据更新周期, 在此基础上, 利用输入时滞法和PDC (Parallel distributed compensation) 技术, 建立网络环境下被控对象和参考模型合并的基于T-S 模糊模型的增广系统模型. 通过Lyapunov 方法, 并充分利用采样特性, 给出系统实现H输出跟踪的充分条件, 以及可靠模糊控制器的设计. 仿真结果表明所设计模糊控制器能够实现该类系统良好的跟踪.     

集成自编码与PCA的高炉多元铁水质量随机权神经网络建模

针对随机权神经网络（Random vector functional-link networks，RVFLNs）建模存在的过拟合和泛化能力差的问题，集成自编码（Autoencoder）和主成分分析（Principal component analysis，PCA）技术，提出一种新型的改进RVFLNs算法，即AE-P-RVFLNs算法，用于建立高炉多元铁水质量在线估计的NARX（Nonlinear autoregressive exogenous）模型.首先，为了尽可能挖掘实际复杂工业数据中的有用信息和充分揭示输入数据之间的内在关系，采用Autoencoder前馈随机网络技术训练建模输入数据，并将训练得到的输出权值作为后续RVFLNs的输入权值；然后，引入PCA技术对RVFLNs的高维隐层输出矩阵进行降维，避免隐层输出矩阵多重共线性问题，从而解决由于隐层节点过多导致模型过拟合的问题；最后，基于所提AE-P-RVFLNs算法建立某大型高炉多元铁水质量在线估计的NARX模型.工业实验和比较分析表明:采用本文算法建立的多元铁水质量在线估计模型可有效提高运算效率和估计精度，尤其是避免常规RVFLNs建模存在的过拟合问题.     

基于PCA和神经网络的农残含量预测模型研究

为提高快速检测农残含量的精度,针对建模数据特征发生明显变化的实际情况,提出了一种结合主成分分析（PCA）和神经网络的分段多模型方法。提取建模数据的前2个主成分作为模型的输入,分别使用主成分回归（PCR）和BP/RBF神经网络建立单一及分段多模型。通过计算模型验证集的输出总误差和误差百分比,对比模型检测精度。试验表明：与单一模型相比,利用神经网络建立的分段多模型可以显著降低农药含量的预测误差,使用BP和RBF网络建立的低浓度段模型的输出误差百分比分别为0.8%和0.4%,RBF网络效果更好。该方法可以在待测农药的较大浓度范围内实现定量检测,具有较强的实用性。     

基于过程输入输出变化关系的模糊建模方法

针对难以建立精确数学模型的复杂过程,提出一种基于过程输入输出数据变化关系的模糊建模方法。首先按过程输出随输入变量变化的程度对输入变量论域进行划分,在此基础上确定模糊模型的规则总数和前件参数;然后根据所建模糊模型可表示为一个前馈模糊神经网络,利用BP学习算法求得过程模糊模型的后件参数。仿真例子验证了模糊建模方法的有效性,同时表明所建模糊规则模型较好的泛化能力。     

局部车流模糊模型研究

随着车辆智能控制系统（AVCS）的研究开发,基础的局部车流特性研究变得十分迫切,针对车辆跟随传统车流跟驰理论存在许多的不足,文中分析了跟驰模型存在的问题,提出采用模糊模型来建立局部车流跟随模型,并针对以往未能解决的隐性知识问题,提出了采用输入-输出数据对来设计模糊规则,应用权重来解决规则冲突问题并简化规则库。最后通过实例验证了模糊模型较之跟驰模型的优势。     

神经模糊系统中模糊规则的优选

提出一种基于两级聚类算法的自组织神经模糊系统，该系统采用两级聚类算法（改进的最近邻域聚类算法和Gustafson-Kessel模糊聚类算法）对输入／输出数据进行模糊聚类，并由模糊聚类的划分熵确定最优划分，建立模糊模型，模型精度可由梯度下降法进一步提高。仿真结果表明，这种神经模糊系统具有结构简单、规则数少、学习速度快以及建模精度高等特点。     

模糊粗糙数据模型:一种数据分析的新方法

提出了一种数据分析的新方法——模糊粗糙数据模型（Fuzzy Rough Data Model,FRDM）.该方法采用动态自适应模糊聚类技术,将Kowalczyk方法中的粗糙数据模型（Rough Data Model,RDM）对输入数据空间的网格状“硬划分”转化为模糊划分,辨识输入数据空间中的模糊模式类,并通过定义各模糊模式类与决策类别之间的类型映射关系ftype：Ci→y,以及输入数据对各模式类分类规则的匹配度（Degree of Fulfillment,DoF（x））概念,建立起相应的FRDM模型.不同数据集的实验测试结果表明,与Kowalczyk的RDM方法相比,文中方法具有更好的数据概括能力、更强的噪声数据处理能力和更高的搜索效率.     

