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Fuzzy Stochastic data envelopment analysis with application to NATO enlargement problem. (English) Zbl 1431.90102

Summary: Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision making units (DMUs) with multiple deterministic inputs and multiple outputs. However, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, decision makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Hence, we formulate a new DEA model to deal with fuzzy stochastic DEA models. The contributions of the present study are fivefold: (1) We formulate a deterministic linear model according to the probability-possibility approach for solving input-oriented fuzzy stochastic DEA model, (2) In contrast to the existing approach, which is infeasible for some threshold values; the proposed approach is feasible for all threshold values, (3) We apply the cross-efficiency technique to increase the discrimination power of the proposed fuzzy stochastic DEA model and to rank the efficient DMUs, (4) We solve two numerical examples to illustrate the proposed approach and to describe the effects of threshold values on the efficiency results, and (5) We present a pilot study for the NATO enlargement problem to demonstrate the applicability of the proposed model.

MSC:

90C15 Stochastic programming
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] N. Aghayi, M. Tavana and M.A. Raayatpanah, Robust efficiency measurement with common set of weights under varying degrees of conservatism and data uncertainty. Eur. J. Ind. Eng. 10 (2016) 385-405. · doi:10.1504/EJIE.2016.076386
[2] M.E. Bruni, D. Conforti, P. Beraldi and E. Tundis, Probabilistically constrained models for efficiency and dominance in DEA. Int. J. Prod. Econ. 117 (2009) 219-228. · doi:10.1016/j.ijpe.2008.10.011
[3] A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decisionmaking units. Eur. J. Oper. Res. 2 (1978) 429-444. · Zbl 0416.90080 · doi:10.1016/0377-2217(78)90138-8
[4] C.B. Chen and C.M. Klein, A simple approach to ranking a group of aggregated fuzzy utilities. IEEE Trans. Syst. Man Cyber. Part B: Cyber. 27 (1997) 26-35. · doi:10.1109/3477.552183
[5] W.W. Cooper, H. Deng, Z.M. Huang and S.X. Li, Chance constrained programming approaches to congestion in stochastic data envelopment analysis. Eur. J. Oper. Res. 155 (2004) 487-501. · Zbl 1043.90038 · doi:10.1016/S0377-2217(02)00901-3
[6] W.W. Cooper, Z.M. Huang, V. Lelas, S.X. Li and O.B. Olesen, Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. J. Prod. Anal. 9 (1998) 530-579. · doi:10.1023/A:1018320430249
[7] D. Dubois and H. Prade, Fuzzy Sets and Systems, Theorey and Applications. Academic Press, New York, NY (1980). · Zbl 0444.94049
[8] R. Farnoosh, R. Khanjani and A. Chaji, Stochastic FDH model with various returns to scale assumptions in data envelopment analysis. J. Adv. Res. Appl. Math. 3 (2011) 21-32. · doi:10.5373/jaram.759.020111
[9] X. Feng and Y.K. Liu, Measurability criteria for fuzzy random vectors. Fuzzy Optim. Decis. Making. 5 (2006) 245-253. · Zbl 1141.28300 · doi:10.1007/s10700-006-0013-0
[10] P. Guo and H. Tanaka, Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst. 119 (2001) 149-160. · doi:10.1016/S0165-0114(99)00106-2
[11] A. Hatami-Marbini, A. Emrouznejad and M. Tavana, A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. Eur. J. Oper. Res. 214 (2011) 457-472. · Zbl 1219.90199
[12] A. Hatami-Marbini, M. Tavana and A. Ebrahimi, A fully fuzzified data envelopment analysis model. Int. J. Inf. Decis. Sci. 3 (2011) 252-264.
