Cross efficiency for fuzzy data envelopment analysis
Subject Areas : International Journal of Data Envelopment Analysis
Mehdi Amiri
1
,
Mohsen Rostamy-Malkhalifeh
2
,
Mohammad Reza Mozaffari
3
,
Tofigh Allahviranloo
4
1 -
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 -
4 -
Keywords: Cross efficiency, data envelopment analysis, fuzzy data,
Abstract :
Data envelopment analysis (DEA)is a non-parametric technique to measure the relative efficiencies of a set of decision making units(DMUs) with common crisp inputs and outputs. Ranking of DMUs is of great importance in DEA. One of the methods for ranking DMUs is to obtain cross efficiency. The cross efficiency method was developed as a DEA extension to rank DMUs with the main idea being to use DEA to do peer evaluation, rather than in pure self-evaluation mode. In this paper, we propose cross efficiency for DMUs with fuzzy data and use the efficiency scores to rank the fuzzy DMUs. We consider the input and output values as triangular fuzzy numbers. Our proposed model is based on input and output α-cuts. We then elaborate on the model with a numerical example
[1] Agarwal, S. (2010). Efficiency measure by
fuzzy data envelopment analysis model, IXX
International Conference: (IMST 2010-FIM XIX)
on Interdisciplinary Mathematical and Statistical
Techniques Held at Patna University, Patna, 18-20.
[2] Agarwal, S. Yadav, S.P. Singh, S.P.(2011). A
new slack DEA model to estimate the impact of
slacks on the efficiencies. International Journal of
Operations Research, 12(3), 241-256.
[3] Ammar, S. Wright, R. (2000). Applying fuzzy
set theory to performance evaluation, Socio-
Economic planning Sciences, 34(4), 285-302.
[4] Banker, R.D., Charnes, A., Cooper, W.W.
(1984). Some models for the estimation of
technical and scale inefficiencies in data
envelopment analysis, Management Science,
30(9), 1078-1092.
[5] Charnes, A., Cooper, W.W. (1962).
Programming with linear fractional functional,
Naval Research Logistics Quarterly, 9(3), 181-186.
[6] Charnes, A., Cooper, W.W. Rhodes, E. (1978).
Measuring the efficiency of decision making units,
European Journal of Operational Research, 2(6),
429-441.
[7] Chen, S.H. (1985). Ranking fuzzy numbers
with maximizing set and minimizing set. Fuzzy
Sets and Systems, 17(2), 113-129.
[8] Guo, P., Tanaka, H. (2001). Fuzzy DEA: A
Perceptual evaluation method. Fuzzy Sets and
Systems, 119(1), 149-160.
[9] Hougaard, J.L. (1999). Fuzzy scores of
technical efficiency. European Journal of
Operational Research, 115(3), 529-541.
[10] Tone, K. (2001). A slack based measure of
efficiency in data envelopment analysis. European
Journal of Operational Research, 130(3), 498-509.
[11] Wen, M., Li, H. (2009). Fuzzy data
envelopment analysis (DEA): Model and ranking
method. Journal of Computational and Applied
Mathematics, 223(2), 872-878.
[12] Zadeh, L.A. (1978). Fuzzy sets as a basis
for a theory of possibility. Fuzzy Sets and Systems,
1(1), 3-28.
[13] Zimmermann, H.J. (2001). Fuzzy sets
Theory and Its Applications, II edition, Kluwer-
Nijhoff, Boston.
