随机模糊环境下的数据包络分析

项目名称： 随机模糊环境下的数据包络分析

项目编号： No.71201005

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 管理科学与工程

项目作者： 文美林

作者单位： 北京航空航天大学

项目金额： 21万元

中文摘要： 数据包络分析（简称DEA）是一种被广泛使用的评价方法，但该方法对于数据很敏感，数据的扰动对评价结果影响重大，因而获取精确的数据是此方法的关键。实际上，由于生产过程复杂，很多数据难以精确测量，因此各种不确定性被引入DEA中，这其中主要包括客观不确定性（随机性）和主观不确定性（模糊性）。在很多情况，决策单元通常处于各种不确定性因素混合的环境之中，呈现出的不再是单一的随机性或模糊性，而是它们共同存在或是相互渗透、相互影响的结果。本项目拟把不确定性理论应用到DEA中，建立随机模糊环境下的DEA评价方法，新方法的提出可以使DEA有更广阔应用空间。研究内容：(1)建立随机模糊DEA模型，给出DEA有效的定义，并研究其数学性质，包括置信水平对模型的影响、灵敏度分析、模型的确定等价类；(2)研究随机模糊DEA的衍生子问题：完全排序和过剩问题；(3)设计有效的算法求解模型；(4)评估国内商业银行的效率问题。

中文关键词： 数据包络分析；DEA有效；随机模糊变量；不确定规划；智能算法

英文摘要： Data envelopment analysis (DEA) is a widely used evaluation method, but one of the most important shortcoming involves its sensitivity to data. Therefore, a key to the success of the DEA approach is the accurate measure of all factors, including inputs and outputs. In fact, such as in a manufacturing system, a production process or a service system, inputs and outputs are volatile and complex so that they are difficult to measure in an accurate way. Thus variety uncertainty is considered to deal with the variation of data in DEA, including subjective uncertainty (randomness) and objective uncertainty (fuzziness). However, in many situations, the decision making units are evaluated in mixed uncertainty environment rather than a single random or fuzzy environment. In these cases, the randomness and fuzziness co-exist and mutual influence. Thus this proposal intends to apply uncertainty theory which is a branch of axionatic mathematics for human uncertainty to DEA and establish a DEA evaluation method under random fuzzy environment. The new method can deal with the evaluation of more complex objects in broader applied fields, which makes DEA have a wider application space. This proposal contributes to the research area of random fuzzy DEA in the following aspects: (1) Some random fuzzy DEA models are proposed as we

英文关键词： Data Envelopment Analysis；DEA Efficiency；Random Fuzzy Variable；Uncertain Programming；Intelligent Algorithm