A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1445-1463.

Possibilistic programming approach is one of the most popular methods used to cope with epistemic uncertainty in optimization models. In this paper, several robust fuzzy data envelopment analysis (RFDEA) models are proposed by the use of different fuzzy measures including possibility, necessity and credibility measures. Despite the regular fuzzy DEA methods, the proposed models are able to endogenously adjust the confidence level of each constraints and produce both conservative and non-conservative methods based on various fuzzy measures. The developed RFDEA models are then linearized and numerically compared to regular fuzzy DEA models. Illustrative results in all of the FDEA and RFDEA models show that, maximum efficiency is obtained for possibility, credibility and necessity-based models, respectively.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2018019
Classification : 90C05, 28E10, 90C70
Mots-clés : Data envelopment analysis, fuzzy DEA, robust fuzzy DEA, robust optimization, uncertainty, possibility measure, necessity measure, credibility measure
Peykani, Pejman 1 ; Mohammadi, Emran 1 ; Pishvaee, Mir Saman 1 ; Rostamy-Malkhalifeh, Mohsen 1 ; Jabbarzadeh, Armin 1

1 
@article{RO_2018__52_4-5_1445_0,
     author = {Peykani, Pejman and Mohammadi, Emran and Pishvaee, Mir Saman and Rostamy-Malkhalifeh, Mohsen and Jabbarzadeh, Armin},
     title = {A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1445--1463},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {4-5},
     year = {2018},
     doi = {10.1051/ro/2018019},
     zbl = {1411.90361},
     mrnumber = {3884156},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2018019/}
}
TY  - JOUR
AU  - Peykani, Pejman
AU  - Mohammadi, Emran
AU  - Pishvaee, Mir Saman
AU  - Rostamy-Malkhalifeh, Mohsen
AU  - Jabbarzadeh, Armin
TI  - A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2018
SP  - 1445
EP  - 1463
VL  - 52
IS  - 4-5
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ro/2018019/
DO  - 10.1051/ro/2018019
LA  - en
ID  - RO_2018__52_4-5_1445_0
ER  - 
%0 Journal Article
%A Peykani, Pejman
%A Mohammadi, Emran
%A Pishvaee, Mir Saman
%A Rostamy-Malkhalifeh, Mohsen
%A Jabbarzadeh, Armin
%T A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2018
%P 1445-1463
%V 52
%N 4-5
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ro/2018019/
%R 10.1051/ro/2018019
%G en
%F RO_2018__52_4-5_1445_0
Peykani, Pejman; Mohammadi, Emran; Pishvaee, Mir Saman; Rostamy-Malkhalifeh, Mohsen; Jabbarzadeh, Armin. A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1445-1463. doi : 10.1051/ro/2018019. http://archive.numdam.org/articles/10.1051/ro/2018019/

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

[2] A. Charnes and W.W. Cooper, Chance-constrained programming. Manag. Sci. 6 (1959) 73–79. | DOI | MR | Zbl

[3] 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

[4] A. Charnes, W.W. Cooper, B. Golany, L. Seiford and J. Stutz, Foundations of data envelopment analysis for Pareto–Koopmans efficient empirical production functions. J. Econ. 30 (1985) 91–107. | DOI | MR | Zbl

[5] W.W. Cooper, Z. Huang and S.X. Li, Satisficing DEA models under chance constraints. Ann. Oper. Res. 66 (1996) 279–295. | DOI | MR | Zbl

[6] D. Dubois and H. Prade, Operations on fuzzy numbers. Int. J. Syst. Sci. 9 (1978) 613–626. | DOI | MR | Zbl

[7] D. Dubois and H. Prade, The mean value of a fuzzy number. Fuzzy Sets Syst. 24 (1987) 279–300. | DOI | MR | Zbl

[8] D. Dubois and H. Prade, Possibility Theory. Plenum Press, New York (1988). | MR | Zbl

[9] A. Emrouznejad and M. Tavana, Performance Measurement With Fuzzy Data Envelopment Analysis. Springer, Berlin and Heidelberg (2014). | DOI

