Fuzzy data envelopment analysis: A fuzzy expected value approach

Performance assessment often has to be conducted under uncertainty. This paper proposes a ''fuzzy expected value approach'' for data envelopment analysis (DEA) in which fuzzy inputs and fuzzy outputs are first weighted, respectively, and their expected values then used to measure the optimistic and pessimistic efficiencies of decision making units (DMUs) in fuzzy environments. The two efficiencies are finally geometrically averaged for the purposes of ranking and identifying the best performing DMU. The proposed fuzzy expected value approach and its resultant models are illustrated with three numerical examples, including the selection of a flexible manufacturing system (FMS).

[1]  Konstantinos Triantis,et al.  Fuzzy non-radial data envelopment analysis (DEA)measures of technical efficiency in support of an integrated performance measurement system , 2003 .

[2]  Jian-Bo Yang,et al.  Measuring the performances of decision-making units using geometric average efficiency , 2007, J. Oper. Res. Soc..

[3]  Abraham Charnes,et al.  Programming with linear fractional functionals , 1962 .

[4]  A. Memariani,et al.  Reducing weight flexibility in fuzzy DEA , 2005, Appl. Math. Comput..

[5]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[6]  Olivier A. Girod,et al.  A Mathematical Programming Approach for Measuring Technical Efficiency in a Fuzzy Environment , 1998 .

[7]  J. Sengupta.  A fuzzy systems approach in data envelopment analysis , 1992 .

[8]  Ebrahim Nasrabadi,et al.  Measure of efficiency in DEA with fuzzy input-output levels: a methodology for assessing, ranking and imposing of weights restrictions , 2004, Appl. Math. Comput..

[9]  Chiang Kao,et al.  Fuzzy efficiency measures in data envelopment analysis , 2000, Fuzzy Sets Syst..

[10]  Majid Soleimani-Damaneh,et al.  Computational and theoretical pitfalls in some current performance measurement techniques; and a new approach , 2006, Appl. Math. Comput..

[11]  José L. Verdegay.  Fuzzy Sets Based Heuristics for Optimization , 2010 .

[12]  C. Kao,et al.  A mathematical programming approach to fuzzy efficiency ranking , 2003 .

[13]  Shiang-Tai Liu,et al.  A fuzzy DEA/AR approach to the selection of flexible manufacturing systems , 2008, Comput. Ind. Eng..

[14]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[15]  Mohamed Dia.  A model of fuzzy data envelopment analysis , 2004 .

[16]  Toshiyuki Sueyoshi,et al.  A unified framework for the selection of a Flexible Manufacturing System , 1995 .

[17]  Peijun Guo,et al.  Fuzzy DEA: a perceptual evaluation method , 2001, Fuzzy Sets Syst..

[18]  Gholam Reza Jahanshahloo,et al.  Efficiency Analysis and Ranking of DMUs with Fuzzy Data , 2002, Fuzzy Optim. Decis. Mak..

[19]  Ying Luo,et al.  Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises , 2009, Expert Syst. Appl..

[20]  Chiang Kao,et al.  Data envelopment analysis with imprecise data: an application of taiwan machinery firms , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[21]  M. Wen,et al.  Fuzzy data envelopment analysis (DEA): Model and ranking method , 2009 .

[22]  Kwai-Sang Chin,et al.  A new approach for the selection of advanced manufacturing technologies: DEA with double frontiers , 2009 .

[23]  Desheng Dash Wu,et al.  Efficiency analysis of cross-region bank branches using fuzzy data envelopment analysis , 2006, Appl. Math. Comput..

[24]  Shiang-Tai Liu,et al.  Fuzzy efficiency measures in fuzzy DEA/AR with application to university libraries , 2009, Expert Syst. Appl..

[25]  Jian-Bo Yang,et al.  Interval efficiency assessment using data envelopment analysis , 2005, Fuzzy Sets Syst..

[26]  Tomoe Entani,et al.  Dual models of interval DEA and its extension to interval data , 2002, Eur. J. Oper. Res..

[27]  Chiang Kao,et al.  Data envelopment analysis with missing data: an application to University libraries in Taiwan , 2000, J. Oper. Res. Soc..

[28]  Teresa León,et al.  A fuzzy mathematical programming approach to the assessment of efficiency with DEA models , 2003, Fuzzy Sets Syst..

[29]  Shu-Cherng Fang,et al.  Fuzzy Data Envelopment Analysis: A Credibility Approach , 2003 .

[30]  Shu-Cherng Fang,et al.  Fuzzy data envelopment analysis (DEA): a possibility approach , 2003, Fuzzy Sets Syst..

[31]  P. F. Frutuoso e Melo,et al.  A fuzzy data envelopment analysis approach for FMEA , 2005 .

[32]  Shu-Cherng Fang,et al.  Fuzzy BCC Model for Data Envelopment Analysis , 2003, Fuzzy Optim. Decis. Mak..