A Fuzzy Data Envelopment Analysis Approach based on Parametric Programming
AbstractIn this paper, a fuzzy version of original data envelopment models, CCR and BCC, is extended and its solution approach is developed. The basic idea of the proposed method is to transform the original DEA model to an equivalent linear parametric programming model, applying the notion of α-cuts. Then, a bi-objective model is constructed which its solution has determined the optimal range of decision making units efficiency. The proposed method can be used both for symmetric and asymmetric fuzzy numbers, while the feasibility of its solution for the original problem is guaranteed. The application of the proposed method is examined in two numerical examples and its results are compared with two current models of fuzzy DEA.
 Bellman R.E., Zadeh L.A., Decision making in a fuzzy environment, MANAGE. SCI. ISSN 0025-1909, 17 (4): 141-164, 1970.
 Bojadziev G., Bojadziev M.,Fuzzy sets, fuzzy logic, applications, World Scientific Publishing, Singapore, 1996.
 Charnes A., Cooper W.W., Programming with linear fractional functions, NAV. RES. LOG. ISSN 0894-069X, 9 (3-4): 181-186, 1962.
 Charnes A., Cooper W.W., Rhodes E., Measuring Efficiency of Decision Making Units, EUR. J. OPER. RES. ISSN 0377-2217, 2: 429-444, 1978.
 Chen C.B., Klein C.M., A simple approach to ranking a group of aggregated fuzzy utilities. IEEE. T. SYST. MAN. CY B. ISSN 1083-4419, 27 (1): 26-35, 1997.
 Coelli T.J., Prasada Rao D.S., O'Donnell C.J., Battese G.E., An Introduction to Efficiency and Productivity Analysis, 2nd edition, Springer, New York, 2005.
 Cook W.D., Seiford L.M., Data envelopment analysis (DEA) " thirty years on. EUR. J. OPER. RES. ISSN 0377-2217, 192 (1): 1-17, 2009.
 Cooper W.W., Seiford L.M., Tone K., Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References, and DEA-Solver Software, 2nd ed., Kluwer Academic Publishers, New York, 2006.
 Das S.K., Goswami A., Alam S.S., Multiple objective transportation problem with interval cost, source and destination parameters, EUR. J. OPER. RES. ISSN 0377-2217, 117 (1): 100-112, 1999.
 Dubois D., Prade H., Operations on fuzzy numbers. INT. J. SYST. SCI. ISSN 0020-7721, 9 (6): 613-626, 1978.
 Emrouznejad A., Parker B.R., Tavares G. Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA, SOCIO. ECON. PLAN. SCI. ISSN 0038-121, 42 (3): 151-157, 2008.
 Fare R., Zelenyuk V., On Farrell's Decomposition and aggregation. INT. J. BUS. ECON. ISSN 1607-0704, 4 (2): 167-171, 2005.
 Guo P. Fuzzy data envelopment analysis and its application to location problems, INFORM. SCIENCES. ISSN 0020-0255, 179 (6): 820-829, 2009.
 Hatami-Marbini A., Emrouznejad A., Tavana M., A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making, EUR. J. OPER. RES. ISSN 0377-2217, 214 (3): 457-472, 2011.
 Hirschey M., Managerial Economics, 12th ed., South Western Cengage Learning, Ohio, 2008.
 Ishibuchi H., Tanaka H., Multiobjective programming in optimization of the interval objective function, EUR. J. OPER. RES. ISSN 0377-2217, 48 (2): 219-225, 1990.
 Jain R., Decision-Making in the presence of fuzzy variables, IEEE. T. SYST. MAN. CY B. ISSN 1083-4419, 6 (10): 698-703, 1976.
 Kao C., Liu S.T., Fuzzy efficiency measures in data envelopment analysis, FUZZY. SET. SYST. ISSN 0165-0114, 113 (3): 427-437, 2000.
 Kumbhakar S.C., Knox Lovell C.A., Stochastic Frontier Analysis, Cambridge University Press, Cambridge, 2003.
 Lertworasirikul S., Fang S.C., Joines J.A., Nuttle H.L.W., Fuzzy data envelopment analysis (DEA): a possibility approach, FUZZY. SET. SYST., ISSN 0165-0114, 139 (2): 379-394, 2003.
 Lertworasirikul S., Fang S.C., Nuttle H.L.W., Joines J.A., Fuzzy BCC model for data envelopment analysis, FUZZY. OPTIM. DECIS. MA. ISSN 1568-4539, 2 (4): 337-358, 2003.
 Luban F., Measuring efficiency of a hierarchical organization with fuzzy DEA method, ECONOMIA. SERIA. MANAGEMENT., ISSN 1454-0320, 12 (1): 87-97, 2009.
 Moore R.E., Baker Kearfott R., Cloud M.J., Introduction to interval analysis, SIAM, Philadelphia, 2009.
 Ray S.C., Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research, first ed., Cambridge University Press, New York, 2004.
 Saati-Mohtadi S., Memariani A., Jahanshahloo G.R., Efficiency analysis and ranking of DMUs with fuzzy data, FUZZY. OPTIM. DECIS. MA., ISSN 1568-4539, 1 (3): 255-267, 2002.
 Sengupta J.K., Data envelopment analysis for efficiency measurement in the stochastic case, COMPUT. OPER. RES. ISSN 0305-0548, 14 (2): 117-129, 1987.
 Sengupta J.K., Measuring economic efficiency with stochastic input-output data, INT. J. SYST. SCI., ISSN 0020-7721, 20 (2): 203-213, 1989.
 Sengupta J.K., A fuzzy systems approach in data envelopment analysis, COMPUT. MATH. APPL. ISSN 0898-1221, 24 (8-9): 259-266, 1992.
 Siler W., Buckley J.J., Fuzzy expert systems and fuzzy reasoning, John Wiley and Sons, New Jersey, 2005.
 Wang C.H., Chuang C.C., Tsai C.C., A fuzzy DEA-neural approach to measuring design service performance in PCM projects, AUTOMAT. CONSTR., ISSN 0926-5805, 18 (5): 702-713, 2009.
 Zadeh L.A., Fuzzy Sets. INFORMATION AND CONTROL., ISSN 0019-9958, 8 (3): 338- 353, 1965.
 Zerafat Angiz M., Emrouznejad A., Mustafa A., Al-Eraqi A.S., Aggregating preference ranking with fuzzy data envelopment analysis, KNOWL-BASED SYST. ISSN 0950-7051, 23 (6): 512-519, 2010.
 Zimmermann H.J., Fuzzy sets theory and its application, forth ed., Kluwer Academic Publishers, Massachusetts, 2001.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.