随机模糊环境下的数据包络分析

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 well as the definitions of the DEA eficiency are given. Followed is the the mathematical properties of the DEA model, including the impact of the confidence level, sensitivity analysis and the equivalence class; (2) The sub-problems of DEA are presented, including fully ranking and congestion problems; (3) In order to solve the random fuzzy DEA models, we will design effective algorithms; (4) The random fuzzy DEA method will be applied to evaluate the efficiency of China's commercial banks.

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。

在使用DEA进行评价时，经常会遇到很多决策单元处于各种不确定性因素混合的环境之中，这种不确定性呈现出的不再是单一的随机性或模糊性，而是他们共同存在或是相互渗透相互影响的结果。项目组首次把随机模糊理论应用到数据包络分析，用随机模糊变量刻画决策单元的输入与输出，建立随机模糊环境下的数据包络分析评价方法，完成了既定的研究内容。建立随机模糊DEA模型，针对每种模型给出DEA有效的定义并证明定义的合理性；研究置信水平对模型的影响，分析得出模型的最优解是置信水平的递减函数；通过灵敏度分析，给出了决策单元保持原评价结果的最大范围；应用随机模糊理论证明模型的确定等价类，简化了模型的求解；给出了四种完全排序方法，并对每种方法的偏重进行了分析；通过过剩研究，给出了消除过剩的策略，提高效率；设计了融合随机模糊模拟、神经元网络和遗传算法的混合智能算法，对所设计算法进行有效性分析；初步将新模型应用于商业银行、设备选址及备件优化问题，评价结果比较理想。新方法适用的环境更广阔，处理的问题更广泛，既能处理客观不确定性（随机性），又能处理主观不确定性（模糊性），还能处理客观与主观同时存在的双重不确定性。在该项目的资助下，项目组在国际SCI检索的期刊Fuzzy Optimization and Decision Making、Soft Computing、Journal of Intelligent & Fuzzy Systems等发表论文7篇，在Springer出版英文专著一部。项目组成员积极参与国内外学术交流，包括：参加2014 the 10th International Conference on Reliability, Maintainability and Safety、RAMS 2015、2014 Prognostics and System Health Management Conference、the First International Conference on Reliability Systems Engineering、2013年中国运筹学会不确定系统年会等；访问香港中文大学系统工程与工程安全学院；邀请美国辛辛那提大学Dan Raluscu教授、香港中文大学龙卓瑜教授、日本早稻田大学的Mitsuo Gen教授访问学院，并做学术报告。