EFFICIENCY IN FUZZY PRODUCTION POSSIBILITY SET

Document Type : Research Paper

Authors

1 Department of Mathematics, Science and Research Branch, Is- lamic Azad University, Tehran, Iran

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

3 Department of Mathematics, Qaemshar Branch, Islamic Azad University, Qaemshahr, Iran

Abstract

The existing Data Envelopment Analysis models for evaluating
the relative eciency of a set of decision making units by using various inputs
to produce various outputs are limited to crisp data in crisp production possibility
set. In this paper, rst of all the production possibility set is extended
to the fuzzy production possibility set by extension principle in constant return
to scale, and then the fuzzy model of Charnes, Cooper and Rhodes in
input oriented is proposed so that it satis es the initial concepts with crisp
data. Finally, the fuzzy model of Charnes, Cooper and Rhodes for evaluating
decision making units is illustrated by solving two numerical examples.

Keywords

References

[1] J. M. Adamo, Fuzzy decision trees, Fuzzy Sets and Systems, 4 (1980), 207-219.
[2] T. Allahviranloo, F. Hosseinzadeh Lot , L. Alizadeh and N. Kiani, Degenercy in fuzzy linear
programming problems, In Journal of the Journal of Fuzzy Mathematics (International Fuzzy
Mathematics Institute), 17(2) (2009).
[3] J. F. Baldwin and N. C. F. Guild, Comparison of fuzzy sets on the same decision space,
Fuzzy Sets and Systems, 2 (1979), 213-233.
[4] R. D. Banker, A. Charnes and W. W. Cooper, Some models for estimating teachnical and
scale eciencies in data envelopment analysis, Manage. Sci., 30 (1984), 1078-1092.
[5] R. E. Bellman and L. A. Zadeh, Decision-making in a fuzzy environment, Management Sci.,
17 (1970), 141-164.
[6] A. Charnes, W. W. Cooper and E. Rhodes, Measuring the eciency of decision making
units, Europian Journal of Operation Research, 2 (1978), 429-444.
[7] W. W. Cooper, L. M. Sieford and K. Tone, Data envelopment analysis: a comprehensive text
with models, applications, References and DEA Solver Software, Kluwer Academic Publishers,
2000.
[8] W. W. Cooper, K. S. Park and J. T. Pastor, RAM: a range adjusted measure of ineciency
for use with additive models, and relations to other models and measures in DEA, J. Product.
Anal., 11 (1999), 5-24.
[9] M. J. Farrell, The measurement of productive eciency, Journal of the Royal Statistical
Society A, 120 (1957), 253-281.
[10] R. Fuller, Neural fuzzy systems, Donner Visiting Professor Abo Akademi University, ISBN
951-650-624-0, ISSN 0358-5654, Abo, 1995.
[11] P. Guo and H. Tanaka, Fuzzy DEA: a perceptual evaluation method, Fuzzy Sets and Systems,
119 (2001), 149-160.
[12] P. Guo, Fuzzy data envelopment analysis and its aplication to location problems, Information
Sciences, 176(6,1) (2009), 820-829.
[13] F. Hosseinzadeh Lot , T. Allahviranloo, M. Alimardani Jondabeh and L. Alizadeh, Solving
a full fuzzy linear programming using lexicography method and fuzzy approximate solution,
Applied Mathematical Modelling, 33(7) (2009), 3151-3156.
[14] G. R. Jahanshahloo, M. Soleimani-Damaneh and E. Nasrabadi, Measure of eciency in DEA
with fuzzy input-output levels: a methodology for assessing, ranking and imposing of weights
restrictions, Applied Mathematics and Computation, 156 (2004), 175-187.
[15] N. Javadian, Y. Maali and N. Mahdavi-Amiri, Fuzzy linear programing with grades of satis-
faction in constraints, Iranian Journal of Fuzzy Systems, 6(3) (2009), 17-35.
[16] C. Kao and Shiang-Tai Liu, Fuzzy eciency measures in data envelopment analysis, Fuzzy
Sets and Systems, 113 (2000), 427-437.
[17] C. Kao and S. T. Liu, A mathematical programming approach to fuzzy eciency ranking,
Internat. J. Production Econom, 86 (2003), 45-154.
[18] S. 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.
[19] T. Leon, V. Lierm, J. L. Ruiz and I. Sirvent, A fuzzy mathematical programing approach to
the assessment eciency with DEA models, Fuzzy Sets and Systems, 139 (2003), 407-419.
[20] S. Lertworasirikul, S. C. Fang, J. A. Joines and H. L. W. Nuttle, Fuzzy data envelopment
analysis(DEA): a possibility aporoach, Fuzzy Sets and Systems, 139(2) (2003), 379-394.
[21] S. T. Liu and M. Chuang, Fuzzy eciency measures in fuzzy DEA/AR with application to
university libraries, Expert Systems with Applications, 36(2) (2009), 1105-1113.
[22] S. Ramezanzadeh, M. Memariani and S. Saati, data envelopment analisis with fuzzy random
inputs and outputs: a chance- constrained programing approach, Iranian Journal of Fuzzy
Systems, 2(2) (2005), 21-29.
[23] M. R. Sa , H. R. Maleki and E. Zaeimazad, A note on the zimmermann method for solving
fuzzy linear programing problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 31-45.
[24] Y. M. Wang, R. Greatbanks and J. B. Yang, Interval eciency assessment using data en-
velopment analysis, Fuzzy Sets and Systems, 153 (2005), 347-370.
[25] Y. M. Wang, Y. Luo and L. Liang, Fuzzy data envelopment analysis based upon fuzzy arith-
metic with an aplication to performance assessment of manufacturing enterprises, Expert
Systems with Applications, 363 (2009), 5205-5211.
[26] M. Wen and H. Li, Fuzzy data envelopment analysis(DEA): model and ranking method,
Journal of Computational and Applied Mathematics, 223(2,15) (2009), 872-878.
[27] H. J. Zimmermann, Fuzzy set theory and its applications, Second ed., Kluwer-Nijho , Boston,
1991.
Iranian Journal of Fuzzy Systems
Volume 9, Issue 4 - Serial Number 4
September and October 2012
Pages 17-30

Files

Share

How to cite

Statistics