A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models

Somayeh Tabatabaee; Habib Hosseini

doi:doi:10.11648/j.ajam.20150306.25

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A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models

Somayeh Tabatabaee, Habib Hosseini

Published in American Journal of Applied Mathematics (Volume 3, Issue 6)

Received: 22 November 2015 Accepted: 31 December 2015 Published: 23 February 2016

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Abstract

Data envelopment analysis is a non-parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common inputs and outputs. In fact, in a real evaluation problem input and output data of entities evaluated often fluctuate. This fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts. For this purpose some researchers have proposed several models to deal with the efficiency evaluation problem with the given fuzzy input and output data. One of these methods is to change fuzzy models in to interval models by using alpha cuts. As we may face with some interval efficiency of several entities that should be compare with each other and ranked, in this paper we compare two methods of ranking interval efficiencies that is obtained from interval models. A sensitive difference between these two methods will be shown by a numerical example.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.ajam.20150306.25
Page(s)	341-344
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Data Envelopment Analysis (DEA), Efficiency, Fuzzy Intervals, Ranking

References

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[2]	A. Charnes, W. W. cooper, and T. Sueyoshi, Least squares/ridge regression and gole programming/constrained regression alternatives, European J. Oper. Res. 88 (1996) 525-536.
[3]	M. Tavana, R. Khanjani Shiraz, A. Hatami-Marbini, P. J. Agrell, Kh. Paryab, Chance-constrained DEA models with random fuzzy inputs and outputs, Knowledge-Based Systems, Volume 52, November 2013, Pages 32-52.
[4]	P. Guo, H. Tanaka, Extended fuzzy DEA, Proc. 3rd Asian Fuzzy Systems Symp., 1998, pp. 517-521.
[5]	Shiang-Tai Liu, Restricting weight flexibility in fuzzy two-stage DEA, Computers & Industrial Engineering, Volume 74, August 2014, Pages 149 160.
[6]	F. Nagano, T. Yamaguchi, and T. Fukukawa, DEA with fuzzy output data, J. Oper. Res. Soc. Jpn. 40 (1995) 425-429.
[7]	Y. M. Wang, J. B. Yang, and D. L. Xu, Two approaches for ranking interval numbers based on decision making under uncertainty, Decis. Support System, submitted for publication.
[8]	Peijum Gue, and H. Tanaka, Fuzzy DEA: a perceptual evaluatin method, Fuzzy sets and systems 119 (2001) 149-160.
[9]	M. Esmaeili, An Enhanced Russell Measure in DEA with interval data, Applied Mathematics and Computation, Volume 219, Issue 4, 1 November 2012, Pages 1589-1593.
[10]	H. Li, W. Yang, Zh. Zhou and Ch. Huang, Resource allocation models’ construction for the reduction of undesirable outputs based on DEA methods, Mathematical and Computer Modelling, Volume 58, Issues 5–6, September 2013, Pages 913-926.
[11]	M. Toloo, E. Keshavarz, A New Two-phase Approach for Holding the Strict Positivity Restriction of Weights in DEA Models, Procedia Economics and Finance, Volume 26, 2015, Pages 575-583.
[12]	P. T. Chang, J. H. Lee, A fuzzy DEA and knapsack formulation integrated model for project selection, Computers & Operations Research, Volume 39, Issue 1, January 2012, Pages 112-125.
[13]	J. Puri, S. P. Yadav, A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector, Expert Systems with Applications 40 (2013) 1437–1450.
[14]	A. Charnes, W. W. Cooper, and E. Rhodes, Measuring the efficiency of decision making units, European J. Oper. Res. 2 (1978) 429-444.

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APA Style

Somayeh Tabatabaee, Habib Hosseini. (2016). A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models. American Journal of Applied Mathematics, 3(6), 341-344. https://doi.org/10.11648/j.ajam.20150306.25

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ACS Style

Somayeh Tabatabaee; Habib Hosseini. A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models. Am. J. Appl. Math. 2016, 3(6), 341-344. doi: 10.11648/j.ajam.20150306.25

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AMA Style

Somayeh Tabatabaee, Habib Hosseini. A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models. Am J Appl Math. 2016;3(6):341-344. doi: 10.11648/j.ajam.20150306.25

