Document Type: Research Paper


1 Department of Mathematics, Islamic Azad University, Masjedsoleiman Branch, Iran

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


In this paper, we show that inverse Data Envelopment Analysis (DEA) models can be used to estimate output with fuzzy data for a Decision Making Unit (DMU) when some or all inputs are increased and deficiency level of the unit remains unchanged.


Main Subjects

[1] Banker R. D., Charnes A., Cooper W.W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management science, 30, 1078-1092, 1984.

[2]  Bazaraa  M. S., Jarvis J. J., and  Sherali H. D., Linear programming and network flows, John Wiley, New York, second edition 1990.

[3]  Charnes A., Cooper W.W. , and Rhodes E.,  Measuring the efficiency of decision making units, European Journal of Operational Research, 429-444, 1978.

[4] Charnes A., Cooper W.W., Lewin A.Y., and Seiford L.M., Data envelopment Analysis- Theory, Methodology and Applications, Kluwer Academic Publishers, Boston 1994.

[5] Joro R., Korhonen P., Wallenius J., Structural comparison of data envelopment analysis and multiple objective linear programming , Management science, 44(7), 926- 970, 1999.

[6] Joro R., Korhonen P., Zionts S., An interactive approach to improve estimates of value efficiency in data envelopment analysis, European Journal of operational research,149, 688-699, 2003.

[7] Klir G. J., Yuan B., Fuzzy sets and fuzzy logic: Theory and Applications, Prentice- Hall, India 2001.

[8] Maleki H. R., Tata M., Mashinchi M., Linear programming with fuzzy variables, Fuzzy sets and systems, 109 , 21-33, 2000.

[9] Wei Q., Zhang  L.J., and  Zhang X., An inverse DEA models for input/output estimate, European Journal of Operational Research 121(1), 151-163, 2000.

[10] Wong B. Y. H., Luque M., Yang J. B., Using interactive multi objective methods to solve DEA problems with value judgments, Computers and Operations research, 36, 623-636, 2009.

[11] Zimmermann H. J., Fuzzy set theory and its application, Kluwer Academic publishers, London 1996.