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Interval efficiency assessment using data envelopment analysis. (English) Zbl 1122.91339
Summary: This paper studies how to conduct efficiency assessment using data envelopment analysis (DEA) in interval and/or fuzzy input-output environments. A new pair of interval DEA models is constructed on the basis of interval arithmetic, which differs from the existing DEA models handling interval data in that the former is a linear CCR model without the need of extra variable alternations and uses a fixed and unified production frontier (i.e. the same constraint set) to measure the efficiencies of decision-making units (DMUs) with interval input and output data, while the latter is usually a nonlinear optimization problem with the need of extra variable alternations or scale transformations and utilizes variable production frontiers (i.e. different constraint sets) to measure interval efficiencies. Ordinal preference information and fuzzy data are converted into interval data through the estimation of permissible intervals and \(\alpha\)-level sets, respectively, and are incorporated into the interval DEA models. The proposed interval DEA models are developed for measuring the lower and upper bounds of the best relative efficiency of each DMU with interval input and output data, which are different from the interval formed by the worst and the best relative efficiencies of each DMU. A minimax regret-based approach (MRA) is introduced to compare and rank the efficiency intervals of DMUs. Two numerical examples are provided to show the applications of the proposed interval DEA models and the preference ranking approach.

MSC:
91B28 Finance etc. (MSC2000)
03E72 Theory of fuzzy sets, etc.
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[1] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision making units, European J. oper. res., 2, 429-444, (1978) · Zbl 0416.90080
[2] Cooper, W.W.; Park, K.S.; Yu, G., IDEA and AR-ideamodels for dealing with imprecise data in DEA, Management sci., 45, 597-607, (1999) · Zbl 1231.90289
[3] Cooper, W.W.; Park, K.S.; Yu, G., An illustrative application of IDEA (imprecise data envelopment analysis) to a Korean mobile telecommunication company, Oper. res., 49, 807-820, (2001) · Zbl 1163.90539
[4] Cooper, W.W.; Park, K.S.; Yu, G., IDEA (imprecise data envelopment analysis) with CMDs (column maximum decision making units), J. oper. res. soc., 52, 176-181, (2001) · Zbl 1131.90377
[5] Despotis, D.K.; Smirlis, Y.G., Data envelopment analysis with imprecise data, European J. oper. res., 140, 24-36, (2002) · Zbl 1030.90055
[6] Entani, T.; Maeda, Y.; Tanaka, H., Dual models of interval DEA and its extension to interval data, European J. oper. res., 136, 32-45, (2002) · Zbl 1087.90513
[7] Guo, P.; Tanaka, H., Fuzzy deaa perceptual evaluation method, Fuzzy sets and systems, 119, 149-160, (2001)
[8] M.S. Haghighat, E. Khorram, The maximum and minimum number of efficient units in DEA with interval data, Appl. Math. Comput. (2004), in press. · Zbl 1116.90380
[9] Jahanshahloo, G.R.; Hosseinzadeh Lofti, F.; Moradi, M., Sensitivity and stability analysis in DEA with interval data, Appl. math. comput., 156, 463-477, (2004) · Zbl 1090.90104
[10] Jahanshahloo, G.R.; Matin, R.K.; Vencheh, A.H., On return to scale of fully efficient DMUs in data envelopment analysis under interval data, Appl. math. comput., 154, 31-40, (2004) · Zbl 1146.90476
[11] Jahanshahloo, G.R.; Matin, R.K.; Vencheh, A.H., On FDH efficiency analysis with interval data, Appl. math. comput., 159, 47-55, (2004) · Zbl 1098.90042
[12] Kao, C.; Liu, S.T., Fuzzy efficiency measures in data envelopment analysis, Fuzzy sets and systems, 113, 427-437, (2000) · Zbl 0965.90025
[13] Kao, C.; Liu, S.T., A mathematical programming approach to fuzzy efficiency ranking, Internat. J. production econom., 86, 45-154, (2003)
[14] Kim, S.H.; Park, C.G.; Park, K.S., An application of data envelopment analysis in telephone offices evaluation with partial data, Comput. oper. res., 26, 59-72, (1999) · Zbl 0957.90084
[15] Lee, Y.K.; Park, K.S.; Kim, S.H., Identification of inefficiencies in an additive model based IDEA (imprecise data envelopment analysis), Comput. operat. res., 29, 1661-1676, (2002)
[16] León, T.; Liern, V.; Ruiz, J.L.; Sirvent, I., A fuzzy mathematical programming approach to the assessment of efficiency with DEA models, Fuzzy sets and systems, 139, 407-419, (2003) · Zbl 1044.90096
[17] Lertworasirikul, S.; Fang, S.C.; Joines, J.A.; Nuttle, H.L.W., Fuzzy data envelopment analysis (DEA)a possibility approach, Fuzzy sets and systems, 139, 379-394, (2003) · Zbl 1047.90080
[18] S. Saati, A. Memariani, Reducing weight flexibility in fuzzy DEA, Appl. Math. Comput. 161 (2005) 611-622. · Zbl 1084.62124
[19] Saati, S.; Memariani, A.; Jahanshahloo, G.R., Efficiency analysis and ranking of DMUs with fuzzy data, Fuzzy optim. decis. mak., 1, 255-267, (2002) · Zbl 1091.90536
[20] Sengupta, J.K., A fuzzy systems approach in data envelopment analysis, Comput. math. appl., 24, 259-266, (1992) · Zbl 0765.90004
[21] Triantis, K.; Girod, O., A mathematical programming approach for measuring technical efficiency in a fuzzy environment, J. productivity anal., 10, 85-102, (1998)
[22] Y.M. Wang, J.B. Yang, D.L. Xu, Two approaches for ranking interval numbers based on decision making under uncertainty, Decis. Support System, submitted for publication.
[23] Zhu, J., Imprecise data envelopment analysis (IDEA)a review and improvement with an application, European J. oper. res., 144, 513-529, (2003) · Zbl 1012.90013
[24] Zimmermann, H.J., Fuzzy set theory and its applications, (1991), Kluwer-Nijhoff Boston · Zbl 0719.04002
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