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@article{10.11648/j.ajam.20150306.25,
  author = {Somayeh Tabatabaee and Habib Hosseini},
  title = {A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {341-344},
  doi = {10.11648/j.ajam.20150306.25},
  url = {https://doi.org/10.11648/j.ajam.20150306.25},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.25},
  abstract = {Data envelopment analysis is a non-parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common inputs and outputs. In fact, in a real evaluation problem input and output data of entities evaluated often fluctuate. This fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts. For this purpose some researchers have proposed several models to deal with the efficiency evaluation problem with the given fuzzy input and output data. One of these methods is to change fuzzy models in to interval models by using alpha cuts. As we may face with some interval efficiency of several entities that should be compare with each other and ranked, in this paper we compare two methods of ranking interval efficiencies that is obtained from interval models. A sensitive difference between these two methods will be shown by a numerical example.},
 year = {2016}
}

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TY  - JOUR
T1  - A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models
AU  - Somayeh Tabatabaee
AU  - Habib Hosseini
Y1  - 2016/02/23
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N1  - https://doi.org/10.11648/j.ajam.20150306.25
DO  - 10.11648/j.ajam.20150306.25
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 341
EP  - 344
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150306.25
AB  - Data envelopment analysis is a non-parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common inputs and outputs. In fact, in a real evaluation problem input and output data of entities evaluated often fluctuate. This fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts. For this purpose some researchers have proposed several models to deal with the efficiency evaluation problem with the given fuzzy input and output data. One of these methods is to change fuzzy models in to interval models by using alpha cuts. As we may face with some interval efficiency of several entities that should be compare with each other and ranked, in this paper we compare two methods of ranking interval efficiencies that is obtained from interval models. A sensitive difference between these two methods will be shown by a numerical example.
VL  - 3
IS  - 6
ER  -

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Author Information

Somayeh Tabatabaee

Department of Mathematics, Firoozabad Branch, Islamic Azad University, Firoozabad, Iran
Habib Hosseini

Department of Mathematics, Firoozabad Branch, Islamic Azad University, Firoozabad, Iran

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APA Style

Somayeh Tabatabaee, Habib Hosseini. (2016). A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models. American Journal of Applied Mathematics, 3(6), 341-344. https://doi.org/10.11648/j.ajam.20150306.25

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ACS Style

Somayeh Tabatabaee; Habib Hosseini. A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models. Am. J. Appl. Math. 2016, 3(6), 341-344. doi: 10.11648/j.ajam.20150306.25

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AMA Style

Somayeh Tabatabaee, Habib Hosseini. A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models. Am J Appl Math. 2016;3(6):341-344. doi: 10.11648/j.ajam.20150306.25

Copy | Download

@article{10.11648/j.ajam.20150306.25,
  author = {Somayeh Tabatabaee and Habib Hosseini},
  title = {A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {341-344},
  doi = {10.11648/j.ajam.20150306.25},
  url = {https://doi.org/10.11648/j.ajam.20150306.25},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.25},
  abstract = {Data envelopment analysis is a non-parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common inputs and outputs. In fact, in a real evaluation problem input and output data of entities evaluated often fluctuate. This fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts. For this purpose some researchers have proposed several models to deal with the efficiency evaluation problem with the given fuzzy input and output data. One of these methods is to change fuzzy models in to interval models by using alpha cuts. As we may face with some interval efficiency of several entities that should be compare with each other and ranked, in this paper we compare two methods of ranking interval efficiencies that is obtained from interval models. A sensitive difference between these two methods will be shown by a numerical example.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A Detailed Comparison Between Two Methods of Ranking Interval Efficiencies for Fuzzy DEA Models
AU  - Somayeh Tabatabaee
AU  - Habib Hosseini
Y1  - 2016/02/23
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20150306.25
DO  - 10.11648/j.ajam.20150306.25
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 341
EP  - 344
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150306.25
AB  - Data envelopment analysis is a non-parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common inputs and outputs. In fact, in a real evaluation problem input and output data of entities evaluated often fluctuate. This fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts. For this purpose some researchers have proposed several models to deal with the efficiency evaluation problem with the given fuzzy input and output data. One of these methods is to change fuzzy models in to interval models by using alpha cuts. As we may face with some interval efficiency of several entities that should be compare with each other and ranked, in this paper we compare two methods of ranking interval efficiencies that is obtained from interval models. A sensitive difference between these two methods will be shown by a numerical example.
VL  - 3
IS  - 6
ER  -

Copy | Download