Modeling fuzzy data envelopment analysis under robust input and output data
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 619-643.

This paper offers a fuzzy optimization framework for data envelopment analysis (DEA) to evaluate the relative efficiency of decision making units (DMUs) with parametric interval-valued fuzzy variable-based inputs and outputs. The parametric interval-valued fuzzy variable-based inputs and outputs is employed to capture the uncertainty of data on the basis of professional judgements or empirical estimations. The DEA problem is formulated as fuzzy expectation model with credibility constraints. When the inputs and outputs are mutually independent parametric interval-valued triangular fuzzy variables, we investigate the parametric equivalent representations of expectation objective function and chance constraints. In order to find the optimal solution of our DEA model, a domain decomposition method is proposed. Finally, the numerical example on the sustainable supplier evaluation and selection problem is provided to demonstrate the efficiency of the proposed DEA model and domain decomposition method.

DOI : 10.1051/ro/2017038
Classification : 90C70, 91B16, 90C90
Mots-clés : Data envelopment analysis, fuzzy programming, parametric interval-valued fuzzy variable, lambda selection variable, domain decomposition method
Bai, Xuejie 1 ; Zhang, Feng 1 ; Liu, Yankui 1

1 
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     title = {Modeling fuzzy data envelopment analysis under robust input and output data},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {619--643},
     publisher = {EDP-Sciences},
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Bai, Xuejie; Zhang, Feng; Liu, Yankui. Modeling fuzzy data envelopment analysis under robust input and output data. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 619-643. doi : 10.1051/ro/2017038. http://archive.numdam.org/articles/10.1051/ro/2017038/

R. Azizi, R.K. Matin, and R.F. Saen, Ranking units and determining dominance relations in the cost efficiency analysis. RAIRO-Operations Res. 49 (2015) 879–896 | DOI | Numdam | MR | Zbl

A. Amirteimoori and A. Emrouznejad, Flexible measures in production process: A DEA-based approach. RAIRO-Oper. Res. 45 (2011) 63–74 | DOI | Numdam | MR | Zbl

R.D. Banker, A. Charnes and W.W. Cooper, Some models for estimating technical and scale efficiencies in data envelopment analysis. Manag. Sci. 30 (1984) 1078–1092 | DOI | Zbl

X. Bai and Y.K. Liu, Semideviations of reduced fuzzy variable: A possibility approach. Fuzzy Optimiz. Decision Making 13 (2014) 173–196 | DOI | MR | Zbl

X. Bai and Y.K. Liu, CVAR reduced fuzzy variables and their second order moments. Iranian J. Fuzzy Syst. 12 (2015) 45–75 | MR | Zbl

X. Bai, Optimization for pre-positioning emergency supplies problem under fuzzy environment. Syst. Eng. – Theory Practice 35 (2015) 1465–1473

X. Bai and Y.K. Liu, Robust optimization of supply chain network design in fuzzy decision system. J. Intel. Manufacturing 27 (2016) 1131–1149 | DOI

A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (1978) 429–444 | DOI | MR | Zbl

M. Dotoli, N. Epicoco, M. Falagario and F. Sciancalepore, A cross-efficiency fuzzy data envelopment analysis technique for performance evaluation of decision making units under uncertainty. Comput. Industrial Eng. 79 (2015) 103–114 | DOI

W.D. Cook and L.M. Seiford, Data envelopment analysis (DEA)–thirty years on. Eur. J. Operat. Res. 192 (2009) 1–17 | DOI | MR | Zbl

W.W. Cooper, K.S. Park and J.T. Pastor, Ram: A range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. J. Productivity Anal. 11 (1999) 5–24 | DOI

G. Egilmez, S. Gumus, M. Kucukvar and O. Tatari, A fuzzy data envelopment analysis framework for dealing with uncertainty impacts of input-output life cycle assessment models on eco-efficiency assessment. J. Cleaner Production 129 (2016) 622–636 | DOI

N.C. Petersen, Data envelopment analysis on a relaxed set of assumptions. Manag. Sci. 36 (1990) 305–313 | DOI | MR | Zbl

