AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
PDF (3.5 MB)
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Article | Open Access

An Inverse BCC Model for Evaluating and Ordering Decision-Making Units under Fuzziness

Hadi Zavieh1( )Parastoo Niksefat1Seyed Hadi Nasseri1
Department of Applied Mathematics, University of Mazandaran, Babolsar 47416-13534, Iran
Show Author Information

Abstract

One of the most ‎prevalent problems in linear programming as one of the convenient models in the field of operation research ‎‎environment is Data Envelopment Analysis (DEA), which supports the ‎efficiency of ‎‎Decision-Making Units (DMUs). Usually, accurate data are common; however, in ‎the real world, we are facing an inaccurate ‎situation. In this paper, a new ‎model for assessing DMUs in a fuzzy environment is presented; we ‎consider the inverse DEA ‎model with the variable return to scale with fuzzy numbers for fluctuating ‎data. A case study is given to ‎illustrate its performance.

References

[1]

S. Pascoe, T. Cannard, N. A. Dowling, C. M. Dichmont, F. Asche, and L. R. Little, Use of Data Envelopment Analysis (DEA) to assess management alternatives in the presence of multiple objectives, Mar. Policy, vol. 148, p. 105444, 2023.

[2]

K. Smętek, D. Zawadzka, and A. Strzelecka, Examples of the use of Data Envelopment Analysis (DEA) to assess the financial effectiveness of insurance companies, Procedia Comput. Sci., vol. 207, pp. 3924–3930, 2022.

[3]

S. H. Nasseri and M. A. Khatir, Fuzzy stochastic undesirable two-stage data envelopment analysis models with application to banking industry, J. Intell. Fuzzy Syst., vol. 37, no. 5, pp. 7047–7057, 2019.

[4]

Q. Wei, J. Zhang, and X. Zhang, An inverse DEA model for inputs/outputs estimate, Eur. J. Oper. Res., vol. 121, no. 1, pp. 151–163, 2000.

[5]

L. Chen, Y. Wang, F. Lai, and F. Feng, An investment analysis for China’s sustainable development based on inverse data envelopment analysis, J. Clean. Prod., vol. 142, pp. 1638–1649, 2017.

[6]

G. R. Amin, S. Al-Muharrami, and M. Toloo, A combined goal programming and inverse DEA method for target setting in mergers, Expert Syst. Appl., vol. 115, pp. 412–417, 2019.

[7]

D. J. Lim, Inverse data envelopment analysis for operational planning: The impact of oil price shocks on the production frontier, Expert Syst. Appl., vol. 161, p. 113726, 2020.

[8]

S. Lertworasirikul, P. Charnsethikul, and S. C. Fang, Inverse data envelopment analysis model to preserve relative efficiency values: The case of variable returns to scale, Comput. Ind. Eng., vol. 61, no. 4, pp. 1017–1023, 2011.

[9]

M. Ghiyasi, On inverse DEA model: The case of variable returns to scale, Comput. Ind. Eng., vol. 87, pp. 407–409, 2015.

[10]

A. Kumar and A. S. Balu, Epistemic uncertainty quantification in structural systems using improved universal grey theory, Structures, vol. 56, p. 104872, 2023.

[11]

G. N. Zhu, J. Ma, and J. Hu, A fuzzy rough number extended AHP and VIKOR for failure mode and effects analysis under uncertainty, Adv. Eng. Inform., vol. 51, p. 101454, 2022.

[12]

R. E. Bellman and L. A. Zadeh, Decision-making in a fuzzy environment, Manag. Sci., vol. 17, no. 4, pp. 141–164, 1970.

[13]

N. Sheth and K. Triantis, Measuring and evaluating effectiveness using goal programming and data envelopment ‎analysis in a fuzzy environment, Yugoslav J. Oper. Res., vol. 13, no. 1, pp. 35–60, 2003.

[14]

P. Peykani, E. Mohammadi, A. Emrouznejad, M. S. Pishvaee, and M. Rostamy-Malkhalifeh, Fuzzy data envelopment analysis: An adjustable approach, Expert Syst. Appl., vol. 136, pp. 439–452, 2019.

[15]

M. R. Mozaffari, S. Mohammadi, P. F. Wanke, and H. L. Correa, Towards greener petrochemical production: Two-stage network data envelopment analysis in a fully fuzzy environment in the presence of undesirable outputs, Expert Syst. Appl., vol. 164, p. 113903, 2021.

[16]

Z. Chen, X. Ming, R. Wang, and Y. Bao, Selection of design alternatives for smart product service system: A rough-fuzzy data envelopment analysis approach, J. Clean. Prod., vol. 273, p. 122931, 2020.

[17]

H. Zavieh, H. Nasseri, and C. Triki, New advances on fuzzy linear programming problem by semi-infinite programming approach, Gazi Univ. J. Sci., vol. 35, no. 3, pp. 1062–1076, 2022.

