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Three-Way Decision Making Based on Data Envelopment Analysis with Interval Data

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Abstract

Three-way decision (3WD) is an extensively used decision theory, and it is inspired by a special way of human cognition known as thinking in three. For this reason, three-way decision has attracted the attention of many scholars. In recent years, research on the methodology and application of 3WD has been widely developed. During the decision process, decision-making units (DMUs) are usually divided as efficient and inefficient in data envelopment analysis (DEA), while the decision losses of individual DMUs are not regarded. Therefore, we introduce 3WD to DEA and propose a novel three-way DEA model to supplement the drawbacks of the traditional DEA model. First, we establish a hybrid matrix by combining the matrix of input and output indicators of DEA and the loss function table of 3WD. Afterward, a new method for obtaining the conditional probability of DMUs is presented. Next, optimistic, pessimistic and neutral strategies are developed to calculate the expected losses of three actions: acceptance, deferment and rejection. Finally, the corresponding three-way decision rules are generated. Illustrative examples are presented to demonstrate the application of our proposed model, and a series of comparative analyses are presented. Our study not only expands the application of three-way decision, but also extends the semantic interpretation of 3WD.

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Acknowledgements

This work is partially supported by the National Science Foundation of China (Nos. 61876157, 71571148), the Science Fund for Distinguished Young Scholars of Sichuan Province (No. 22JCQN0135) and the Yanghua Scholar Plan (Part A) of SWJTU.

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  1. School of Economics and Management, Southwest Jiaotong University, Chengdu, 610031, P.R. China

    Qinxia Chen, Dun Liu & Lu Zhang

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  1. Qinxia Chen
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Correspondence to Dun Liu.

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Chen, Q., Liu, D. & Zhang, L. Three-Way Decision Making Based on Data Envelopment Analysis with Interval Data. Cogn Comput 14, 2054–2073 (2022). https://doi.org/10.1007/s12559-021-09964-0

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