IDEAS home Printed from https://ideas.repec.org/a/spr/fuzodm/v19y2020i3d10.1007_s10700-020-09321-0.html
   My bibliography  Save this article

A fuzzy evaluation approach with the quasi-ordered set: evaluating the efficiency of decision making units

Author

Listed:
  • Xiao-Li Meng

    (Peking University
    Peking University)

  • Liu-Tang Gong

    (Peking University
    Peking University)

  • Jen-Chih Yao

    (China Medical University)

Abstract

This work proposes an inequality approach with the quasi-ordered set to evaluate the performances of decision making units (DMUs). In real world applications, input and output data are often imprecise and fluctuated. In this case, a fuzzy inequality approach is proposed to evaluate DMUs with fuzzy data. Fuzzy inequalities consist of fuzzy expressions of the production possibility set and the line segment joining the origin to the evaluated DMU. Moreover, under constant returns to scale, the production possibility set is spanned by all the DMUs without the evaluated DMU. Fuzzy efficiency is dependent upon whether the solution set of fuzzy inequalities is empty or not. The quasi-ordered set is used to distinguish the fuzzy efficiency. Finally, numerical examples are used to illustrate the approach.

Suggested Citation

  • Xiao-Li Meng & Liu-Tang Gong & Jen-Chih Yao, 2020. "A fuzzy evaluation approach with the quasi-ordered set: evaluating the efficiency of decision making units," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 297-310, September.
  • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:3:d:10.1007_s10700-020-09321-0
    DOI: 10.1007/s10700-020-09321-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10700-020-09321-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10700-020-09321-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Triantis, Konstantinos & Sarangi, Sudipta & Kuchta, Dorota, 2003. "Fuzzy pair-wise dominance and fuzzy indices: An evaluation of productive performance," European Journal of Operational Research, Elsevier, vol. 144(2), pages 412-428, January.
    2. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
    3. Adel Hatami-Marbini & Madjid Tavana & Ali Emrouznejad & Saber Saati, 2012. "Efficiency measurement in fuzzy additive data envelopment analysis," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 10(1), pages 1-20.
    4. Dariush Khezrimotlagh & Yao Chen, 2018. "Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Decision Making and Performance Evaluation Using Data Envelopment Analysis, chapter 0, pages 217-234, Springer.
    5. Hatami-Marbini, Adel & Emrouznejad, Ali & Tavana, Madjid, 2011. "A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making," European Journal of Operational Research, Elsevier, vol. 214(3), pages 457-472, November.
    6. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    7. Jahanshahloo, G.R. & Hosseinzadeh Lotfi, F. & Shahverdi, R. & Adabitabar, M. & Rostamy-Malkhalifeh, M. & Sohraiee, S., 2009. "Ranking DMUs by l1-norm with fuzzy data in DEA," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2294-2302.
    8. HATAMI-MARBINI, Adel & TAVANA, Madjid & EMROUZNEJAD, Ali & SAATI, Saber, 2012. "Efficiency measurement in fuzzy additive data envelopment analysis," LIDAM Reprints CORE 2393, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Barak, Sasan & Dahooei, Jalil Heidary, 2018. "A novel hybrid fuzzy DEA-Fuzzy MADM method for airlines safety evaluation," Journal of Air Transport Management, Elsevier, vol. 73(C), pages 134-149.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yutong Chen & Yongchuan Tang, 2021. "An Improved Approach of Incomplete Information Fusion and Its Application in Sensor Data-Based Fault Diagnosis," Mathematics, MDPI, vol. 9(11), pages 1-16, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. S. Mohammad Arabzad & Mazaher Ghorbani & Arash Shahin, 2013. "Ranking players by DEA the case of English Premier League," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 15(4), pages 443-461.
    2. Utsav Pandey & Sanjeet Singh, 2022. "Data envelopment analysis in hierarchical category structure with fuzzy boundaries," Annals of Operations Research, Springer, vol. 315(2), pages 1517-1549, August.
