基于白化值的区间DEA建模  

Interval DEA Model Based on Whitening Value

作　　者：赵伟[1] 巩在武[1] 

机构地区：[1]南京信息工程大学经济管理学院,江苏南京210044

出　　处：《数学的实践与认识》2017年第6期78-86,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金"群体共识快速收敛:建模;实验及仿真分析研究"(71571104);江苏省自然科学基金"基于灰色灾变理论的气象灾害风险分析建模及方法研究"(BK20141481)

摘　　要：传统数据包络分析要求输入输出数据为精确数,然而在某些实际应用中,区间形式的数据相较于精确数更容易获得.将区间数转化为白化值,并基于传统C^2R模型提出了基于白化值的区间C^2R模型.考虑到决策单元的有效性不易通过基于白化值的区间C^2R模型来判断,因此将非阿基米德无穷小概念引入到上述模型,构建了具有非阿基米德无穷小的区间C^2R模型.此外,还给出了用于判断决策单元有效性的区间目标规划方法:分别通过G_(IC^2R)模型和WG_(IC^2R)模型判断决策单元是否为区间DEA有效与区间弱DEA有效.The conventional data envelopment analysis （DEA） requires the exact data of inputs and outputs. However, it is easier to obtain interval date rather than exact data practi- cally. Based on the conventional C2R model, an interval C2R model based on whitening value is constructed in this paper, where the interval can be converted to whitening value. Consid- ering the interval C2R model based on whitening value is difficult to judge the effectiveness of decision making units （DMUs）, so the concept of non-archimedes infinitesimal is introduced and then the interval C2R model with non-archimedes infinitesimal is built. Besides, a goal programming method is proposed to judge the effectiveness of DMUs： the GIc2R model can judge whether the decision making unit is interval DEA effective and the WG^c2R model can judge whether the decision making unit is interval weak DEA effective respectively.

关 键 词：区间DEA 白化值 区间C2R模型 有效性 非阿基米德无穷小 区间目标规划 

分 类 号：O221.1[理学—运筹学与控制论]