Sage Journals: Discover world-class research

Abstract

Data envelopment analysis (DEA) has become an accepted tool for assessing efficiency in a wide range of cases since it was first proposed in 1978. However, traditional DEA models need accurate inputs and outputs, which can’t be obtained or measured in many practical cases. This paper will apply DEA into uncertain environment, and propose a new DEA model with uncertain inputs and outputs based on uncertain theory. Furthermore, the uncertainty theory is utilized to convert the new uncertain DEA model into an equivalent deterministic model for simplification. Finally, this new uncertain DEA model is applied to the evaluation of scientific research personnel to illustrate the effectiveness.

Keywords

Data envelopment analysis uncertainty theory uncertain variable uncertainty distribution efficiency

Get full access to this article

View all access options for this article.

References

Charnes ,

W.W.

Cooper and

Rhodes , Measuring the effciency of decision making units, European Journal of Operational Research 2 (1978), 429–444.

R.D.

Banker ,

Charnes and

W.W.

Cooper , Some models for estimating technical and scale effciencies in data envelopment analysis, Management Science 30 (1984), 1078–1092.

Charnes ,

W.W.

Cooper ,

Golany ,

Seiford and

Stutz , Foundations of data envelopment analysis for Pareto-Koopmans effcient empirical production functions, Journal of Econometrics 30 (1985), 91–107.

N.C.

Petersen , Data envelopment analysis on a relaxed set of assumptions, Management Science 36(3) (1990), 305–313.

Tone , A slack-based measure of effciency in data envelopment analysis, European Journal of Operational Research 130 (2001), 498–509.

J.K.

Sengupta , Effciency measurement in stochastic input-output systems, International Journal of Systems Science 13 (1982), 273–287.

R.D.

Banker , Maximum likelihood, consistency and DEA: Statistical foundations, Management Science 39 (1993), 1265–1273.

Wei ,

Chen and

Wang , Stochastic effciency analysis with a reliability consideration, Omega 48 (2014), 1–9.

Olesen and

N.C.

Petersen , Chance constrained effciency evaluation, Management Science 141 (1995), 442–457.

10.

R.D.

Banker , Stochastic Data Envelopment Analysis, Pittsburgh: Carnegie-Mellon University, 1986.

11.

Grosskopf , Statistical inference and nonparametric effciency: A selective survey, Journal of Productivity Analysis 7 (1996), 161–176.

12.

W.W.

Cooper ,

Z.M.

Huang and

S.X.

Li , Satisfying DEA models under chance constraints, Annals of Operations Research 66 (1996), 279–295.

13.

W.W.

Cooper ,

Z.M.

Huang ,

Lelas ,

S.X.

Li and

O.B.

Olesen , Chance constrained programming formulations for stochastic characterizations of effciency and dominance in DEA, Journal of Productivity Analysis 9 (1998), 53–79.

14.

A.D.

Kiureghian and

Ditlevsen , Aleatory or epistemic? Does it matter? Structural Safety 31(2) (2009), 105–112.

15.

W.W.

Cooper ,

K.S.

Park and

Gang , Idea and ar-idea: Models for dealing with imprecise data in dea, Management Science 45(4) (1999), 597–607.

16.

Wei and

Wang , A comparative study of robust effciency analysis and data envelopment analysis with imprecise data, Expert Systems with Applications 81 (2017), 28–38.

17.

M.L.

Wen and

H.S.

Li , Fuzzy data envelopment analysis (DEA): Model and ranking method, Journal of Computational and Applied Mathematics 223 (2009), 872–878.

18.

Kao and

S.T.

Liu , Fuzzy effciency measures in data envelopment analysis, Fuzzy Sets and Systems 113 (2000), 427–437.

19.

Entani ,

Maeda and

Tanaka , Dual models of interval DEA and its extension to interval data, European Journal of Operational Research 136 (2002), 32–45.

20.

