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The Efficiency Evaluation of DEA Model Incorporating Improved Possibility Theory

Author

Listed:
  • Shenzi Yang

    (College of Air Traffic Management, Civil Aviation Flight University of China, Guanghan 618307, China)

  • Guoqing Zhao

    (College of Air Traffic Management, Civil Aviation Flight University of China, Guanghan 618307, China)

  • Fan Li

    (CAAC Key Laboratory of Flight Techniques and Flight Safety, Civil Aviation Flight University of China, Guanghan 618307, China)

Abstract

The data envelopment analysis (DEA) models have been widely recognized and applied in various fields. However, these models have limitations, such as their inability to globally rank DMUs, the efficiency values are definite numerical values, they are unable to reflect potential efficiency changes, and they fail to adequately reflect the degree of the decision maker’s preference. In order to address these shortcomings, this paper combines possibility theory with self-interest and non-self-interest principles to improve the DEA model to provide a more detailed reflection of the differences between DMUs. First, the self-interest and non-self-interest principles are employed to establish the DEA evaluation model, and the determined numerical efficiency is transformed into efficiency intervals. Second, an attitude function is added to the common possible-degree formula to reflect the decision maker’s preference, and a more reasonable method for solving the attitude function is presented. Finally, the improved possible-degree formula proposed in this paper is used to rank and compare the interval efficiencies. This improved method not only provides more comprehensive ranking information but also better captures the decision maker’s preferences. This model takes preference issues into account and has improved stability and accuracy compared with existing models. The application of the improved model in airlines shows that the model proposed in this paper effectively achieved a full ranking. From a developmental perspective, the efficiency levels of Chinese airlines were generally comparable. Joyair and One Two Three performed poorly, exhibiting significant gaps compared with other airlines.

Suggested Citation

  • Shenzi Yang & Guoqing Zhao & Fan Li, 2024. "The Efficiency Evaluation of DEA Model Incorporating Improved Possibility Theory," Mathematics, MDPI, vol. 12(19), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3116-:d:1492496
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    References listed on IDEAS

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    1. Cheng, Gang & Zervopoulos, Panagiotis D., 2014. "Estimating the technical efficiency of health care systems: A cross-country comparison using the directional distance function," European Journal of Operational Research, Elsevier, vol. 238(3), pages 899-910.
    2. Qingxian An & Fanyong Meng & Beibei Xiong, 2018. "Interval cross efficiency for fully ranking decision making units using DEA/AHP approach," Annals of Operations Research, Springer, vol. 271(2), pages 297-317, December.
    3. Chen, Lei & Huang, Yan & Li, Mei-Juan & Wang, Ying-Ming, 2020. "Meta-frontier analysis using cross-efficiency method for performance evaluation," European Journal of Operational Research, Elsevier, vol. 280(1), pages 219-229.
    4. 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.
    5. John S. Liu & Louis Y. Y. Lu & Wen-Min Lu, 2016. "Research Fronts and Prevailing Applications in Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, chapter 0, pages 543-574, Springer.
    6. Barbot, Cristina & Costa, Ã lvaro & Sochirca, Elena, 2008. "Airlines performance in the new market context: A comparative productivity and efficiency analysis," Journal of Air Transport Management, Elsevier, vol. 14(5), pages 270-274.
    7. Maiquiel Schmidt de Oliveira & Mauro Lizot & Hugo Siqueira & Paulo Afonso & Flavio Trojan, 2023. "Efficiency Analysis of Oil Refineries Using DEA Window Analysis, Cluster Analysis, and Malmquist Productivity Index," Sustainability, MDPI, vol. 15(18), pages 1-19, September.
    8. Ghasemi, Mohammad Reza & Ignatius, Joshua & Rezaee, Babak, 2019. "Improving discriminating power in data envelopment models based on deviation variables framework," European Journal of Operational Research, Elsevier, vol. 278(2), pages 442-447.
    9. Min, Hokey & Joo, Seong-Jong, 2016. "A comparative performance analysis of airline strategic alliances using data envelopment analysis," Journal of Air Transport Management, Elsevier, vol. 52(C), pages 99-110.
    10. Wu, Jie & Chu, Junfei & Sun, Jiasen & Zhu, Qingyuan, 2016. "DEA cross-efficiency evaluation based on Pareto improvement," European Journal of Operational Research, Elsevier, vol. 248(2), pages 571-579.
    11. 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.
    12. Lee, Boon L. & Worthington, Andrew C., 2014. "Technical efficiency of mainstream airlines and low-cost carriers: New evidence using bootstrap data envelopment analysis truncated regression," Journal of Air Transport Management, Elsevier, vol. 38(C), pages 15-20.
    13. Ruiz, José L., 2013. "Cross-efficiency evaluation with directional distance functions," European Journal of Operational Research, Elsevier, vol. 228(1), pages 181-189.
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