[13] Z. Huang and S.X. Li, Dominance stochastic models in data envelopment analysis. Eur. J. Oper. Res. 95 (1996) 390-403. · Zbl 0943.90587 · doi:10.1016/0377-2217(95)00293-6
[14] C. Kao and S.T. Liu, Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst. 113 (2000) 427-437. · Zbl 0965.90025 · doi:10.1016/S0165-0114(98)00137-7
[15] R.K. Shiraz, M. Tavana and K. Paryab, Fuzzy free disposal hull models under possibility and credibility measures. Int. J. Data Anal. Tech. Strat. 6 (2014) 286-306. · doi:10.1504/IJDATS.2014.063072
[16] R.K. Shiraz, V. Charles and L. Jalalzadeh, Fuzzy Rough DEA Model: a possibility and expected value approaches. Expert Syst. App. 41 (2014) 434-444. · doi:10.1016/j.eswa.2013.07.069
[17] H. Kwakernaak, Fuzzy random variables. Part I: definitions and theorems. Inf. Sci. 15 (1978) 1-29. · Zbl 0438.60004 · doi:10.1016/0020-0255(78)90019-1
[18] H. Kwakernaak, Fuzzy random variables. Part II: algorithms and examples for the discrete case. Inf. Sci. 17 (1979) 253-278. · Zbl 0438.60005 · doi:10.1016/0020-0255(79)90020-3
[19] K. Land, C.A.K. Lovell and S. Thore, Chance-constrained data envelopmentanalysis. Manage. Decis. Econ. 14 (1994) 541-554. · doi:10.1002/mde.4090140607
[20] S. Lertworasirikul, F. Shu-Cherng, J.A. Joines and H.L.W. Nuttle, Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst. 139 (2003) 379-394. · Zbl 1047.90080 · doi:10.1016/S0165-0114(02)00484-0
[21] S.X. Li, Stochastic models and variable returns to scales in data envelopment analysis. Eur. J. Oper. Res. 104 (1998) 532-548. · Zbl 0960.90508 · doi:10.1016/S0377-2217(97)00002-7
[22] B. Liu, Uncertainty Theory. Springer-Verlag, Berlin (2004). · Zbl 1072.28012 · doi:10.1007/978-3-540-39987-2
[23] B. Liu and Y.K. Liu, Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10 (2002) 445-450.
[24] Y. Liu and B. Liu, Fuzzy random variable: a scalar expected value operator. Fuzzy Optim. Decis. Making 2 (2003) 43-160. · Zbl 1436.60009
[25] E. Momeni, M. Tavana, H. Mirzagoltabar and S.M. Mirhedayatian, A new fuzzy network slacks-based DEA model for evaluating performance of supply chains with reverse logistics. J. Intell. Fuzzy Syst. 27 (2014) 793-804. · Zbl 1305.90068
[26] S.H. Nasseri, A. Ebrahimnejad and O. Gholami, Fuzzy stochastic data envelopment analysis with undesirable outputs and its application to banking industry. Int. J. Fuzzy Syst. 20 (2018) 534-548. · doi:10.1007/s40815-017-0367-1
[27] O.B. Olesen and N.C. Petersen, Chance constrained efficiency evaluation. Manage. Sci. 41 442-457. · Zbl 0833.90004 · doi:10.1287/mnsc.41.3.442
[28] O.B. Olesen and N.C. Petersen, Stochastic data envelopment analysis-a review. Eur. J. Oper. Res. 251 (2015) 2-21. · Zbl 1346.90595 · doi:10.1016/j.ejor.2015.07.058
[29] R. Parameshwaran, P.S.S. Srinivasan, M. Punniyamoorthy, S. Charunyanath and C. Ashwin, Integrating fuzzy analytical hierarchy process and data envelopment analysis for performance management in automobile repair shops. Eur. J. Ind. Eng. 3 (2009) 450-467. · doi:10.1504/EJIE.2009.027037
[30] K. Paryab, R. Khanjani Shiraz, L. Jalalzadeh and H. Fukuyama, Imprecise data envelopment analysis model with bifuzzy variables. J. Intell. Fuzzy Syst. 27 (2014) 37-48. · Zbl 1305.91108
[31] A. Payan, Common set of weights approach in fuzzy DEA with an application. J. Intell. Fuzzy Syst. 29 (2015) 187-194. · doi:10.3233/IFS-151586