[10] M.J. Farrell, The measurement of productive efficiency. J. R. Stat. Soc. A (Gen.) 120 (1957) 253–290. | DOI

[11] P.A. Garcia and R. Schirru, A fuzzy data envelopment analysis approach for FMEA. Prog. Nucl. Energy 46 (2005) 359–373. | DOI

[12] M.R. Ghasemi, J. Ignatius, S. Lozano, A. Emrouznejad and A. Hatami-Marbini, A fuzzy expected value approach under generalized data envelopment analysis. Knowl. Based Syst. 30 (2015) 148–159. | DOI

[13] P. Guo, H. Tanaka and M. Inuiguchi, Self-organizing fuzzy aggregation models to rank the objects with multiple attributes. IEEE Trans. Syst. Man Cybern. A: Syst. Hum. 30 (2000) 573–580. | DOI

[14] 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. | DOI | MR | Zbl

[15] A. Hatami-Marbini, P.J. Agrell, M. Tavana and A. Emrouznejad, A stepwise fuzzy linear programming model with possibility and necessity relations. J. Intel. Fuzzy Syst. 25 (2013) 81–93. | DOI | MR | Zbl

[16] S. Heilpern, The expected value of a fuzzy number. Fuzzy Sets Syst. 47 (1992) 81–86. | DOI | MR | Zbl

[17] F. Hossainzadeh, G.R. Jahanshahloo, M. Kodabakhshi and F. Moradi, A fuzzy chance constraint multi objective programming method in data envelopment analysis. Afr. J. Bus. Manag. 5 (2011) 12873.

[18] J. Ignatius, M.R. Ghasemi, F. Zhang, A. Emrouznejad and A. Hatami-Marbini, Carbon efficiency evaluation: an analytical framework using fuzzy DEA. Eur. J. Oper. Res. 253 (2016) 428–440. | DOI | MR | Zbl

[19] M. Inuiguchi and J. Ram"I"K, Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets Syst. 111 (2000) 3–28. | DOI | MR | Zbl

[20] N. Jiang and Y. Yang, A fuzzy chance-constrained DEA model based on Cr measure. Int. J. Bus. Manag. 2 (2007) 17–21.

[21] M. Khodabakhshi, Y. Gholami and H. Kheirollahi, An additive model approach for estimating returns to scale in imprecise data envelopment analysis. Appl. Math. Model. 34 (2010) 1247–1257. | DOI | MR | Zbl

[22] S. Lertworasirikul, Fuzzy Data Envelopment Analysis (DEA). Ph. D. Dissertation, Department of Industrial Engineering, North Carolina State University (2002).

[23] S. Lertworasirikul, S.C. Fang, J.A. Joines and H.L.W. Nuttle, A possibility approach to fuzzy data envelopment analysis, in Vol. 6 of Proceedings of the Joint Conference on Information Sciences, Duke University/Association for Intelligent Machinery, Durham, US (2002) 176–179.

[24] S. Lertworasirikul, S.C. Fang, J.A. Joines, H.L.W. Nuttle and J.A. Joines, Fuzzy data envelopment analysis, in Proceedings of the 9th Bellman Continuum, Beijing (2002) 342.

[25] S. Lertworasirikul, S.C. Fang, J.A. Joines and H.L.W. Nuttle, Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst. 139 (2003) 379–394. | DOI | MR | Zbl

[26] S. Lertworasirikul, S.C. Fang, J.A. Joines and H.L.W. Nuttle, Fuzzy data envelopment analysis: a credibility approach. Fuzzy Sets Based Heuristics for Optimization. Springer, Berlin, Heidelberg (2003) 141–158. | MR | Zbl

[27] S. Lertworasirikul, S.C. Fang, J.A. Joines, H.L.W. Nuttle and J.A. Joines, Fuzzy BCC model for data envelopment analysis. Fuzzy Optim. Decis. Mak. 2 (2003) 337–358. | DOI | MR | Zbl

[28] H.T. Lin, Personnel selection using analytic network process and fuzzy data envelopment analysis approaches. Comput. Ind. Eng. 59 (2010) 937–944. | DOI

