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A multi-objective optimization approach for DEA models in a fuzzy environment

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Abstract

Data envelopment analysis (DEA) is an important managerial tool for evaluating the performance of decision-making units (DMUs). The conventional DEA models are mostly in the static environment using deterministic/crisp data for input and output parameters. However, in real situations, input and output data cannot always be obtained accurately because of vagueness due to fluctuating market conditions. Such vagueness in input and output data can be tackled with fuzzy numbers. So, the aim of the current study is to extend the crisp DEA into fuzzy DEA (FDEA). In this study, the input and output data are considered as fuzzy numbers (FNs), particularly the triangular fuzzy numbers (TFNs). Then, a multi-objective approach is developed to solve the FDEA model to measure the performance efficiencies of DMUs. Further, the DMUs are ranked according to their efficiencies obtained. Finally, the developed FMODEA model and rankings of DMUs are illustrated with an application on real data 13 educational institutions in India.

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References

  • Arcelus FJ, Coleman D (1995) An efficiency review of university departments. University of New Brunswick, Faculty of Administration

  • Arya A, Yadav SP (2018) Development of fdea models to measure the performance efficiencies of dmus. Int J Fuzzy Syst 20(1):163–173

    Article  MathSciNet  Google Scholar 

  • Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manage Sci 30(9):1078–1092

    Article  Google Scholar 

  • Boubaker S, Do DT, Hammami H, Ly KC (2020) The role of bank affiliation in bank efficiency: a fuzzy multi-objective data envelopment analysis approach. Ann Oper Res 1–29

  • Breu TM, Raab RL (1994) Efficiency and perceived quality of the nation’s “top 25” national universities and national liberal arts colleges: an application of data envelopment analysis to higher education. Socio Econ Plann Sci 28(1):33–45

  • Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444

    Article  MathSciNet  Google Scholar 

  • Chen W, Li SS, Zhang J, Mehlawat MK (2020) A comprehensive model for fuzzy multi-objective portfolio selection based on dea cross-efficiency model. Soft Comput 24(4):2515–2526

    Article  Google Scholar 

  • Cooper WW, Seiford L, Tone K (2000) Data envelopment analysis: theory, methodology, and applications, references and dea-solver software

  • Ghasemi MR, Ignatius J, Lozano S, Emrouznejad A, Hatami-Marbini A (2015) A fuzzy expected value approach under generalized data envelopment analysis. Knowl Based Syst 89:148–159

    Article  Google Scholar 

  • Guo P (2009) Fuzzy data envelopment analysis and its application to location problems. Inform Sci 179(6):820–829

    Article  MathSciNet  Google Scholar 

  • Guo P, Tanaka H (2001) Fuzzy dea: a perceptual evaluation method. Fuzzy Sets Syst 119(1):149–160

    Article  MathSciNet  Google Scholar 

  • Guo P, Tanaka H (2008) Decision making based on fuzzy data envelopment analysis. In: Intelligent decision and policy making support systems. Springer, pp 39–54

  • Hatami-Marbini A, Emrouznejad A, Tavana M (2011) A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. Eur J Oper Res 214(3):457–472

    Article  MathSciNet  Google Scholar 

  • Kao C, Liu ST (2000) Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst 113(3):427-437

    Article  Google Scholar 

  • Kumar H, Singh AP, Yadav SP (2019) Nsga-ii based analysis of fuzzy multi-objective reliability-redundancy allocation problem using various membership functions. INAE Lett 4(3):191–206

  • Lertworasirikul S, Fang SC, Joines JA, Nuttle HL (2008) A possibility approach to fuzzy data envelopment analysis. In: JCIS, pp 176–179

  • Marler RT, Arora JS (2010) The weighted sum method for multi-objective optimization: new insights. Struct Multidisc Optim 41(6):853–862

    Article  MathSciNet  Google Scholar 

  • Mogha SK, Yadav SP, Singh S (2014) New slack model based efficiency assessment of public sector hospitals of uttarakhand: state of India. Int J Syst Assur Eng Manage 5(1):32–42

    Article  Google Scholar 

  • Mogha SK, Yadav SP, Singh S (2016) Estimating technical efficiency of public sector hospitals of Uttarakhand (India). Int J Oper Res 25(3):371–399

    Article  Google Scholar 

  • Puri J, Yadav SP (2013) Performance evaluation of public and private sector banks in India using dea approach. Int J Oper Res 18(1):91–121

    Article  Google Scholar 

  • Puri J, Yadav SP (2015) A fully fuzzy approach to dea and multi-component dea for measuring fuzzy technical efficiencies in the presence of undesirable outputs. Int J Syst Assur Eng Manage 6(3):268–285

    Article  Google Scholar 

  • Sengupta JK (1992) A fuzzy systems approach in data envelopment analysis. Comput Math Appl 24(8–9):259–266

    Article  MathSciNet  Google Scholar 

  • Tavana M, Khalili-Damghani K, Arteaga FJS, Hosseini A (2019) A fuzzy multi-objective multi-period network dea model for efficiency measurement in oil refineries. Comput Indus Eng 135:143–155

    Article  Google Scholar 

  • Tyagi P, Yadav SP, Singh S (2009) Relative performance of academic departments using dea with sensitivity analysis. Eval Program Plann 32(2):168–177

    Article  Google Scholar 

  • Wang YM, Luo Y, Liang L (2009) Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Exp Syst Appl 36(3):5205–5211

    Article  Google Scholar 

  • Wang WK, Lu WM, Liu PY (2014) A fuzzy multi-objective two-stage dea model for evaluating the performance of us bank holding companies. Exp Syst Appl 41(9):4290–4297

    Article  Google Scholar 

  • Wen M, You C, Kang R (2010) A new ranking method to fuzzy data envelopment analysis. Comput Math Appl 59(11):3398–3404

    Article  MathSciNet  Google Scholar 

  • Zamani P (2020) The position of multiobjective programming methods in fuzzy data envelopment analysis. Int J Math Modell Comput 10(2 (SPRING)):95–101

  • Zimmermann HJ (2011) Fuzzy set theory-and its applications. Springer Science & Business Media

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Acknowledgements

The authors are thankful to The Ministry of Education, the Govt. of India, for financial support in pursuing this research.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Awadh Pratap Singh & Shiv Prasad Yadav

  2. Indian Institute of Management Jammu, Jammu, 180016, India

    Sujeet Kumar Singh

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  1. Awadh Pratap Singh
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  2. Shiv Prasad Yadav
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Singh, A.P., Yadav, S.P. & Singh, S.K. A multi-objective optimization approach for DEA models in a fuzzy environment. Soft Comput 26, 2901–2912 (2022). https://doi.org/10.1007/s00500-021-06627-y

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