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Improvement of cross-efficiency based on TODIM method

  • Fuzzy systems and their mathematics
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Abstract

Cross-efficiency evaluation is an extended form of DEA evaluation. The main difference from other models is that the evaluation of cross-efficiency takes the self-evaluation value and other evaluation values as the final efficiency score, and then ranks the decision-making units (DMUs). However, the traditional cross-efficiency model cannot guarantee the uniqueness of input weights and output weights, and the final result does not reach Pareto optimal. Also, the simple average aggregation of cross-efficiency values ignores the relative weight of DMUs and loses a lot of decision-making information, which leads to the lack of credibility of the results. Considering the decision information carried by the data and the weight of the decision-makers (DMs), this paper proposes an aggregate method of interval cross-efficiency matrix to realize the relative efficiency evaluation and the accurate ranking of the DMUs. In which DMUs are regarded as DMs, and then the relative weights of DMUs are determined by using the method of Decision-making trial and evaluation laboratory (DEMATEL), and the relative advantage scores are obtained by considering the risk attitude of decision-makers based on the principle of the improved TODIM method. Finally, a numerical example is used to verify the feasibility and effectiveness of the proposed method, and the stability of the proposed method is verified by changing the value of \(\theta\). Compared with the simple average aggregation method of cross-efficiency values, the proposed method is more reasonable and feasible.

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Acknowledgements

This work was supported in part by the Fund for Shanxi “1331 Project” Key Innovative Research Team (TD201710), and in part by “The Discipline Group Construction Plan for Serving Industries Innovation,” Shanxi, China: The Discipline Group Program Intelligent Logistics Management for Serving Industries Innovation (XKQ201801).

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Jian Ping Fan was involved in funding acquisition. Mei Qin Wu was involved in methodology. Xiaoqing Hou was involved in writing an original draft and writing—review & editing.

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Correspondence to Jianping Fan.

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Wu, M., Hou, X. & Fan, J. Improvement of cross-efficiency based on TODIM method. Soft Comput 26, 8427–8439 (2022). https://doi.org/10.1007/s00500-022-07229-y

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