针对传统 DEA-Malmquist 生产率指数建立在精确数据基础之上, 缺乏对非精 确数据的分析与研究, 应用区间数来刻画投入产出数据的不确定性, 同时考虑决策单元 组间异质性、参考前沿面单一以及生产率不具可比性等问题, 建立了基于双前沿面数据 包络分析的区间全局 Meta-frontier Malmquist 指数, 并提出了一种基于可能度的考 虑决策者乐观水平的区间数排序方法. 将构建的理论应用于 2013--2016 年中国 30 个 省市的工业能源环境生产率的研究中. 结果表明: 1) 基于双前沿面研究视角下, 北京、安徽、贵州和云南的综合生产率提高了, 内蒙古、江西、河南、广西的综合生产率降低了. 2) 贵州的综合技术效率提高促进了其综合生产率指数的提升. 吉林的群组技术水平的提高促进了其共同前沿的技术效率水平的提高, 山东的群组技术水平和技术效率共同促进了其共同前沿的技术效率水平的提高. 3) 黑龙江和贵州的群组技术效率水平的提高促进了其共同前沿的技术效率水平的提高.

Because the conventional DEA-Malmquist productivity index supposes that the research data is precise and does not consider the fuzziness and uncertainties of research data, this paper uses the intervals to describe this fuzziness and uncertainties. To deal with the technology heterogeneity of decision making units, the biased technology frontier, and the incompatibility of productivity, this paper proposes to construct an interval global meta-frontier Malmquist index based on double frontier data envelopment analysis and introduces an interval ranking approach based on modified possibility degree, which considers the optimism degree of decision makers. The proposed interval global meta-frontier Malmquist index based on double frontier data envelopment analysis is employed to analyze the industrial energy and environment productivity of 30 regions in China during 2013--2016. It finds that: 1) From the double frontier's point of view, the comprehensive productivity of Beijing, Anhui, Guizhou and Yunnan all increases, while that of Inner Mongolia, Jiangxi, Henan and Guangxi decreases. 2) The improvement of Guizhou's comprehensive technical efficiency promotes its comprehensive productivity. The improved group technology level in Jilin makes its meta-frontier technical efficiency enhanced, while the meta-frontier technical efficiency of Shandong is promoted by its enhanced group technology progress and group technology efficiency. 3) The improvement of group technology efficiency in Heilongjiang and Guizhou pushes their meta-frontier technology efficiency enhanced.