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The role of multiplier bounds in fuzzy data envelopment analysis

Author

Listed:
  • Adel Hatami-Marbini

    (De Montfort University)

  • Per J. Agrell

    (Université catholique de Louvain)

  • Hirofumi Fukuyama

    (Fukuoka University)

  • Kobra Gholami

    (Islamic Azad University)

  • Pegah Khoshnevis

    (KU Leuven University)

Abstract

The non-Archimedean epsilon $$\varepsilon $$ ε is commonly considered as a lower bound for the dual input weights and output weights in multiplier data envelopment analysis (DEA) models. The amount of $$\varepsilon $$ ε can be effectively used to differentiate between strongly and weakly efficient decision making units (DMUs). The problem of weak dominance particularly occurs when the reference set is fully or partially defined in terms of fuzzy numbers. In this paper, we propose a new four-step fuzzy DEA method to re-shape weakly efficient frontiers along with revisiting the efficiency score of DMUs in terms of perturbing the weakly efficient frontier. This approach eliminates the non-zero slacks in fuzzy DEA while keeping the strongly efficient frontiers unaltered. In comparing our proposed algorithm to an existing method in the recent literature we show three important flaws in their approach that our method addresses. Finally, we present a numerical example in banking with a combination of crisp and fuzzy data to illustrate the efficacy and advantages of the proposed approach.

Suggested Citation

  • Adel Hatami-Marbini & Per J. Agrell & Hirofumi Fukuyama & Kobra Gholami & Pegah Khoshnevis, 2017. "The role of multiplier bounds in fuzzy data envelopment analysis," Annals of Operations Research, Springer, vol. 250(1), pages 249-276, March.
  • Handle: RePEc:spr:annopr:v:250:y:2017:i:1:d:10.1007_s10479-017-2404-8
    DOI: 10.1007/s10479-017-2404-8
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    2. Matthias Klumpp & Dominic Loske, 2021. "Sustainability and Resilience Revisited: Impact of Information Technology Disruptions on Empirical Retail Logistics Efficiency," Sustainability, MDPI, Open Access Journal, vol. 13(10), pages 1-20, May.
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    4. Dariush Akbarian, 2020. "Overall profit Malmquist productivity index under data uncertainty," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-20, December.
    5. Zahra Mohmmad Nejad & Alireza Ghaffari-Hadigheh, 2018. "A novel DEA model based on uncertainty theory," Annals of Operations Research, Springer, vol. 264(1), pages 367-389, May.

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    More about this item

    Keywords

    Data envelopment analysis; Epsilon; Fuzzy data; Weak frontier;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D20 - Microeconomics - - Production and Organizations - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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