[18]

H. Zavieh, A. Javadpour, Y. Li, F. Ja’fari, S. H. Nasseri, and A. S. Rostami, Task processing optimization using cuckoo particle swarm (CPS) algorithm in cloud computing infrastructure, Clust. Comput., vol. 26, no. 1, pp. 745–769, 2023.

[19]

H. Cheng, W. Huang, Q. Zhou, and J. Cai, Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method, Appl. Math. Model., vol. 37, nos.10&11, pp. 6855–6869, 2013.

[20]
T. S. Su, A fuzzy multi-objective linear programming model for solving remanufacturing planning problems with multiple products and joint components, Comput. Ind. Eng., vol. 110, pp. 242–254, 2017.
[21]

R. Tavakkoli-Moghaddam, B. Javadi, F. Jolai, and A. Ghodratnama, The use of a fuzzy multi-objective linear programming for solving a multi-objective single-machine scheduling problem, Appl. Soft Comput., vol. 10, no. 3, pp. 919–925, 2010.

[22]

G. Yang, X. Li, L. Huo, and Q. Liu, A solving approach for fuzzy multi-objective linear fractional programming and application to an agricultural planting structure optimization problem, Chaos Solitons Fractals, vol. 141, p. 110352, 2020.

[23]

H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets Syst., vol. 1, no. 1, pp. 45–55, 1978.

[24]

A. Hatami-Marbini, A. Emrouznejad, and M. Tavana, A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making, Eur. J. Oper. Res., vol. 214, no. 3, pp. 457–472, 2011.

[25]
A. Emrouznejad, M. Tavana, A. Hatami-Marbini, The state of the art in fuzzy data envelopment analysis, in Performance Measurement with Fuzzy Data Envelopment Analysis, A. Emrouznejad and M. Tavana, eds. Berlin, Germany: Springer, 2014, pp. 1–45.
[26]

H. Zavieh, A. Javadpour, F. Ja’fari, A. K. Sangaiah, and A. Słowik, Enhanced efficiency in fog computing: A fuzzy data-driven machine selection strategy, Int. J. Fuzzy Syst., vol. 26, no. 1, pp. 368–389, 2024.

[27]

J. M. Adamo, Fuzzy decision trees, Fuzzy Sets Syst., vol. 4, no. 3, pp. 207–219, 1980.

[28]

L. M. de Campos Ibáñez and A. González Muñoz, A subjective approach for ranking fuzzy numbers, Fuzzy Sets Syst., vol. 29, no. 2, pp. 145–153, 1989.

[29]

R. R. Yager, A procedure for ordering fuzzy subsets of the unit interval, Inf. Sci., vol. 24, no. 2, pp. 143–161, 1981.

[30]

D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Inf. Sci., vol. 30, no. 3, pp. 183–224, 1983.

[31]

N. Mahdavi-Amiri and S. H. Nasseri, Duality in fuzzy number linear programming by use of a certain linear ranking function, Appl. Math. Comput., vol. 180, no. 1, pp. 206–216, 2006.

[32]

N. Mahdavi-Amiri and S. H. Nasseri, Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables, Fuzzy Sets Syst., vol. 158, no. 17, pp. 1961–1978, 2007.

[33]

N. Mahdavi-Amiri, S. H. Nasseri, and A. Yazdani, Fuzzy primal simplex algorithms for solving fuzzy linear programming problems, Iranian J. Oper. Res., vol. 1, no. 2, pp. 68–84, 2009.

[34]

A. Charnes, W. W. Cooper, and E. Rhodes, Measuring the efficiency of decision making units, Eur. J. Oper. Res., vol. 2, no. 6, pp. 429–444, 1978.

[35]

R. D. Banker, A. Charnes, and W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Manag. Sci., vol. 30, no. 9, pp. 1078–1092, 1984.

[36]

B. Ebrahimi, M. Tavana, M. Rahmani, and F. J. Santos-Arteaga, Efficiency measurement in data envelopment analysis in the presence of ordinal and interval data, Neural Comput. Appl., vol. 30, no. 6, pp. 1971–1982, 2018.

[37]

S. Lertworasirikul, S. C. Fang, J. A. Joines, and H. L. W. Nuttle, Fuzzy data envelopment analysis (DEA): A possibility approach, Fuzzy Sets Syst., vol. 139, no. 2, pp. 379–394, 2003.

[38]

S. H. Nasseri and H. Zavieh, A multi-objective method for solving fuzzy linear programming based on semi-infinite model, Fuzzy Information and Engineering, vol. 10, no. 1, pp. 91–98, 2018.

Fuzzy Information and Engineering
Pages 89-101
Cite this article:
Zavieh H, Niksefat P, Nasseri SH. An Inverse BCC Model for Evaluating and Ordering Decision-Making Units under Fuzziness. Fuzzy Information and Engineering, 2024, 16(1): 89-101. https://doi.org/10.26599/FIE.2023.9270034

285

Views

34

Downloads

0

Crossref

0

Web of Science

0

Scopus

Altmetrics

Received: 21 March 2023
Revised: 07 November 2023
Accepted: 01 March 2024
Published: 30 March 2024
© The Author(s) 2024. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Return