In this paper, we develop a novel fuzzy data envelopment analysis (DEA) model, using fuzzy Choquet integral as an aggregating tool to evaluate the efficiencies of the decision making units (DMUs). The proposed model can be used to evaluate the fuzzy efficiency of the DMU with interactive fuzzy variables (fuzzy inputs or fuzzy outputs), and meanwhile, a ranking method of the fuzzy efficiency is introduced. At the end of the paper, we will use numerical examples to illustrate the performance of the proposed model.
CharnesA., CooperW.W., RhodesE., Measuring the efficiency of decision making units, European Journal of Operational Research2 (6) (1978), 429–44.
2.
BankerR., CharnesA., CooperW.W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science30 (1984), 1078–1092.
3.
CharnesA., CooperW.W., GolanyB., SeifordL., StutzJ., Foundations of data envelopment analysis for pareto-koopmans efficient empirical production functions, Journal of Econometrics30 (1985), 91–107.
4.
BardhanI., BowlinW.F., CooperW.W., SueyoshiT., models and measures for efficiency dominance in DEA, Journal of the Operations Research39 (3) (1996), 333–344.
5.
CooperW.W., TimothyW.R., DengH., WuJ., ZhangZ., Are state-owned banks less efficient? A long-vs short-run data envelopment analysis of Chinese banks, International Journal of Operational Research3 (5) (2008), 533–556.
6.
KaoC., LiuS.-T., Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks, European Journal of Operational Research196 (1) (2009), 312–322.
7.
PuriJ., YadavS.P., A fully fuzzy DEA approach for cost and revenue efficiency measurements in the presence of undesirable outputs and its application to the banking sector in India, International Journal of Fuzzy Systems18 (2) (2016), 212–226.
8.
RayS.C., JeonY., Reputation and efficiency: A non-parametric assessment of America’s top-rated MBA programs, European Journal of Operational Research189 (1) (2008), 245–268.
9.
AbbasiA., ShariatmadariA., NaderiE., MoghaddasZ., Comparing performance of educational system of world’s continents: A fuzzy three-stage DEA model, International Mathematical Forum58 (5) (2010), 2885–2900.
10.
AncaraniA., Di MauroC. and GiammancoM.D., The impact of managerial and organizational aspects on hospital wards’ efficiency: Evidence from a case study, European Journal of Operational Research194 (1) (2009), 280–293.
11.
AryaA., YadavS.P., Development of FDEA models to measure the performance efficiencies of DMUs, International Journal of Fuzzy Systems (6) (2017), 1–11.
12.
YongmingH., .,Energy efficiency analysis method based on fuzzy DEA cross-model for ethylene production systems in chemical industry, 83 (2015), 685–695.
13.
SenguptaJ.K., A fuzzy systems approach in data envelopment analysis, Computers and Mathematics with Applications24 (8–9) (1992), 259–266.
14.
AgarwalS., Efficiency measure by fuzzydata envelopment analysis model, Fuzzy Information and Engineering and Systems6 (2014), 59–70.
15.
PuriJ., YadavS.P., A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking, Expert Systems with Applications40 (5) (2013), 1437–1450.
16.
Ashrafi and Mansouri KaleibarM., Cost, revenue and profit efficiency models in generalized fuzzy data envelopment analysis, Fuzzy Information and Engineering9 (2) (2017), 237–246.
17.
GuoP., TanakaH., Fuzzy DEA: A perceptual evaluation method, Fuzzy Sets and Systems119 (1) (2001), 149–160.
18.
LeónT., LiernV., RuizJ.L., SirventI., A fuzzy mathematical programming approach to the assessment of efficiency with DEA models, Fuzzy Sets and Systems139 (2) (2003), 407–419.
19.
GuoP., TanakaH., InuiguchiM., Self-organizing fuzzy aggregation models to rank the objects with multiple attributes, IEEE Transactions on Systems, Man and Cybernetics, Part A – Systems and Humans30 (5) (2000), 573–580.
20.
LertworasirikulS., Shu-CherngF., JoinesJ.A., NuttleH.L.W., Fuzzy data envelopment analysis (DEA): A possibility approach, Fuzzy Sets and Systems139 (2) (2003), 379–394.
21.
Muren, MaZ. and CuiW., Generalized fuzzy data envelopment analysis methods, Applied Soft Computing19 (2014), 215–225.
22.
MingqiangM., A hybrid particle swarm optimization algorithm for satisficing data envelopment analysis under fuzzy chance constraints, Expert Systems with Applications41 (2014), 2074–2082.
23.
TavanaM., ., Chance-constrained DEA models with random fuzzy inputs and outputs, Knowledge-Based Systems52 (2013), 32–52.
24.
AdlerN., GolanyB., Evaluation of deregulated airline networks using data envelopment analysis combined with principal component analysis with an application to Western Europe, European Journal of Operational Research132 (2) (2001), 18–31.
25.
AdlerN., GolanyB., Including principal component weights to improve discrimination in data envelopment analysis, Journal of the Operational Research Society53 (9) (2002), 985–991.
26.
AdlerN., YazhemskyE., Improving discrimination in data envelopment analysis: PCA– DEA or variable reduction, European Journal of Operational Research202 (1) (2010), 273–284.
27.
Ling-jingK., Chi-JieL., Chih-ChouC., Efficiency measurement Using independent component analysis and data envelopment analysis, European Journal of Operational Research210 (2011), 310–317.
28.
JiA.-B., LiuH., QiuH.-J., LinH.-B., Data envelopment analysis with interactive variables, Management Decision53 (10) (2015), 2390–2406.
29.
WangZ., KlirG.J., Generalized Measure TheorySpringer, New York, 2008.
30.
DuboisD., PradeH., (eds.) Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
31.
ChenS.H., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems17 (1985), 113–129.
32.
ChenC.B., KleinC.M., A simple approach to ranking a group of aggregated fuzzy utilities, IEEE Trans Systems Man Cybernet Part B: Cybemet27 (1997), 26–35.
33.
WeiW., ZhenyuanW., Total ordering defined on the set of all fuzzy numbers, Fuzzy Set and Systems243 (2014), 131–141.
34.
DiaM., A model of fuzzy data envelopment analysis, Infor42 (4) (2004), 267–179.