[29] B. Liu, Dependent-chance programming with fuzzy decisions. IEEE Trans. Fuzzy Syst. 7 (1999) 354–360. | DOI

[30] B. Liu and K. Iwamura, Chance constrained programming with fuzzy parameters. Fuzzy Sets Syst. 94 (1998) 227–237. | DOI | MR | Zbl

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

[32] G.P. Mccormick, Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems. Math. Program. 10 (1976) 147–175. | DOI | MR | Zbl

[33] M.J. Naderi, M.S. Pishvaee and S.A. Torabi, Applications of fuzzy mathematical programming approaches in supply chain planning problems. Fuzzy Logic in its 50th Year. Springer International Publishing (2016) 369–402. | MR

[34] R. Nedeljković and D. Drenovac, Efficiency measurement of delivery post offices using fuzzy data envelopment analysis (possibility approach). Int. J. Traffic Transp. Eng. 2 (2012) 22–29.

[35] A. Payan and M. Shariff, Scrutiny Malmquist productivity index on fuzzy data by credibility theory with an application to social security organizations. J. Uncertain. Syst. 7 (2013) 36–49.

[36] M.S. Pishvaee, J. Razmi and S.A. Torabi, Robust possibilistic programming for socially responsible supply chain network design: a new approach. Fuzzy Sets Syst. 206 (2012) 1–20. | DOI | MR | Zbl

[37] M.S. Pishvaee, S.A. Torabi and J. Razmi, Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty. Comput. Ind. Eng. 62 (2012) 624–632. | DOI

[38] S. Ramezanzadeh, A. Memariani and S. Saati, Data envelopment analysis with fuzzy random inputs and outputs: a chance-constrained programming approach. Iran. J. Fuzzy Syst. 2 (2005) 21–29. | MR | Zbl

[39] J.L. Ruiz and I. Sirvent, Fuzzy cross-efficiency evaluation: a possibility approach. Fuzzy Optim. Decis. Mak. 16 (2017) 111-126. | MR

[40] Y.M. Wang and K.S. Chin, Fuzzy data envelopment analysis: a fuzzy expected value approach. Expert Syst. Appl. 38 (2011) 11678–11685. | DOI

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

[42] M. Wen and C. You, A Fuzzy Data Envelopment Analysis (DEA) Model With Credibility Measure. Technical report (2007).

[43] M. Wen,C. You and R. Kang, A new ranking method to fuzzy data envelopment analysis. Comput. Math. Appl. 59 (2010) 3398–3404. | MR | Zbl

[44] M. Wen, Z. Qin and R. Kang, Sensitivity and stability analysis in fuzzy data envelopment analysis. Fuzzy Optim. Decis. Mak. 10 (2011) 1–10. | DOI | Zbl

[45] D.D. Wu, Z. Yang and L. Liang, Efficiency analysis of cross-region bank branches using fuzzy data envelopment analysis. Appl. Math. Comput. 181 (2006) 271–281. | MR | Zbl

[46] R.R. Yager, A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24 (1981) 143–161. | DOI | MR | Zbl

[47] L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1 (1978) 3–28. | DOI | MR | Zbl

[48] M.L. Zerafat-Angiz, A. Emrouznejad and A. Mustafa, Fuzzy assessment of performance of a decision making units using DEA: a non-radial approach. Expert Syst. Appl. 37 (2010) 5153–5157. | DOI

[49] M.L. Zerafat-Angiz, A. Emrouznejad and A. Mustafa, Fuzzy data envelopment analysis: a discrete approach. Expert Syst. Appl. 39 (2012) 2263–2269. | DOI

[50] M.L. Zerafat-Angiz, M.K.M. Nawawi, R. Khalid, A. Mustafa, A. Emrouznejad, R. John and G. Kendall, Evaluating decision-making units under uncertainty using fuzzy multi-objective nonlinear programming. Inf. Syst. Oper. Res. 55 (2017) 1–15. | MR | Zbl

[51] X. Zhao and W. Yue, A multi-subsystem fuzzy DEA model with its application in mutual funds management companies’ competence evaluation. Proc. Comput. Sci. 1 (2010) 2469–2478. | DOI

Cité par Sources :