A Fuzzy Data Envelopment Analysis Approach based on Parametric Programming

  • Seyed Hossein Razavi Hajiagha Institute for Trade Studies and Research
  • Hannan Amoozad Mahdiraji Kashan Branch, Islamic Azad University
  • Edmundas Kazimieras Zavadskas
  • Shide Sadat Hashemi Kashan Branch, Islamic Azad University

Abstract

In 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.

References

[1] Banker R.D., Charnes A., Cooper W.W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, MANAGE. SCI. ISSN 0025-1909, 30 (9): 1078- 1092, 1984.

[2] Bellman R.E., Zadeh L.A., Decision making in a fuzzy environment, MANAGE. SCI. ISSN 0025-1909, 17 (4): 141-164, 1970.

[3] Bojadziev G., Bojadziev M.,Fuzzy sets, fuzzy logic, applications, World Scientific Publishing, Singapore, 1996.
http://dx.doi.org/10.1142/2867

[4] Charnes A., Cooper W.W., Programming with linear fractional functions, NAV. RES. LOG. ISSN 0894-069X, 9 (3-4): 181-186, 1962.

[5] Charnes A., Cooper W.W., Rhodes E., Measuring Efficiency of Decision Making Units, EUR. J. OPER. RES. ISSN 0377-2217, 2: 429-444, 1978.

[6] 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.

[7] 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.

[8] 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.

[9] 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.

[10] 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.

[11] Dubois D., Prade H., Operations on fuzzy numbers. INT. J. SYST. SCI. ISSN 0020-7721, 9 (6): 613-626, 1978.

[12] 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.

[13] Fare R., Zelenyuk V., On Farrell's Decomposition and aggregation. INT. J. BUS. ECON. ISSN 1607-0704, 4 (2): 167-171, 2005.

[14] Guo P. Fuzzy data envelopment analysis and its application to location problems, INFORM. SCIENCES. ISSN 0020-0255, 179 (6): 820-829, 2009.

[15] 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.

[16] Hirschey M., Managerial Economics, 12th ed., South Western Cengage Learning, Ohio, 2008.

[17] 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.

[18] Jain R., Decision-Making in the presence of fuzzy variables, IEEE. T. SYST. MAN. CY B. ISSN 1083-4419, 6 (10): 698-703, 1976.

[19] Kao C., Liu S.T., Fuzzy efficiency measures in data envelopment analysis, FUZZY. SET. SYST. ISSN 0165-0114, 113 (3): 427-437, 2000.

[20] Kumbhakar S.C., Knox Lovell C.A., Stochastic Frontier Analysis, Cambridge University Press, Cambridge, 2003.

[21] 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.

[22] 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.

[23] Luban F., Measuring efficiency of a hierarchical organization with fuzzy DEA method, ECONOMIA. SERIA. MANAGEMENT., ISSN 1454-0320, 12 (1): 87-97, 2009.

[24] Moore R.E., Baker Kearfott R., Cloud M.J., Introduction to interval analysis, SIAM, Philadelphia, 2009.
http://dx.doi.org/10.1137/1.9780898717716

[25] Ray S.C., Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research, first ed., Cambridge University Press, New York, 2004.
http://dx.doi.org/10.1017/CBO9780511606731

[26] 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.

[27] Sengupta J.K., Data envelopment analysis for efficiency measurement in the stochastic case, COMPUT. OPER. RES. ISSN 0305-0548, 14 (2): 117-129, 1987.

[28] Sengupta J.K., Measuring economic efficiency with stochastic input-output data, INT. J. SYST. SCI., ISSN 0020-7721, 20 (2): 203-213, 1989.

[29] Sengupta J.K., A fuzzy systems approach in data envelopment analysis, COMPUT. MATH. APPL. ISSN 0898-1221, 24 (8-9): 259-266, 1992.

[30] Siler W., Buckley J.J., Fuzzy expert systems and fuzzy reasoning, John Wiley and Sons, New Jersey, 2005.

[31] 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.

[32] Zadeh L.A., Fuzzy Sets. INFORMATION AND CONTROL., ISSN 0019-9958, 8 (3): 338- 353, 1965.

[33] 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.

[34] Zimmermann H.J., Fuzzy sets theory and its application, forth ed., Kluwer Academic Publishers, Massachusetts, 2001.
Published
2013-08-01
How to Cite
RAZAVI HAJIAGHA, Seyed Hossein et al. A Fuzzy Data Envelopment Analysis Approach based on Parametric Programming. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 8, n. 4, p. 594-607, aug. 2013. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/580>. Date accessed: 08 july 2020. doi: https://doi.org/10.15837/ijccc.2013.4.580.

Keywords

Data envelopment analysis; Fuzzy numbers; α-cuts; Parametric programming