    3. Rafael Benítez & Vicente Coll-Serrano & Vicente J. Bolós, 2021. "deaR-Shiny: An Interactive Web App for Data Envelopment Analysis," Sustainability, MDPI, vol. 13(12), pages 1-19, June.
    4. Hashem Omrani & Arash Alizadeh & Ali Emrouznejad & Tamara Teplova, 2024. "Data envelopment analysis model with decision makers’ preferences: a robust credibility approach," Annals of Operations Research, Springer, vol. 339(3), pages 1269-1306, August.
    5. Adel Hatami-Marbini & Zahra Ghelej Beigi & Hirofumi Fukuyama & Kobra Gholami, 2015. "Modeling Centralized Resources Allocation and Target Setting in Imprecise Data Envelopment Analysis," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1189-1213, November.
    6. HATAMI-MARBINI, Adel & AGRELL, Per & AGHAYI, Nazila, 2013. "Imprecise data envelopment analysis for the two-stage process," LIDAM Discussion Papers CORE 2013004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Aydın, Umut & Karadayi, Melis Almula & Ülengin, Füsun, 2020. "How efficient airways act as role models and in what dimensions? A superefficiency DEA model enhanced by social network analysis," Journal of Air Transport Management, Elsevier, vol. 82(C).
    8. Azarnoosh Kafi & Behrouz Daneshian & Mohsen Rostamy-Malkhalifeh, 2021. "Forecasting the confidence interval of efficiency in fuzzy DEA," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 41-59.
    9. Matthias Klumpp & Dominic Loske, 2021. "Sustainability and Resilience Revisited: Impact of Information Technology Disruptions on Empirical Retail Logistics Efficiency," Sustainability, MDPI, vol. 13(10), pages 1-20, May.
    10. Leonidas Sotirios Kyrgiakos & Georgios Kleftodimos & George Vlontzos & Panos M. Pardalos, 2023. "A systematic literature review of data envelopment analysis implementation in agriculture under the prism of sustainability," Operational Research, Springer, vol. 23(1), pages 1-38, March.
    11. Josef Jablonský, 2019. "Data Envelopment Analysis Models in Non-Homogeneous Environment," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 67(6), pages 1535-1540.
    12. 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.
    13. Adel Hatami-Marbini & Saber Saati & Seyed Mojtaba Sajadi, 2018. "Efficiency analysis in two-stage structures using fuzzy data envelopment analysis," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 909-932, December.
    14. Thies, Christian & Kieckhäfer, Karsten & Spengler, Thomas S. & Sodhi, Manbir S., 2019. "Operations research for sustainability assessment of products: A review," European Journal of Operational Research, Elsevier, vol. 274(1), pages 1-21.
    15. Zhou, Anhua & Li, Jun, 2021. "Investigate the impact of market reforms on the improvement of manufacturing energy efficiency under China’s provincial-level data," Energy, Elsevier, vol. 228(C).
    16. Abbas Mardani & Dalia Streimikiene & Tomas Balezentis & Muhamad Zameri Mat Saman & Khalil Md Nor & Seyed Meysam Khoshnava, 2018. "Data Envelopment Analysis in Energy and Environmental Economics: An Overview of the State-of-the-Art and Recent Development Trends," Energies, MDPI, vol. 11(8), pages 1-21, August.
    17. Taylan G. Topcu & Konstantinos Triantis, 2022. "An ex-ante DEA method for representing contextual uncertainties and stakeholder risk preferences," Annals of Operations Research, Springer, vol. 309(1), pages 395-423, February.
    18. Ruomeng Zhou & Yunsheng Zhang, 2023. "Measurement of Urban Green Total Factor Productivity and Analysis of Its Temporal and Spatial Evolution in China," Sustainability, MDPI, vol. 15(12), pages 1-32, June.
    19. Ghasemi, M.-R. & Ignatius, Joshua & Emrouznejad, Ali, 2014. "A bi-objective weighted model for improving the discrimination power in MCDEA," European Journal of Operational Research, Elsevier, vol. 233(3), pages 640-650.
    20. Santos, Sérgio P. & São José, José M.S., 2018. "Measuring and decomposing the gender pay gap: A new frontier approachAuthor-Name: Amado, Carla A.F," European Journal of Operational Research, Elsevier, vol. 271(1), pages 357-373.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:fuzodm:v:19:y:2020:i:3:d:10.1007_s10700-020-09321-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.