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A Dual SBM Model with Fuzzy Weights in Fuzzy DEA

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Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 236))

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Abstract

The dual part of a SBM model in data envelopment analysis (DEA) aims to calculate the optimal virtual costs and prices (also known as weights) of inputs and outputs for the concerned decision-making units (DMUs). In conventional dual SBM model, the weights are found as crisp quantities. However, in real-world problems, the weights of inputs and outputs in DEA may have fuzzy essence. In this paper, we propose a dual SBM model with fuzzy weights for input and output data. The proposed model is then reduced to a crisp linear programming problem by using ranking function of a fuzzy number (FN). This model gives the fuzzy efficiencies and the fuzzy weights of inputs and outputs of the concerned DMUs as triangular fuzzy numbers (TFNs). The proposed model is illustrated with a numerical example.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Chen, S.M.: Fuzzy system reliability analysis using fuzzy number arithmetic operations. Fuzzy Set. Syst. 66, 31–38 (1994)

    Article  Google Scholar 

  3. Cooper, W. W., Seiford, L. M., Zhu, J.: Handbook on Data Envelopment Analysis. 2nd edn. International Series in Operations Research and Management Science, Springer, 164, p. 200 (2011)

    Google Scholar 

  4. Goudarzi, M.R.M.: A slack-based model for estimating returns to scale under weight restrictions. Appl. Math. Sci. 6(29), 1419–1430 (2012)

    MATH  MathSciNet  Google Scholar 

  5. Hatami-Marbini, A., Saati, S., Makui, A.: An application of fuzzy numbers ranking in performance analysis. J. Appl. Sci. 9(9), 1770–1775 (2009)

    Article  Google Scholar 

  6. Jahanshahloo, G.R., Soleimani-damaneh, M., Nasrabadi, E.: Measure of efficiency in DEA with fuzzy input-output levels: A methodology for assessing, ranking and imposing of weights restrictions. Appl. Math. Comput. 156, 175–187 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kao, C., Liu, S.T.: Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst. 113, 427–437 (2000)

    Article  MATH  Google Scholar 

  8. Lertworasirikul, S., Fang, S.C., Joines, J.A., Nuttle, H.L.W.: Fuzzy data envelopment analysis: A possibility approach. Fuzzy Set. Syst. 139(2), 379–394 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mahdavi-Amiri, N., Nasseri, S.H.: Duality in fuzzy number linear programming by use of a certain linear ranking function. Appl. Math. Comput. 180, 206–216 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mansourirad, E., Rizam, M.R.A.B., Lee, L.S., Jaafar, A.: Fuzzy weights in data envelopment analysis. Int. Math. Forum 5(38), 1871–1886 (2010)

    MathSciNet  Google Scholar 

  11. Puri, J., Yadav, S.P.: A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector. Expert Syst. Appl. 40, 1437–1450 (2013)

    Article  Google Scholar 

  12. Saati, S., Memariani, A.: SBM model with fuzzy input-output levels in DEA. Aust. J. Basic Appl. Sci. 3(2), 352–357 (2009)

    Google Scholar 

  13. Saen, R.F.: Developing a nondiscretionary model of slacks-based measure in data envelopment analysis. Appl. Math. Comput. 169, 1440–1447 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sengupta, J.K.: A fuzzy systems approach in data envelopment analysis. Comput. Math. Appl. 24(8–9), 259–266 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  15. Tone, K.: A slacks-based measure of efficiency in data envelopment analysis. Eur. J. Oper. Res. 130, 498–509 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  16. Zimmermann, H.J.: Fuzzy Set Theory and its Applications, 3rd edn. Kluwer-Nijhoff Publishing, Boston (1996)

    Book  MATH  Google Scholar 

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Acknowledgments

The first author is thankful to the University Grants Commission (UGC), Government of India, for financial assistance.

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Authors and Affiliations

  1. Department of Mathematics, I.I.T. Roorkee, Roorkee, 247667, India

    Jolly Puri & Shiv Prasad Yadav

Authors
  1. Jolly Puri
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  2. Shiv Prasad Yadav
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Corresponding author

Correspondence to Jolly Puri .

Editor information

Editors and Affiliations

  1. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    B. V. Babu

  2. Department of Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya Nagar

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  4. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, India

    Millie Pant

  5. Department of Applied Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

  6. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    Kanad Ray

  7. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    Umesh Gupta

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Puri, J., Yadav, S.P. (2014). A Dual SBM Model with Fuzzy Weights in Fuzzy DEA. In: Babu, B., et al. Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012. Advances in Intelligent Systems and Computing, vol 236. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1602-5_34

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  • DOI: https://doi.org/10.1007/978-81-322-1602-5_34

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1601-8

  • Online ISBN: 978-81-322-1602-5

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