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A cross-efficiency model based on super-efficiency for ranking units through the TOPSIS approach and its extension to the interval case. (English) Zbl 1219.90099

Math. Comput. Modelling 53, No. 9-10, 1946-1955 (2011); corrigendum 54, No. 11-12, 3210 (2011) .
Summary: One of the most important approaches for ranking decision-making units in data envelopment analysis is the cross-efficiency method. The main idea of cross-efficiency is to use data envelopment analysis in peer evaluation, instead of only a self evaluation. However, in the cross-efficiency method, optimal weights corresponding to evaluation of decision-making units may not be unique. In this research with modifying the cross-efficiency method we are going to overcome this problem. Then with regard to the changes and using the TOPSIS method we present a new super-efficient method to rank all decision-making units. Furthermore, we extend the proposed method to the case that data are intervals.

MSC:

90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90B50 Management decision making, including multiple objectives
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[1] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429-444 (1978) · Zbl 0416.90080
[2] Adler, N.; Friedman, L.; Sinuany-Stern, Z., Review of ranking methods in data envelopment analysis context, European Journal of Operational Research, 140, 249-265 (2002) · Zbl 1001.90048
[3] Sexton, T. R.; Silkman, R. H.; Hogan, H. J., Data envelopment analysis: critique and extensions, (Silkman, R. H., Measuring Efficiency: An Assessment of Data Envelopment Analysis (1986), Jossey-Bass: Jossey-Bass San Francisco, CA), 73-150
[4] Doyle, J.; Green, R., Efficiency and cross-efficiency in DEA: derivation, meanings and uses, Journal of the Operational Research Society, 567-578 (1994) · Zbl 0807.90016
[5] Liang, L.; Wu, J.; Cook, W. D.; Zhu, J., Alternative secondary goals in DEA cross-efficiency evaluation, International Journal of Production Economics, 113, 1025-1030 (2008)
[6] Jahanshahloo, G. R.; Hosseinzadeh Lotfi, F.; Davoodi, A. R., Extension of TOPSIS for decision-making problems with interval data: interval efficiency, Mathematical and Computer Modelling, 49, 1137-1142 (2009) · Zbl 1165.90498
[7] Sengupta, A.; Pal, T. K., On comparing interval numbers, European Journal of Operational Research, 127, 1, 28-43 (2000) · Zbl 0991.90080
[8] Delgado, M.; Vila, M. A.; Voxman, W., On a canonical representation of fuzzy numbers, Fuzzy Sets and Systems, 94, 1, 205-216 (1998) · Zbl 0922.04008
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