[32] J. Puri and S.P. Yadav, A fuzzy DEA model with undesirable fuzzy outputs and its application. Expert Syst. App. 41 (2014) 6419-6432. · doi:10.1016/j.eswa.2014.04.013
[33] R. Qin and Y.K. Liu, Modeling data envelopment analysis by chance method in hybrid uncertain environments. Math. Comput. Simul. 80 (2010) 922-995. · Zbl 1185.62095 · doi:10.1016/j.matcom.2009.10.005
[34] S. Saati, A. Memariani and G.R. Jahanshahloo, Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy Optim. Decis. Making 1 (2002) 255-267. · Zbl 1091.90536 · doi:10.1023/A:1019648512614
[35] M. Sakawa, Fuzzy Sets and Interactive Multiobjective Optimization. Plenum Press, New York, NY (1993). · Zbl 0842.90070 · doi:10.1007/978-1-4899-1633-4
[36] J.K. Sengupta, A fuzzy systems approach in data envelopment analysis. Comput. Math. App. 24 (1992) 259-266. · Zbl 0765.90004
[37] R.K. Shiraz, M. Tavana and D. Di Caprio, Chance-constrained data envelopment analysis modeling with random-rough data. RAIRO: OR 52 (2018) 259-284. · Zbl 1397.90222 · doi:10.1051/ro/2016076
[38] M. Tavana, R. Khanjani Shiraz and A. Hatami-Marbini, A new chance-constrained DEA model with Birandom input and output data. J. Oper. Res. Soc. 65 (2014) 1824-1839. · doi:10.1057/jors.2013.157
[39] M. Tavana, R. Khanjani Shiraz, A. Hatami-Marbini, P.J. Agrell and P. Paryab, Fuzzy stochastic data envelopment analysis withapplication to base realignment and closure (BRAC). Expert Syst. App. 39 (2012) 12247-12259. · doi:10.1016/j.eswa.2012.04.049
[40] M. Tavana, R. Khanjani Shiraz, A. Hatami-Marbini, P.J. Agrell and P. Paryab, Chance-constrained DEA models with random fuzzy inputs and outputs. Knowl.-Based Syst. 52 (2013) 32-52. · doi:10.1016/j.knosys.2013.05.014
[41] E.G. Tsionas and E.N. Papadakis, A bayesian approach to statistical inference in stochastic DEA. Omega 38 (2010) 309-314. · doi:10.1016/j.omega.2009.02.003
[42] K.P. Triantis and O. Girod, A mathematical programming approach for measuring technical efficiency in a fuzzy environment. J. Prod. Anal. 10 (1998) 85-102. · doi:10.1023/A:1018350516517
[43] J.E. Tsolas and V. Charles, Incorporating risk into bank efficiency: a satisficing DEA approach to assess the Greek banking crisis. Expert Syst. Appl. 42 (2015) 3491-3500. · doi:10.1016/j.eswa.2014.12.033
[44] A. Udhayakumar, V. Charles and M. Kumar, Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems. Omega 39 (2011) 387-397. · doi:10.1016/j.omega.2010.09.002
[45] Y.M. Wang, Y. Luo and L. Liang, Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert Syst. App. 36 (2009) 5205-5211. · doi:10.1016/j.eswa.2008.06.102
[46] P. Wanke, C. Barros and A. Emrouznejad, A comparison between stochastic DEA and Fuzzy DEA approaches: revisiting efficiency in Angolan banks. RAIRO: OR 52 (2018) 285-303. · Zbl 1403.90440 · doi:10.1051/ro/2016065
[47] C. Wu, Y. Li, Q. Liu and K. Wang, A stochastic DEA model considering undesirable outputs with weak disposability. Math. Comput. Model. 58 (2013) 980-989. · doi:10.1016/j.mcm.2012.09.022
[48] H.J. Zimmermann, Fuzzy set theory and its applications. 2nd edn. Kluwer Academic Publishers, Dordrecht, The Netherlands (1996). · Zbl 0845.04006 · doi:10.1007/978-94-015-8702-0
[49] L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1 (1978) 3-28. · Zbl 0377.04002 · doi:10.1016/0165-0114(78)90029-5
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