Fuzzy efficiency without convexity

In this paper we develop a fuzzy version of the crisp Free Disposal Hull (FDH) method for measuring technical efficiency for samples of similar production units. The FDH-method is basically Data Envelopment Analysis (DEA) without the underlying assumption of convexity of the technology set. Our approach builds directly upon the definition of Farrell’s indexes of technical efficiency used in crisp FDH. Therefore we do not require the use of fuzzy programming techniques but only utilize ranking probabilities of intervals as well as a related definition of dominance between pairs of intervals. We illustrate the approach using a data set of 200 Lithuanian family farms for the period of 2004–2009. © 2014 Elsevier B.V. All rights reserved.

[1]  Chiang Kao,et al.  Interval efficiency measures in data envelopment analysis with imprecise data , 2006, Eur. J. Oper. Res..

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

[3]  Y. Ku,et al.  Introduction to fuzzy arithmetic—theory and applications : Arnold Kaufmann and Madan M. Gupta. 351 pages, diagrams, figures. Van Nostrand Reinhold Company, New York, 1985. , 1986 .

[4]  Dorota Kuchta,et al.  Fuzzy pair-wise dominance and fuzzy indices: An evaluation of productive performance , 2003, Eur. J. Oper. Res..

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

[6]  P. Bogetoft,et al.  Benchmarking with DEA, SFA, and R , 2011 .

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

[8]  Adel Hatami-Marbini,et al.  A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making , 2011, Eur. J. Oper. Res..

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

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

[11]  W. Cooper,et al.  Idea and Ar-Idea: Models for Dealing with Imprecise Data in Dea , 1999 .

[12]  K. Triantis,et al.  Fuzzy Pair-wise Dominance and Implications for Technical Efficiency Performance Assessment , 1996 .

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

[14]  Jens Leth Hougaard,et al.  A simple approximation of productivity scores of fuzzy production plans , 2005, Fuzzy Sets Syst..

[15]  Henry Tulkens,et al.  On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts, and urban transit , 1993 .

[16]  Gholam Reza Jahanshahloo,et al.  On FDH efficiency analysis with interval data , 2004, Appl. Math. Comput..

[17]  W. Cooper,et al.  Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software , 1999 .

[18]  Caroline M. Eastman,et al.  Response: Introduction to fuzzy arithmetic: Theory and applications : Arnold Kaufmann and Madan M. Gupta, Van Nostrand Reinhold, New York, 1985 , 1987, Int. J. Approx. Reason..

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

[20]  Dominique Deprins,et al.  Measuring Labor-Efficiency in Post Offices , 2006 .

[21]  G. Debreu.  The Coefficient of Resource Utilization , 1951 .

[22]  Jens Leth Hougaard,et al.  Theory and Methodology Fuzzy scores of technical e ciency , 1999 .

[23]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .