Uncertain BCC Data Envelopment Analysis Model with Belief Degree: A case study in Iranian Banks
الموضوعات : مجله بین المللی ریاضیات صنعتی
M. Jamshidi
1
(
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Central Tehran, Iran.
)
M. Sanei
2
(
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Central Tehran, Iran.
)
A. Mahmoodirad
3
(
Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Iran.
)
G. Tohidi
4
(
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Central Tehran, Iran.
)
F. Hosseinzade Lotfi
5
(
Department of Mathematics, Science and Rsearch Branch, Islamic Azad University, Tehran, Iran.
)
الکلمات المفتاحية: BCC model, Iranian Banks, Data Envelopment Analysis, Belief degree, Uncertainty, uncertainty theory,
ملخص المقالة :
The BCC model is studied in this paper in an uncertain environment where uncertain inputs and outputs were belief degree-based uncertainty‚ useful for the cases for which no historical information of an uncertain event is available. As the solution method‚ the uncertain BCC model was converted to a crisp form using two approaches, separately. Finally, an applied example regarding the Iranian Banking system is presented to document the proposed models.
[1] A. I. Ali, L. M. Seiford, Translation Invariance in data envelopment analysis, Operations Research Letters 9 (1990) 403-405.
[2] R. D. Banker, A. Charnes, W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science 30 (1984) 1031-1142.
[3] R. D. Banker, Maximum likelihood consistency and data envelopment analysis: A statistical foundation, Management Science 39 (1993) 1265-1273.
[4] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research 2 (1978) 429-444.
[5] W. Chen, Y. Wang, P. Gupta, M. K. Mehlawat, A novel hybrid heuristic algorithm for a new uncertain mean-varianceskewness portfolio selection model with real constraints, Applied Intelligence 11 (2018) 1-23.
[6] W. W. Cooper, Z. Huang, V. Lelas, S. X. Li, O. B. Olesen, Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA, Journal of Productivity Analysis 9 (1998) 53-79.
[7] W. W. Cooper, K. S. Park, J. T. Pastor, RAM: a range adjusted measure of on efficiency for use with additive models and relations to other models and measures in DEA, Journal of Productivity Analysis 11 (1999) 5-24.
[8] W. W. Cooper, K. S. Park, G. Yu, Idea and AR-IDEA: models for dealing with imprecise data in DEA, Management Science 45 (1999) 597-607.
[9] W. W. Cooper, k. S. Park, G. Yu, An illustrative application of idea (imprecise data envelopment analysis) to Korean mobil telecommunication compant, Operations Research 49 (2001) 807-820.
[10] H. Dalman, Entropy-based multi-item solid transportation problems with uncertain variables, Soft Computing http://doi.org/10.1007/s00500-018-3255-1/.
[11] D. Deprins, L. Simar, H. Tulkens, Measuring labor efficiency in post offices. In: Marchand M. Pestieau P. Tulkens H. (Eds) The performance of public enterprises, Elsevier, Science Publishers Amesterdam (1984) pp. 243-267.
[12] T. Entan, Y. Maeda, H. Tanaka, Dual models of interval DEA and its extension to interval data, European Journal of Operational Research 136 (2002) 32-45.
[13] M. J. Farrell, The measurement of productive efficiency, Journal of the Royal Statistical Society A 120 (1957) 253-281.
[14] S. Grosskopf, Statistical inference and nonparametric efficiency: a selective survey, Journal of Productivity Analysis 7 (1996) 161-176.
[15] P. Guo, H. Tanaka, Fuzzy DEA: a perceptual evaluation method, Fuzzy Sets and System 119 (2001) 149-160.
[16] M. Jamshidi, M. Sanei, A. Mahmoodirad, F. Hoseinzadeh Lotfi, G. Tohidi, Uncertain RUSSEL data envelopment analysis model: A case study in Iranian banks, Journal of Intelligent & Fuzzy Systems 37 (2019) 2937-2951.
[17] C. Kao, S. Liu, Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets and Systems 113 (2000) 427-437.
[18] S. Lertworasirikul, S. Fang, J. A. Joines, H. L. W. Nuttle, Fuzzy data envelopment analysis (DEA): a possibility approach, Fuzzy Sets and Systems 139 (2003) 379-394.
[19] B. Liu, Uncertain Theory, Springer, Berlin 2nd edition, (2007).
[20] B. Liu, Some research problems in uncertainty theory, Journal of Uncertain System 3 (2009) 3-10.
[21] B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer, Berlin, (2010).
[22] B. Liu, Why is there a need for uncertainty theory, Journal of Uncertain Systems 6 (2012) 3-10.
[23] W. Lio, B. Liu, Uncertain data envelopment analysis with imprecisely observed inputs and outputs, Fuzzy Optimization and Decision Making 17 (2017) 357-373.
[24] W. Lio, B. Liu, Residual and confidence interval for uncertain regression model with imprecise observations, Journal of Intelligent & Fuzzy Systems, (2018), http://dx.doi.org/10.3233/JIFS-18353/.
[25] A. Mahmoodirad, R. Dehghan, S. Niroomand, Modelling linear fractional transportation problem in belief degree-based uncertain environment, Journal of Experimental & Theoretical Intelligence 31 (2019) 393-408.
[26] S. Majumder, P. Kundu, S. Kar, T. Pal, Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint, Soft Computing (2018).
[27] O. Olsen, N. C. Petersen, Chance constrained efficiency evaluation, Management Science 131 (1995) 442-457.
[28] T. Sueyosh, DEA non-parametric ranking test and index measurement: Slack-adjust DEA and an application to Japanese agriculture cooperative, Omega 27 (1999) 315-326.
[29] J. K. Sengupta, Efficiency measurement in stochastic input-output system, International Journal of Systems Science 13 (1982) 273-287.
[30] K. Tone, A slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research 130 (2001) 498-509.
[31] M. Wen, Z. Qin, R. Kang, Y. Yang, Sensitivity and stability analysis of the additive model in uncertain data envelopment analysis, Springer, Berlin, (2014).
[32] J. Zha, M. Bai, Mean-variance model for portfolio optimization with background risk based on uncertainty theory, International Journal of General Systems 47 (2018) 294-312.
