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.
Accepté le :
DOI : 10.1051/ro/2018075
Mots-clés : Data envelopment analysis, fuzzy random variable, possibility—probability, ranking
@article{RO_2019__53_2_705_0, author = {Ebrahimnejad, Ali and Nasseri, Seyed Hadi and Gholami, Omid}, title = {Fuzzy stochastic {Data} {Envelopment} {Analysis} with application to {NATO} enlargement problem}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {705--721}, publisher = {EDP-Sciences}, volume = {53}, number = {2}, year = {2019}, doi = {10.1051/ro/2018075}, zbl = {1431.90102}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2018075/} }
TY - JOUR AU - Ebrahimnejad, Ali AU - Nasseri, Seyed Hadi AU - Gholami, Omid TI - Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 705 EP - 721 VL - 53 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2018075/ DO - 10.1051/ro/2018075 LA - en ID - RO_2019__53_2_705_0 ER -
%0 Journal Article %A Ebrahimnejad, Ali %A Nasseri, Seyed Hadi %A Gholami, Omid %T Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 705-721 %V 53 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018075/ %R 10.1051/ro/2018075 %G en %F RO_2019__53_2_705_0
Ebrahimnejad, Ali; Nasseri, Seyed Hadi; Gholami, Omid. Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 705-721. doi : 10.1051/ro/2018075. http://www.numdam.org/articles/10.1051/ro/2018075/
[1] Robust efficiency measurement with common set of weights under varying degrees of conservatism and data uncertainty. Eur. J. Ind. Eng. 10 (2016) 385–405.
, and ,[2] Probabilistically constrained models for efficiency and dominance in DEA. Int. J. Prod. Econ. 117 (2009) 219–228.
, , and ,[3] Measuring the efficiency of decisionmaking units. Eur. J. Oper. Res. 2 (1978) 429–444. | Zbl
, and ,[4] A simple approach to ranking a group of aggregated fuzzy utilities. IEEE Trans. Syst. Man Cyber. Part B: Cyber. 27 (1997) 26–35.
and ,[5] Chance constrained programming approaches to congestion in stochastic data envelopment analysis. Eur. J. Oper. Res. 155 (2004) 487–501. | Zbl
, , and ,[6] Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. J. Prod. Anal. 9 (1998) 530–579.
, , , and ,[7] Fuzzy Sets and Systems, Theorey and Applications. Academic Press, New York, NY (1980). | Zbl
and ,[8] Stochastic FDH model with various returns to scale assumptions in data envelopment analysis. J. Adv. Res. Appl. Math. 3 (2011) 21–32.
, and ,[9] Measurability criteria for fuzzy random vectors. Fuzzy Optim. Decis. Making. 5 (2006) 245–253. | Zbl
and ,[10] Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst. 119 (2001) 149–160.
and ,[11] 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
, and ,[12] A fully fuzzified data envelopment analysis model. Int. J. Inf. Decis. Sci. 3 (2011) 252–264.
, and ,[13] Dominance stochastic models in data envelopment analysis. Eur. J. Oper. Res. 95 (1996) 390–403. | Zbl
and ,[14] Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst. 113 (2000) 427–437. | Zbl
and ,[15] Fuzzy free disposal hull models under possibility and credibility measures. Int. J. Data Anal. Tech. Strat. 6 (2014) 286–306.
, and ,[16] Fuzzy Rough DEA Model: a possibility and expected value approaches. Expert Syst. App. 41 (2014) 434–444.
, and ,[17] Fuzzy random variables. Part I: definitions and theorems. Inf. Sci. 15 (1978) 1–29. | Zbl
,[18] Fuzzy random variables. Part II: algorithms and examples for the discrete case. Inf. Sci. 17 (1979) 253–278. | Zbl
,[19] Chance-constrained data envelopmentanalysis. Manage. Decis. Econ. 14 (1994) 541–554.
, and ,[20] Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst. 139 (2003) 379–394. | Zbl
, , and ,[21] Stochastic models and variable returns to scales in data envelopment analysis. Eur. J. Oper. Res. 104 (1998) 532–548. | Zbl
,[22] Uncertainty Theory. Springer-Verlag, Berlin (2004). | Zbl
,[23] Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10 (2002) 445–450.
and ,[24] Fuzzy random variable: a scalar expected value operator. Fuzzy Optim. Decis. Making 2 (2003) 43–160.
and ,[25] 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
, , and ,[26] Fuzzy stochastic data envelopment analysis with undesirable outputs and its application to banking industry. Int. J. Fuzzy Syst. 20 (2018) 534–548.
, and ,[27] Chance constrained efficiency evaluation. Manage. Sci. 41 442–457. | Zbl
and ,[28] Stochastic data envelopment analysis-a review. Eur. J. Oper. Res. 251 (2015) 2–21.
and ,[29] Integrating fuzzy analytical hierarchy process and data envelopment analysis for performance management in automobile repair shops. Eur. J. Ind. Eng. 3 (2009) 450–467.
, , , and ,[30] Imprecise data envelopment analysis model with bifuzzy variables. J. Intell. Fuzzy Syst. 27 (2014) 37–48. | Zbl
, , and ,[31] Common set of weights approach in fuzzy DEA with an application. J. Intell. Fuzzy Syst. 29 (2015) 187–194.
,[32] A fuzzy DEA model with undesirable fuzzy outputs and its application. Expert Syst. App. 41 (2014) 6419–6432.
and ,[33] Modeling data envelopment analysis by chance method in hybrid uncertain environments. Math. Comput. Simul. 80 (2010) 922–995. | Zbl
and ,[34] Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy Optim. Decis. Making 1 (2002) 255–267. | Zbl
, and ,[35] Fuzzy Sets and Interactive Multiobjective Optimization. Plenum Press, New York, NY (1993). | Zbl
,[36] A fuzzy systems approach in data envelopment analysis. Comput. Math. App. 24 (1992) 259–266. | Zbl
,[37] Chance-constrained data envelopment analysis modeling with random-rough data. RAIRO: OR 52 (2018) 259–284. | Zbl
, and ,[38] A new chance-constrained DEA model with Birandom input and output data. J. Oper. Res. Soc. 65 (2014) 1824–1839.
, and ,[39] Fuzzy stochastic data envelopment analysis withapplication to base realignment and closure (BRAC). Expert Syst. App. 39 (2012) 12247–12259.
, , , and ,[40] Chance-constrained DEA models with random fuzzy inputs and outputs. Knowl.-Based Syst. 52 (2013) 32–52.
, , , and ,[41] A bayesian approach to statistical inference in stochastic DEA. Omega 38 (2010) 309–314.
and ,[42] A mathematical programming approach for measuring technical efficiency in a fuzzy environment. J. Prod. Anal. 10 (1998) 85–102.
and ,[43] Incorporating risk into bank efficiency: a satisficing DEA approach to assess the Greek banking crisis. Expert Syst. Appl. 42 (2015) 3491–3500.
and ,[44] Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems. Omega 39 (2011) 387–397.
, and ,[45] Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert Syst. App. 36 (2009) 5205–5211.
, and ,[46] A comparison between stochastic DEA and Fuzzy DEA approaches: revisiting efficiency in Angolan banks. RAIRO: OR 52 (2018) 285–303. | Zbl
, and ,[47] A stochastic DEA model considering undesirable outputs with weak disposability. Math. Comput. Model. 58 (2013) 980–989.
, , and ,[48] Fuzzy set theory and its applications. 2nd edn. Kluwer Academic Publishers, Dordrecht, The Netherlands (1996). | Zbl
,[49] Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1 (1978) 3–28. | Zbl
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