no. 4-5
Fuzzy integer-valued data envelopment analysis
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1429-1444.

In conventional data envelopment analysis (DEA) models, the efficiency of decision making units (DMUs) is evaluated while data are precise and continuous. Nevertheless, there are occasions in the real world that the performance of DMUs must be calculated in the presence of vague and integer-valued measures. Therefore, the current paper proposes fuzzy integer-valued data envelopment analysis (FIDEA) models to determine the efficiency of DMUs when fuzzy and integer-valued inputs and/or outputs might exist. To illustrate, fuzzy number ranking and graded mean integration representation methods are used to solve some integer-valued data envelopment analysis models in the presence of fuzzy inputs and outputs. Two examples are utilized to illustrate and clarify the proposed approaches. In the provided examples, two cases are discussed. In the first case, all data are as fuzzy and integer-valued measures while in the second case a subset of data is fuzzy and integer-valued. The results of the proposed models indicate that the efficiency scores are calculated correctly and the projections of fuzzy and integer factors are determined as integer values, while this issue has not been discussed in fuzzy DEA, and projections may be estimated as real-valued data.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2018015
Classification : 90C10, 90C70
Mots clés : Data envelopment analysis, efficiency, fuzzy data, integer values
Kordrostami, Sohrab 1 ; Amirteimoori, Alireza 1 ; Noveiri, Monireh Jahani Sayyad 1

1 
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     title = {Fuzzy integer-valued data envelopment analysis},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1429--1444},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {4-5},
     year = {2018},
     doi = {10.1051/ro/2018015},
     zbl = {1411.90226},
     mrnumber = {3884155},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2018015/}
}
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Kordrostami, Sohrab; Amirteimoori, Alireza; Noveiri, Monireh Jahani Sayyad. Fuzzy integer-valued data envelopment analysis. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1429-1444. doi : 10.1051/ro/2018015. http://archive.numdam.org/articles/10.1051/ro/2018015/

[1] A. Azadeh, M. Moghaddam, S.M. Asadzadeh and A. Negahban, An integrated fuzzy simulation-fuzzy data envelopment analysis algorithm for job-shop layout optimization: the case of injection process with ambiguous data. Eur. J. Oper. Res. 214 (2011) 768–779. | DOI | MR | Zbl

[2] A. Azadeh, M. Sheikhalishahi and S.M. Asadzadeh, A flexible neural network fuzzy data envelopment analysis approach for location optimization of solar plants with uncertainty and complexity. Renew. Energy 36 (2011) 3394–3401. | DOI

[3] M. Brunelli and J. Mezei, How different are ranking methods for fuzzy numbers? A numerical study. Int. J. Approx. Reason. 54 (2013) 627–639. | DOI | MR | Zbl

[4] 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

[5] 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. Ind. Eng. 79 (2015) 103–114. | DOI

[6] M. Ehrgott and J. Tind, Column generation with free replicability in DEA. Omega 37 (2009) 943–950. | DOI

[7] A. Emrouznejad and M. Tavana, Performance Measurement With Fuzzy Data Envelopment Analysis. Vol. 309 of Studies in Fuzzinessand Soft Computing. Springer-Verlag (2014). | DOI

[8] 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. 89 (2015) 148–159. | DOI

[9] P. Guo and H. Tanaka, Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst. 119 (2001) 149–160. | DOI | MR

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

[11] A. Hatami-Marbini, A. Emrouznejad and M. Tavana, A taxonomy and review of the fuzzy DEA literature: two decades in the making. Eur. J. Oper. Res. 214 (2011) 457–472. | DOI | MR | Zbl

[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] F. Herrera and J.L. Verdegay, Approaching fuzzy integer linear programming problems, in Interactive Fuzzy Optimization, edited by M. Fedrizzi, J. Kacprzyk and M. Roubens. Springer-Verlag, Berlin (1991). | DOI | Zbl

[14] F. Herrera and J.L. Verdegay, Three models of fuzzy integer linear programming. Eur. J. Oper. Res. 83 (1995) 581–593. | DOI | Zbl

[15] T. Jie, Q. Yan and W. Xu, A technical note on “A note on integer-valued radial model in DEA”. Comput. Ind. Eng. 87 (2015) 308–310. | DOI

[16] C. Kahraman, E. Tolga, Data envelopment analysis using fuzzy concept, 28th IEEE International Symposium on Multiple-Valued Logic, May 1998(1998) 338–343.