K. Tone, A slack-based measure of efficiency in data envelopment analysis. Eur. J. Oper. Res. 130 (2001) 498–509 | DOI | MR | Zbl

Y. Liu and Y.K. Liu, The lambda selections of parametric interval-valued fuzzy variables and their numerical characteristics. Fuzzy Optimiz. Decision Making 15 (2016) 255–279 | DOI | MR | Zbl

J.S. Liu, L.Y.Y. Lu, W.M. Lu and B.J.Y. Lin, A survey of DEA applications. Omega 41 (2013) 893–902 | DOI

J. Ignatius, M.R. Ghasemi, F. Zhang, A. Emrouznejad and A. Hatami−Marbini, Carbon efficiency evaluation: An analytical framework using fuzzy DEA. Europ. J. Operat. Res. 253 (2016) 428–440 | DOI | MR | Zbl

W.W. Cooper, L.M. Seiford and K. Tone, Data envelopment analysis. Springer Science and Business Media, New York (2007) | Zbl

C. Kao and S.T. Liu, Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets and Syst. 119 (2000) 149–160

J.S. Liu, L.Y.Y. Lu, W.M. Lu, and B.J.Y. Lin, Data envelopment analysis 1978–2010: A citation-based literature survey. Omega 41 (2013) 3–15 | DOI

J.S. Liu, L.Y.Y. Lu and W.M. Lu, Research fronts in data envelopment analysis. Omega 58 (2016) 33–45 | DOI

Z. Liu and Y.K. Liu, Type-2 fuzzy variables and their arithmetic. Soft Comput. 14 (2010) 729–747 | DOI | Zbl

B. Liu and Y. Liu, Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10 (2002) 445–450 | DOI

M.Q. Meng, A hybrid particle swarm optimization algorithm for satisficing data envelopment analysis under fuzzy chance constraints. Expert Syst. Appl. 41 (2014) 2074–2082 | DOI

Z. Muren, Ma and W. Cui, Generalized fuzzy data envelopment analysis methods. Appl. Soft Comput. 19 (2014) 215–225 | DOI

R. Qin, Y.K. Liu and Z. Liu, Modeling fuzzy data envelopment analysis by parametric programming method. Expert Syst. Appl. 38 (2011a) 8648–8663 | DOI

R. Qin, Y.K. Liu and Z. Liu, Methods of critical value reduction for type-2 fuzzy variables and their applications. J. Comput. Appl. Math. 235 (2011b) 1454–1481 | DOI | MR | Zbl

J.K. Sengupta, A fuzzy systems approach in data envelopment analysis. Comput. Math. Appl. 24 (1992) 259–266 | MR | Zbl

K. Triantis and O. Girod, A mathematical programming approach for measuring technical efficiency in a fuzzy environment. J. Productivity Anal. 10 (1998) 85–102 | DOI

X.Q. Feng, M.Q. Meng and Y.K. Liu, Modeling credibilistic data envelopment analysis under fuzzy input and output data. J. Uncertain Syst. 9 (2015) 230–240

P. Guo and H. Tanaka, Fuzzy Dea: A perceptual evaluation method. Fuzzy Sets Syst. 119 (2001) 149–160 | DOI | MR

M.R. Ghasemi, J. Ignatius, S. Lozano, A. Emrouznejad and A. Hatami−Marbini, A fuzzy expected value approach under generalized data envelopment analysis. Knowledge-Based Syst. 89 (2015) 148–159 | DOI

M.L. Wen and H.S. Li, Fuzzy data envelopment analysis (DEA): Model and ranking method. J. Comput. Appl. Math. 223 (2009) 872–878 | DOI | Zbl

M.L. Wen, Z.F. Qin and R. Kang, Sensitivity and stability analysis in fuzzy data envelopment analysis. Fuzzy Optimiz. Decision Making 10 (2011) 1–10 | DOI | Zbl

X. Wu and Y.K. Liu, Optimizing fuzzy portfolio selection problems by parametric quadratic programming. Fuzzy Optimiz. Decision Making 11 (2012) 411–449 | DOI | MR | Zbl

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