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Improving discrimination in data envelopment analysis without losing information based on Renyi’s entropy

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Abstract

Data envelopment analysis (DEA) heavily depends on the dimensionality of the variables, and previous studies address the problem by decreasing the dimensionality with a minimal loss of information. Since the lost information can also have the impact on the evaluation performance, this paper accordingly proposes an approach to improve the discriminatory power of DEA without losing any variables information and without requiring any additional preferential information. Furthermore, an accelerating approach based on the concept of parallel computing is introduced to solve the multi-subsets problem. Listing all the possible variables subsets as the nodes, then the DEA efficiencies under each node are calculated, and the corresponding purity of information can be scientifically generated based on Renyi’s entropy. Subsequently, the important degrees of nodes are obtained by normalizing the purities of information, and the comprehensive efficiency scores can be finally generated by the weighted sum between the important degrees and the efficiencies under the corresponding node. Two specific examples are provided to evaluate the performance.

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Acknowledgements

This research is supported by National Natural Science Foundation of China under Grants (Nos. 61673381 and 61773029), Social Science Foundation of Beijing under Grant (No. 16JDGLC005) and the Project of Great Wall Scholar, Beijing Municipal Commission of Education (CIT&TCD20180305).

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Authors and Affiliations

  1. School of Economics and Management, Beijing University of Technology, Beijing, 100124, China

    Qiwei Xie & Chao Liu

  2. Research Base of Beijing Modern Manufacturing Development, Beijing, 100124, China

    Qiwei Xie & Chao Liu

  3. Faculty of Mathmatics and statistics, Hubei Univeristy, Wuhan, 430062, China

    Yuanyuan Li

  4. School of Management, University of Science and Technology of China, Hefei, 230026, China

    Lizheng Wang

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  1. Qiwei Xie
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  2. Yuanyuan Li
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  3. Lizheng Wang
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  4. Chao Liu
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Correspondence to Chao Liu.

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Xie, Q., Li, Y., Wang, L. et al. Improving discrimination in data envelopment analysis without losing information based on Renyi’s entropy. Cent Eur J Oper Res 26, 1053–1068 (2018). https://doi.org/10.1007/s10100-018-0550-y

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  • DOI: https://doi.org/10.1007/s10100-018-0550-y

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