Document Type : Research Paper


1 Department of Mathematics, Islamic Azad University, Arak Branch, Arak, Iran.

2 Department of Mathematics, Islamic Azad University, Science and Research, Tehran Branch, Tehran, Iran.


In many real applications, the data of production processes cannot be precisely measured. Hence the input and output of Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) may be imprecise or fuzzy-numbered. In original DEA models, inputs and outputs are measured by exact values on a ratio scale, therefore conventional DEA can't easily measure the performance of DMUs and rank them. The researchers have introduced mane deferent model for ranking DMUs by fuzzy number. In this paper, we proposed a new method by using the Tchebycheff norm for ranking DMUs with fuzzy data. We explain our method by numerical example with the triangular fuzzy number.


Main Subjects

[1]     Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management science39(10), 1261-1264.
[2]     Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science30(9), 1078-1092.
[3]     Duckstein, L. (1995). Fuzzy rule-based modeling with applications to geophysical, biological, and engineering systems (Vol. 8). CRC press.
[4]     Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research2(6), 429-444.
[5]     Cooper, W. W., Park, K. S., & Yu, G. (1999). IDEA and AR-IDEA: models for dealing with imprecise data in DEA. Management science45(4), 597-607.
[6]     Delgado, M., Vila, M. A., & Voxman, W. (1998). On a canonical representation of fuzzy numbers. Fuzzy sets and systems93(1), 125-135.
[7]     DuboisandH, D. (1988). Prade, possibility theory: an approach to computerized processing of uncertainty. New York, NY, USA: Plenum.
[8]     Goetschel Jr, R., & Voxman, W. (1986). Elementary fuzzy calculus. Fuzzy sets and systems18(1), 31-43.
[9]     Jahanshahloo. G. R., Hosseinzadeh Lotfi. F., Shahverdi, R., Adabitabar, M., Rostamy-Malkhalifeh, M., & Sohraiee, S. (2009) .Ranking DMUs by -norm with fuzzy data in DEA. Chaos, solitons and fractals, 39, 2294–2302.
[10]  Jahanshahloo, G. R., Lotfi, F. H., Shoja, N., Tohidi, G., & Razavyan, S. (2004). Ranking using l1-norm in data envelopment analysis. Applied mathematics and computation153(1), 215-224.
[11]  Kao, C., & Liu, S. T. (2000). Fuzzy efficiency measures in data envelopment analysis. Fuzzy sets and systems113(3), 427-437.
[12]  Mehrabian, S., Alirezaee, M. R., & Jahanshahloo, G. R. (1999). A complete efficiency ranking of decision making units in data envelopment analysis. Computational optimization and applications14(2), 261-266.
[13]  Balf, F. R., Rezai, H. Z., Jahanshahloo, G. R., & Lotfi, F. H. (2012). Ranking efficient DMUs using the Tchebycheff norm. Applied mathematical modelling36(1), 46-56.
[14]  Seaver, B. L., & Triantis, K. P. (1992). A fuzzy clustering approach used in evaluating technical efficiency measures in manufacturing. Journal of productivity analysis3(4), 337-363.
[15]  Seiford, L. M., & Zhu, J. (1999). Infeasibility of super-efficiency data envelopment analysis models. INFOR: information systems and operational research37(2), 174-187.
[16]  Sengupta, J. K. (1992). A fuzzy systems approach in data envelopment analysis. Computers & mathematics with applications24(8-9), 259-266.
[17]  Tavares, G., & Antunes, C. H. (2001). A Tchebycheff DEA model. Working Paper, Rutgers University, 640 Bartholomew Road, Piscataway, NJ 08854-8003.
[18]  Tran, L., & Duckstein, L. (2002). Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy sets and systems130(3), 331-341.
[19] Yao, J. S., & Wu, K. (2000). Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy sets and systems116(2), 275-288.
[20]  Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.