A Fully Fuzzy Approach to Data Envelopment Analysis
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Authors
Mostafa Kazemi
- Department of Management, Ferdowsi university of Mashhad, Mashhad, Iran.
Amir Alimi
- Department of Management, Ferdowsi university of Mashhad, Mashhad, Iran.
Abstract
Data envelopment analysis (DEA) is a method to evaluate the efficiency of some decision making units which by using one or more inputs will make one or more outputs. In real world, most of the problems don’t have a certain mode. Fuzzy theory is one of the ways of considering uncertainty in the mathematical programming problems. In this study by using this idea, the DEA model on a fully fuzzy mode is proposed. The feature of this proposed model is that it considers 3 situations for problem and solving them simultaneously. The first situation occurs on a desired condition with the highest output and lowest input. The second is made of centric point of inputs and outputs and is analogous with the first condition. The third or undesired situation is when there are upper bound of input and lower bound of output. Results showed that the highest efficiency of some units is 1, so these units are efficient. To collate the efficient units on the proposed method, we can use the obtained centric points for efficiency of units.
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ISRP Style
Mostafa Kazemi, Amir Alimi, A Fully Fuzzy Approach to Data Envelopment Analysis, Journal of Mathematics and Computer Science, 11 (2014), no. 3, 238-245
AMA Style
Kazemi Mostafa, Alimi Amir, A Fully Fuzzy Approach to Data Envelopment Analysis. J Math Comput SCI-JM. (2014); 11(3):238-245
Chicago/Turabian Style
Kazemi, Mostafa, Alimi, Amir. "A Fully Fuzzy Approach to Data Envelopment Analysis." Journal of Mathematics and Computer Science, 11, no. 3 (2014): 238-245
Keywords
- Data envelopment analysis
- fully fuzzy model
- Decision making unit
- Triangular fuzzy number
- efficiency.
MSC
References
-
[1]
A. Charnes, W. W. Cooper, E. L. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444.
-
[2]
L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338-353.
-
[3]
A. Azadeh, S. M. Alem, A flexible deterministic, stochastic and fuzzy data envelopment analysis approach for supply chain risk and vendor selection problem: simulation analysis, Expert Systems with Applications, 37 (12) (2010), 7438–7448.
-
[4]
L. M. ZerafatAngiz, A. Emrouznejad, A. Mustafa, Fuzzy assessment of performance of a decision making units using DEA: a non-radial approach, Expert Systems with Applications, 37 (7) (2010), 5153–5157.
-
[5]
L. M. ZerafatAngiz, A. Emrouznejad, A. Mustafa, Fuzzy data envelopment analysis: a discrete approach, Expert Systems with Applications, 39 (2012), 2263–2269.
-
[6]
C. Kao, S. T. Liu, Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets and Systems, 113 (3) (2000), 427–437.
-
[7]
C. Kao, S. T. Liu, Data envelopment analysis with missing data: an application to University libraries in Taiwan, Journal of Operational Research Society, 51 (8) (2000), 897–905.
-
[8]
F. HosseinzadehLotfi, M. AdabitabarFirozja, V. Erfani, Efficiency measures in data envelopment analysis with fuzzy and ordinal data, International Mathematical Forum, 4 (20) (2009), 995–1006.
-
[9]
G. R. Jahanshahloo, F. HosseinzadehLotfi, R. Shahverdi, M. Adabitabar, M. Rostamy-Malkhalifeh, S. Sohraiee, Ranking DMUs by l1 _ normwith fuzzy data in DEA, Chaos, Solitons and Fractals, 39 (2009), 2294–2302.
-
[10]
M. Soleimani-damaneh, Establishing the existence of a distance-based upper bound for a fuzzy DEA model using duality, Chaos, Solitons and Fractals, 41 (2009), 485–490.
-
[11]
Y. K. Juan, A hybrid approach using data envelopment analysis and case-based reasoning for housing refurbishment contractors selection and performance Improvement, Expert Systems with Applications, 36 (3) (2009), 5702–5710.
-
[12]
S. Lertworasirikul, Fuzzy Data Envelopment Analysis (DEA), Ph.D. Dissertation, Dept. of Industrial Engineering, North Carolina State University (2002)
-
[13]
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 (2) (2003), 379–394.
-
[14]
Y. M. Wang, Y. Luo, L. Liang, Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises, Expert Systems with Applications, 36 (2009), 5205–5211.
-
[15]
S. Saati, A. Hatami-Marbini, M. Tavana, A data envelopment analysis model with discretionary and non-discretionary factors in fuzzy environments, Int. J. Productivity and Quality Management, 8(1) (2011), 45–63.
-
[16]
A. Hatami-Marbini, M.Tavana, A. Ebrahimi, A fully fuzzified data envelopment analysis model, International Journal of Information and Decision Sciences, 3(3) (2011), 252-264.
-
[17]
T. Allahviranloo, F. HosseinzadehLotfi, M. Kh. Kiasary, N. A. Kiani, L. Alizadeh, Solving fully fuzzy linear programming problem by the ranking function, Applied Mathematical Sciences, 2 (2008), 19–32.
-
[18]
A. Kumar, J. Kaur, P. Singh, Fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints, International Journal of Mathematical and Computer Sciences, 6 (2010), 37-41.
-
[19]
M. Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Applied Mathematics and Computations, 179 (2006), 328–343.
-
[20]
T. S. Liou, M. J. Wang, Ranking fuzzy numbers with integral value, Fuzzy Sets and Systems, 50 (1992), 247–255.
-
[21]
V. Kreinovich, A. V. Lakeyev, J. Rohn, P. T. Kahl, Computational Complexity and Feasibility of Data Processing and Interval Computations, Applied Optimization, vol. 10 ( 1998)
-
[22]
P. Guo, H. Tanaka, Fuzzy DEA: a perceptual evaluation method, Fuzzy Sets and Systems, 119 (2001), 149–160.
-
[23]
M. Wen, C. You, R. Kang, A new ranking method to fuzzy data envelopment analysis, Computers and Mathematics with Applications, 59 (2010), 3398-3404.