存在保证域的模糊非径向偏好DEA模型——基于中科院24个研究所的实证分析

中国管理科学 ›› 2014, Vol. 22 ›› Issue (2): 75-84.

存在保证域的模糊非径向偏好DEA模型——基于中科院24个研究所的实证分析

周忠宝¹, 孙亮¹, 刘德彬¹, 马超群¹, 刘文斌^1,2

1. 湖南大学工商管理学院, 湖南长沙 410082;
2. Business School, University of KENT, KENT CT2 7PE

收稿日期:2011-12-15 修回日期:2012-11-07 出版日期:2014-02-20 发布日期:2014-02-18
基金资助:
国家杰出青年科学基金资助项目（70825006）；国家自然科学基金资助项目（71371067，70901024）；中国博士后科学基金资助

Fuzzy Non-radial DEA/PS Model with Assurance Regions——an Empirical Analysis based on 24 Institutes of CAS

ZHOU Zhong-bao¹, SUN Liang¹, LIU De-bin¹, MA Chao-qun¹, Liu Wen-bin^1,2

1. School of Business Administration, Hunan University, Changsha 410082, China;
2. Business School, University of KENT, KENT, CT2 7PE, England

Received:2011-12-15 Revised:2012-11-07 Online:2014-02-20 Published:2014-02-18

摘要/Abstract

摘要： 数据包络分析（DEA）是一种非参数化的方法，用于评价具有类似输入和输出的决策单元的效率。传统的非径向DEA模型假设输入和输出数据均为准确值，且对权重变量不加以限制，本文构建了存在保证域的模糊非径向偏好DEA模型，并给出了一种基于模糊数截集的模型求解方法，有效地解决了输入和输出全部或部分为模糊数的决策单元评价问题。最后给出了一个中科院研究所效率评价的实例说明了方法的有效性。

关键词: 模糊DEA, 非径向DEA, 偏好结构, 保证域, α截集

Abstract: Data Envelopment Analysis (DEA) is a non-parametric approach for performance assessment of a set of homogeneous Decision Making Units (DMUs), which use similar inputs to produce similar outputs. Crisp data are commonly used in non-radial DEA models. However, inputs and outputs have been observed imprecise in many applications. At the same time, multipliers must be maintained at given levels for the production mechanism to work in reality. In this paper, a fuzzy non-radial DEA/PS model is proposed, which can deal with fuzzy data and decision maker's preference. The lower and upper bounds of fuzzy efficiency scores at different levels are determined based on α cuts. The proposed model and algorithm are used to evaluate the performance of 24 institutes of Chinese Academy of Sciences in the end.

Key words: fuzzy DEA, non-radial DEA, preference structure, assurance regions, α-cut

中图分类号:

C934

周忠宝, 孙亮, 刘德彬, 马超群, 刘文斌. 存在保证域的模糊非径向偏好DEA模型——基于中科院24个研究所的实证分析[J]. 中国管理科学, 2014, 22(2): 75-84.

ZHOU Zhong-bao, SUN Liang, LIU De-bin, MA Chao-qun, Liu Wen-bin. Fuzzy Non-radial DEA/PS Model with Assurance Regions——an Empirical Analysis based on 24 Institutes of CAS[J]. Chinese Journal of Management Science, 2014, 22(2): 75-84.

