DEA (data envelopment analysis) is a non-parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs. In fact, in a real evaluation problem input and output data of entities evaluated often fluctuate. These fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts. Based on the fundamental CCR model, a fuzzy DEA model is proposed to deal with the efficiency evaluation problem with the given fuzzy input and output data. Furthermore, a fuzzy aggregation model for integrating multiple attribute fuzzy values of objects is proposed based on the fuzzy DEA model. Using the proposed fuzzy DEA models, the crisp efficiency in CCR model is generalized to be a fuzzy efficiency to reflect the inherent uncertainty in real evaluation problems. Using the proposed fuzzy aggregation models, the objects can be ranked objectively.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P.W. Bauer, Recent developments in the econometric estimation of frontiers, Journal of Econometrics 46 (1990) 39–56
T. Calvo, G. Mayor, R. Mesiar (Eds.), Aggregation Operators, Physica-Verlag, Wurzburg, 2002
A. Charnes, W.W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research 2 (1978) 429–444
A. Charnes, A. Gallegos, H. Li, Robustly efficient parametric frontiers via multiplicative DEA for domestic and international operations of the Latin American airline industry, European Journal of Operational Research 88 (1996) 525–536
W.W. Cooper, K.S. Park, G. Yu, IDEA and AR-IDEA: models for dealing with imprecise data in DEA, Management Science 45 (1999) 597–607
D.K. Despotis, Y.G. Smirlis, Data envelopment analysis with imprecision data, European Journal of Operational Research 140 (2002) 24–36
D. Dubois, H. Prade, On the use of aggregation operations in information fusion process, Fuzzy Sets and Systems, Fuzzy Sets and Systems 142 (2004) 143–161
H. Dyckhoff, W. Pedrycz, Generalized means as a model of compensative connectives, Fuzzy Sets and Systems 14 (1984) 143–154
W.H. Greene, A gamma-distributed stochastic frontier model, Journal of Econometrics 46 (1990) 141–163
P. Guo, H. Tanaka, Fuzzy DEA: a perceptual method, Fuzzy Sets and Systems 119 (2001) 149–160
P. Guo, H. Tanaka, M. Inuiguchi, Self-organizing fuzzy aggregation models to rank the objects with multiple attributes, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 30 (2000) 573–580
G.R. Jahanshahloo, R.K. Matin, A.H. Vencheh, On return to scale of fully efficient DMUs in data envelopment analysis under interval data, Applied Mathematics and Computation 154 (2004) 31–40
C. Kao, S.T. Liu, Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets and Systems 113 (2000) 427–437
T. Leon, V. Liern, J.L. Ruiz, I. Sirvent, A fuzzy mathematical programming approach to the assessment of efficiency with DEA models, Fuzzy Sets and Systems 139 (2003) 407–419
S. Lertworasirikul, S.C. Fang, J.A. Joines, H.L.W. Nuttle, Fuzzy data envelopment analysis (DEA): a possibility approach, Fuzzy Sets and Systems 139 (2003) 379–394
F. Nagano, T. Yamaguchi, T. Fukukawa, DEA with fuzzy output data, Journal of the Operations Research Society of Japan 40 (1995) 425–429
V. Peneva, I. Popchev, Properties of the aggregation operators related with fuzzy relations, Fuzzy Sets and Systems 139 (2003) 615–633
S. Saati, A. Memariani, G.R. Jahanshahloo, Efficiency analysis and ranking of DMU with fuzzy data, Fuzzy Optimization and Decision Making 1 (2002) 255–267
P. Schmidt, T.F. Lin, Simple tests of alternative specifications in stochastic frontier models, Journal of Econometrics 24 (1984) 349–361
T. Tsabadze, A method for fuzzy aggregation based on group expert evaluations, Fuzzy Sets and Systems 157 (2006) 1346–1361
Y.M. Wang, R. Greatbanks, J.B. Yang, Interval efficiency assessment using data envelopment analysis, Fuzzy Sets and Systems 153 (2005) 347–370
R.R. Yager, On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transaction on Systems Man and Cybernetics 18 (1988) 183–190
R.R. Yager, Families of OWA operators, Fuzzy Sets and Systems 59 (1993) 125–148
J. Zhu, Imprecise data envelopment analysis (IDEA): a review and improvement with an application, European Journal of Operational Research 144 (2003) 513–529
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Guo, P., Tanaka, H. (2008). Decision Making Based on Fuzzy Data Envelopment Analysis. In: Da Ruan, Hardeman, F., van der Meer, K. (eds) Intelligent Decision and Policy Making Support Systems. Studies in Computational Intelligence, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78308-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-78308-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78306-0
Online ISBN: 978-3-540-78308-4
eBook Packages: EngineeringEngineering (R0)