基于DEA交叉评价的模糊综合评价模型及其应用

借鉴数据包络分析(DEA)交叉评价的思想,首先将评价系统内的指标分为量化指标和非量化指标,在定义平均交叉效率、最小交叉效率和最大交叉效率概念的基础上,采用交叉评价方法对量化数据进行处理;然后对最小交叉效率值、平均交叉效率值和最大交叉效率值进行模糊化,模糊化之后将其作为模糊综合评价的指标与非量化指标一起进行二次评价,以建立基于DEA交叉评价的模糊综合评价模型;最后通过评价实例验证了所提出的模型在处理客观数据与主观因素并存的多属性决策中的客观性和全面性.     

Weight determination in the cross-efficiency evaluation

A neutral data envelopment analysis (DEA) model for cross-efficiency evaluation was recently proposed by Wang and Chin [Wang and Chin (2010b). A neutral DEA model for cross-efficiency evaluation and its extension. Expert Systems with Applications, 37(5), 3666–3675], which maximinimizes the relative efficiency of each output and effectively reduces the number of zero weights of outputs. Since a large number of zero weights may still exist among inputs, this paper proposes a simultaneously input- and output-oriented weight determination DEA model for the cross-efficiency evaluation. The new DEA model proves to reduce the number of zero weights for both inputs and outputs very significantly, as illustrated by numerical examples. The weights determined by the new DEA model are neutral, neither aggressive nor benevolent.     

Modeling fuzzy data envelopment analysis by parametric programming method

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiency of decision making units (DMUs) consuming the same types of inputs and producing the same types of outputs. This paper studies the DEA models with type-2 data variations. In order to deal with the existed type-2 fuzziness, we propose the mean reduction methods for type-2 fuzzy variables. Based on the mean reductions of the type-2 fuzzy inputs and outputs, we formulate a new class of fuzzy generalized expectation DEA models. When the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we discuss the equivalent parametric forms for the constraints and the generalized expectation objective, where the parameters characterize the degree of uncertainty of the type-2 fuzzy coefficients so that the information cannot be lost via our reduction method. For any given parameters, the proposed model becomes nonlinear programming, which can be solved by standard optimization solvers. To illustrate the modeling idea and the efficiency of the proposed DEA model, we provide one numerical example.     

Sensitivity analysis of the additive model in data envelopment analysis while inputs and outputs are fuzzy data

Data envelopment analysis (DEA) requires input and output data to be precisely known. This is not always the case in real applications. Sensitivity analysis of the additive model in DEA is studied in this paper while inputs and outputs are symmetric triangular fuzzy numbers. Sufficient conditions for simultaneous change of all outputs and inputs of an efficient decision-making unit (DMU) which preserves efficiency are established. Two kinds of changes on inputs and outputs are considered. For the first state, changes are exerted on the core and margin of symmetric triangular fuzzy numbers so that the value of inputs increase and the value of outputs decrease. In the second state, a non-negative symmetric triangular fuzzy number is subtracted from outputs to decrease outputs and it is added to inputs to increase inputs. A numerical illustration is provided.     

Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC)

Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and outputs. Conventional DEA models assume that inputs and outputs are measured by exact values on a ratio scale. However, the observed values of the input and output data in real-world problems are often vague or random. Indeed, decision makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Several researchers have proposed various fuzzy methods for dealing with the ambiguous and random data in DEA. In this paper, we propose three fuzzy DEA models with respect to probability-possibility, probability-necessity and probability-credibility constraints. In addition to addressing the possibility, necessity and credibility constraints in the DEA model we also consider the probability constraints. A case study for the base realignment and closure (BRAC) decision process at the U.S. Department of Defense (DoD) is presented to illustrate the features and the applicability of the proposed models.     