参考文献

[1] Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units[J]. European Journal of Operational Research, 1978, 2(6): 429-444.
[2] Cooper W W, Seiford L M, Thanassaulis E, et al. DEA and its uses in different countries[J]. European Journal of Operational Research, 2004, 154: 337-344.
[3] Cook W D, Seiford L M. Data envelopment analysis (DEA) -Thirty years on[J]. European Journal of Operational Research, 2009, 192(1): 1-17.
[4] 孙立成, 周德群, 李群, 等. 基于非径向超效率DEA聚类模型的FEEEP系统协调发展[J]. 系统工程理论与实践, 2009, 29(7): 139-146.
[5] Cooper W W, Park K, Pastor J T. RAM: Range adjusted measure of inefficiency for use with additive models and relations to other models and measures in DEA[J]. Journal of Productivity Analysis, 1999, 11(1): 5-42.
[6] Tone K. A slacks-based measure of efficiency in data envelopment analysis[J]. European Journal of Operational Research, 2001, 130(3): 498-509.
[7] Zhu J. Data envelopment analysis with preference structure[J]. The Journal of the Operational Research Society, 1996, 47(1): 136-150.
[8] Sueyoshi T, Sekitani K. Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach[J]. European Journal of Operational Research, 2007, 176(3): 1918-1946.
[9] Zhou, Peng, Poh K L, Ang B W. A non-radial DEA approach to measuring environmental performance[J]. European Journal of Operational Research, 2007, 178(1): 1-9.
[10] Guo Pengjun, Tanaka H. Fuzzy DEA: A perceptual evaluation method[J]. Fuzzy Sets and Systems, 2001, 119(1): 149-160.
[11] Lertworasirikul S, Fang S C, Joines J A, et al. Fuzzy data envelopment analysis (DEA): A possibility approach[J]. Fuzzy Sets and Systems, 2003, 139(2): 379-394.
[12] Kao C, Liu S T. Fuzzy efficiency measures in data envelopment analysis[J]. Fuzzy Sets and Systems, 2000, 113(3): 427-437.
[13] 吴海平, 宣国良, 帅旭. 基于LR 模糊数的置信DEA 模型[J]. 系统工程理论与实践, 2003, (9): 28-34.
[14] 张茂勤, 李光金, 尚文娟. 基于Campos 指数的模糊DEA[J]. 系统工程理论与实践, 2004, (4): 41-48.
[15] 郭均鹏, 吴育华. 超效率DEA模型的区间扩展[J]. 中国管理科学, 2005, 13(2): 40-43.
[16] 王美强, 梁樑, 李勇军. 超效率DEA 模型的模糊扩展[J]. 中国管理科学, 2009, 17(2): 117-124.
[17] Triantis K. Fuzzy non-radial data envelopment analysis (DEA) measures of technical efficiency in support of an integrated performance measurement system[J]. International Journal of Automotive Technology and Management, 2003, 3: 328-353.
[18] Jahanshahloo G R, Soleimani-damaneh M, Nasrabadi E. Measure of efficiency in DEA with fuzzy input-output levels: A methodology for assessing, ranking and imposing of weights restrictions[J]. Applied Mathematics and Computation, 2004, 156(1): 175-187.
[19] Zerafat Angiz L M, Emrouznejad A, Mustafa A. Fuzzy assessment of performance of a decision making units using DEA: A non-radial approach[J]. Expert Systems with Applications, 2010, 37(7): 5153-5157.
[20] Thompson R G, Brinkmann E J, Dharmapala P S, et al. DEA/AR profit ratios and sensitivity of 100 large U.S. banks[J]. European Journal of Operational Research, 1997, 98(2): 213-229.
[21] Liu S T. A fuzzy DEA/AR approach to the selection of flexible manufacturing systems[J]. Computers & Industrial Engineering, 2008, 54(1): 66-76.
[22] Chen S M, Wang C H. Fuzzy risk analysis based on ranking fuzzy numbers using a-cuts, belief features and signal/noise ratios[J]. Expert Systems with Applications, 2009, 36(3): 5576-5581.
[23] Avkiran N K. Investigating technical and scale efficiencies of Australian Universities through data envelopment analysis[J]. Socio-Economic Planning Sciences, 2001, 35(1): 57-80.
[24] Johnes J. Data envelopment analysis and its application to the measurement of efficiency in higher education[J]. Economics of Education Review, 2006, 25(3): 273-288.
[25] Meng, Wei, Zhang Daqun, Qi Li, et al. Two-level DEA approaches in research evaluation[J]. Omega, 2008, 36(6): 950-957.
[26] Merton R K. Priorities in scientific discovery: A chapter in the sociology of science[J]. American Sociological Review, 1957, 22(6): 635-659.
[27] Worthington A C, Lee B L. Efficiency, technology and productivity in Australian universities 1998-2003[J]. Economics of Education Review, 2008. 27: 285-298.
[28] Glass J C, McCallion G, McKillop D G, et al. Implications of variant efficiency measures for policy evaluations in UK higher education[J]. Socio-Economic Planning Sciences, 2006, 40: 119-142.
[29] Abbott M, Doucouliagos C. The efficiency of Australian universities: A data envelopment analysis[J]. Economics of Education Review, 2003, 22(1): 89-97.
[30] 关忠诚, 许惠, 熊慧琴. 基于模糊的偏好DEA在科研机构评价中的应用[J]. 科研管理, 2007, 28(2): 9-14.
[31] Chen, S.J., C.L. Hwang, F.P. Hwang. Fuzzy multiple attribute decision making method and applications[M]. Berlin: Springer-Verlag, 1992.