Zhou ,

Pedrycz ,

Kuang and

Zhang , Type-2 fuzzy multi-objective dea model: An application to sustainable supplier evaluation, Applied Soft Computing (2016), S1568494616301946.

21.

Hatami-Marbini ,

P.J.

Agrell ,

Fukuyama ,

Gholami and

Khoshnevis , The role of multiplier bounds in fuzzy data envelopment analysis, Annals of Operations Research 250(1) (2017), 249–276.

22.

L.A.

Zadeh , Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978), 3–28.

23.

Guo and

Tanaka , Fuzzy DEA: A perceptual evaluation method, Fuzzy Sets and Systems 119 (2001), 149–160.

24.

Lertworasirikul ,

S.C.

Fang ,

J.A.

Joines and

H.L.W.

Nuttle , Fuzzy data envelopment analysis (DEA): A possibility approach, Fuzzy Sets and Systems 139 (2003), 379–394.

25.

Liu , Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.

26.

Liu , Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin, 2010a.

27.

Wen ,

Guo ,

Kang and

Yang , Data envelopment analysis with uncertain inputs and outputs, Journal of Applied Mathematics 2014 (2014), 307108.

28.

Wen ,

Qin ,

Kang and

Yang , Sensitivity and stability analysis of the additive model in uncertain data envelopment analysis, Soft Computing 19(7) (2015), 1987–1996.

29.

Z.M.

Nejad and

Ghaffarihadigheh , A novel dea model based on uncertainty theory, Annals of Operations Research 264 (2018), 1–23.

30.

Liu , Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems 2(1) (2008), 3–16.

31.

Liu , Some research problems in uncertainty theory, Journal of Uncertain Systems 3(1) (2009a), 3–10.

32.

Liu , Theory and practice of Uncertain Programming, 2nd ed., Springer-Verlag, Berlin, 2009b.

33.

Liu and

X.W.

Chen , Uncertain multiobjective programming and uncertain goal programming, Technical Report, 2013.

34.

Liu and

Yao , Uncertain multilevel programming: Algorithm and application, http://orsc.edu.cn/online/120114.pdf

35.

Chen and

Liu , Existence and uniqueness theorem for uncertain differential equations, Fuzzy Optimization and Decision Making 9(1) (2010), 69–81.

36.

Peng and

Yao , A new option pricing model for stocks in uncertainty markets, International Journal of Operations Research 7(4) (2010), 213–224.

37.

Liu , Extreme value theorems of uncertain process with application to insurance risk model, Soft Computing 17(4) (2013), 549–556.

38.

Liu , Uncertain risk analysis and uncertain reliability analysis, Journal of Uncertain Systems 4(3) (2010b), 163–170.

39.

Zeng ,

Wen and

Kang , Belief reliability: A new metrics for products' reliability, Fuzzy Optimization and Decision Making 12(1) (2013), 15–27.

40.

Zhang ,

Kang and

Wen , A new method of level-2 uncertainty analysis in risk assessment based on uncertainty theory, Soft Computing 22(17) (2018), 5867–5877.

41.

Wen and

Kang , Reliability analysis in uncertain random system, Fuzzy Optimization and Decision Making 15(4) (2016), 491–506.

42.

X.L.

Gao , Cycle index of uncertain graph, Information: An International Interdisciplinary Journal 16(2(A)) (2013), 131–1138.

43.

X.L.

Gao and

Gao , Connectedness index of uncertainty graphs, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21(1) (2013), 127–137.

44.

Li and

Lo Hong , An energy-effcient scheduling and speed control approach for metro rail operations, Transportation Research Part B 64 (2014), 73–89.

45.

Li ,

Wang ,

Li and

Gao , A green train scheduling model and fuzzy multi-objective optimization algorithm, Applied Mathematical Modelling 37 (2013), 2063–2073.

46.

Yao and

Ji , Uncertain decision making and its application to portfolio selection problem, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22(1) (2014), 113–123.