A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector

Data envelopment analysis (DEA) is a linear programming based non-parametric technique for evaluating the relative efficiency of homogeneous decision making units (DMUs) on the basis of multiple inputs and multiple outputs. There exist radial and non-radial models in DEA. Radial models only deal with proportional changes of inputs/outputs and neglect the input/output slacks. On the other hand, non-radial models directly deal with the input/output slacks. The slack-based measure (SBM) model is a non-radial model in which the SBM efficiency can be decomposed into radial, scale and mix-efficiency. The mix-efficiency is a measure to estimate how well the set of inputs are used (or outputs are produced) together. The conventional mix-efficiency measure requires crisp data which may not always be available in real world applications. In real world problems, data may be imprecise or fuzzy. In this paper, we propose (i) a concept of fuzzy input mix-efficiency and evaluate the fuzzy input mix-efficiency using α – cut approach, (ii) a fuzzy correlation coefficient method using expected value approach which calculates the expected intervals and expected values of fuzzy correlation coefficients between fuzzy inputs and fuzzy outputs, and (iii) a new method for ranking the DMUs on the basis of fuzzy input mix-efficiency. The proposed approaches are then applied to the State Bank of Patiala in the Punjab state of India with districts as the DMUs.     

A comprehensive fuzzy DEA model for emerging market assessment and selection decisions

The changing economic conditions have challenged many financial institutions to search for more efficient and effective ways to assess emerging markets. Data envelopment analysis (DEA) is a widely used mathematical programming technique that compares the inputs and outputs of a set of homogenous decision making units (DMUs) by evaluating their relative efficiency. In the conventional DEA model, all the data are known precisely or given as crisp values. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. In addition, performance measurement in the conventional DEA method is based on the assumption that inputs should be minimized and outputs should be maximized. However, there are circumstances in real-world problems where some input variables should be maximized and/or some output variables should be minimized. Moreover, real-world problems often involve high-dimensional data with missing values. In this paper we present a comprehensive fuzzy DEA framework for solving performance evaluation problems with coexisting desirable input and undesirable output data in the presence of simultaneous input–output projection. The proposed framework is designed to handle high-dimensional data and missing values. A dimension-reduction method is used to improve the discrimination power of the DEA model and a preference ratio (PR) method is used to rank the interval efficiency scores in the resulting fuzzy environment. A real-life pilot study is presented to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms in assessing emerging markets for international banking.     

Modeling data envelopment analysis by chance method in hybrid uncertain environments

This article first presents several formulas of chance distributions for trapezoidal fuzzy random variables and their functions, then develops a new class of chance model (C-model for short) about data envelopment analysis (DEA) in fuzzy random environments, in which the inputs and outputs are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. Since the objective and constraint functions contain the chance of fuzzy random events, for general fuzzy random inputs and outputs, we suggest an approximation method to compute the chance. When the inputs and outputs are mutually independent trapezoidal fuzzy random variables, we can turn the chance constraints and the chance objective into their equivalent stochastic ones by applying the established formulas for the chance distributions. In the case when the inputs and the outputs are mutually independent trapezoidal fuzzy random vectors, the proposed C-model can be transformed to its equivalent stochastic programming one, in which the objective and the constraint functions include a number of standard normal distribution functions. To solve such an equivalent stochastic programming, we design a hybrid algorithm by integrating Monte Carlo (MC) simulation and genetic algorithm (GA), in which MC simulation is used to calculate standard normal distribution functions, and GA is used to solve the optimization problems. Finally, one numerical example is presented to demonstrate the proposed modeling idea and the efficiency in the proposed model.     

Application of centralised DEA approach to capital budgeting in Spanish ports

In this paper, we propose a number of non-radial, output-oriented, centralised DEA models to determine individual and collective output target levels, input slacks and input reallocations as well as additional inputs acquisitions under a capital budget constraint. The application of the proposed approach to the Spanish Port Agency is presented. The overall amount of inefficiency currently found in the system allows for the determination of potential total output increases ranging from 24% to 114% without additional resources. Considering inputs reallocation would allow for an additional 20% output expansion. The acquisition of additional input resources would make feasible to expand outputs further, to levels whose exact values monotonously depend on the capital budget considered.     

Data envelopment analysis of integer-valued inputs and outputs

This paper addresses DEA scenarios whose inputs and outputs are naturally restricted to take integer values. Conventional DEA models would project the DMU onto targets that generally do not respect such type of integrality constraints. Although integer-valued inputs and outputs can be considered as a special case of ordinal inputs and outputs, the use of that type of models has many drawbacks. In this paper a MILP DEA model that guarantees the required integrality of the computed targets is proposed.