[17] C. Kao and S.T. Liu, A mathematical programming approach to fuzzy efficiency ranking. Int. J. Prod. Econ. 86 (2003) 145–154. | DOI

[18] R. Kazemi Matin and A. Emrouznejad, An integer-valued data envelopment analysis model with bounded outputs. Int. Trans. Oper. Res. 18 (2011) 741–749. | DOI | MR | Zbl

[19] R. Kazemi Matin and T. Kuosmanen, Theory of integer-valued data envelopment analysis under alternative returns to scale axioms. Omega 37 (2009) 988–995. | DOI

[20] D. Khezrimotlagh, S. Salleh and Z. Mohsenpour, A note on integer-valued radial model in DEA. Comput. Ind. Eng. 66 (2013) 199–200. | DOI

[21] S. Kordrostami, G. Farajpour and M. Jahani Sayyad Noveiri, Evaluating the efficiency and classifying the fuzzy data: a DEA-based approach. Int. J. Ind. Math. 6 (2014) 321–327.

[22] T. Kuosmanen and R. Kazemi Matin Theory of integer-valued data envelopment analysis. Eur. J. Oper. Res. 192 (2009) 658–667. | DOI | MR | Zbl

[23] Y.J. Lai and C.L. Hwang, Fuzzy Mathematical Programming. Springer-Verlag, NY (1992). | DOI | MR | Zbl

[24] Y.J. Lai and C.L. Hwang, A new approach to some possibilistic linear programming problems. Fuzzy Sets Syst. 49 (1992) 121–133. | DOI | MR

[25] T. Leon, V. Liern, J.L. Ruiz and I. Sirvent, A fuzzy mathematical programming approach to the assessment of efficiency with DEA models. Fuzzy Sets Syst. 139 (2003) 407–419. | DOI | MR | Zbl

[26] 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

[27] S. Lozano and G. Villa, Data envelopment analysis of integer-valued inputs and outputs. Comput. Oper. Res. 33 (2006) 3004–3014. | DOI | MR | Zbl

[28] Muren, Z. Ma and W. Cui, Fuzzy data envelopment analysis approach based on sample decision making units. J. Syst. Eng. Electron. 23 (2012) 399–407. | DOI

[29] J. Puri and S.P. Yadav, A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector. Expert Syst. Appl. 40 (2013) 1437–1450. | DOI

[30] R. Qin and Y-K. Liu, A new data envelopment analysis model with fuzzy random inputs and outputs. J. Appl. Math. Comput. 33 (2010) 327–356. | DOI | MR | Zbl

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

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

[33] J.K. Sengupta, Measuring efficiency by a fuzzy statistical approach. Fuzzy Sets Syst. 46 (1992) 73–80. | DOI

[34] M. Soleimani-Damaneh, Establishing the existence of a distance-based upper bound for a fuzzy DEA model using duality. Chaos Solitons Fractals 41 (2009) 485–490. | DOI | Zbl

[35] H. Tulkens, On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts, and urban transit. J. Prod. Anal. 4 (1993) 183–210. | DOI

[36] L.X. Wang, A Course in Fuzzy Systems and Control. Prentice-Hall, London, UK (1997). | Zbl

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

[38] G. Wang, Q. Nan and J. Li, Fuzzy integers and methods of constructing them to represent uncertain or imprecise integer information. Int. J. Innov. Comput. Inf. 11 (2015) 1483–1494.

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

[40] R.R. Yager, Ranking fuzzy subsets over the unit interval, in Proc. of 17th IEEE International Conference on Decision and Control, San Diego, CA (1979) 1435–1437. | Zbl

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

[42] L.M. Zerafat Angiz, A. Emrouznejad, A. Mustafa and A.S. Al-Eraqi. Aggregating preference ranking with fuzzy data envelopment analysis. Knowl. Based Syst. 23 (2010) 512–519. | DOI

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