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Optimal scale selection based on three-way decisions with decision-theoretic rough sets in multi-scale set-valued decision tables

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Abstract

Optimal scale selection (OSS) is a fundamental topic in the studies of multi-scale decision tables (MSDTs). Multi-scale set-valued decision tables (MSSVDTs) widely exist in practical applications, and the attribute value is a linguistic set-value. Existing studies of OSS in the MSDT with cost-sensitive learning have constructed total cost mainly from two aspects: test cost and delay cost. Moreover, they are given subjectively, resulting in a lack of objectivity in the construction of total cost. Therefore, constructing a relatively objective and comprehensive total cost for OSS based on cost-sensitive learning is worthwhile in MSSVDTs. In this paper, we firstly propose a quantization method to reasonably transform the linguistic set-value into a numerical value according to the granular structures. Then, based on three-way decisions with decision-theoretic rough sets, loss functions of every object on different scales are constructed, and uncertainty is quantified. Afterwards, loss functions are introduced into the construction of total cost with regard to OSS. This helps us obtain relatively objective total cost, including test cost, delay cost, and misclassification cost. Furthermore, in light of the idea of Technique for Order Preferences by Similarity to an Ideal Solution, we design an OSS algorithm to select the optimal scale according to the ordered change of uncertainty and total cost. Finally, the feasibility and effectiveness of the proposed algorithm are verified through experiments on UCI data sets.

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by National Science Foundation of China (Nos. 61673285), Sichuan Science and Technology Program of China (Nos. 2021YJ0085), and Natural Science Foundation of Sichuan Province (Nos. 2022NSFSC0569, Nos. 2022NSFSC0929).

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Authors and Affiliations

  1. Department of Computer Science, Sichuan Normal University, Chengdu, 610068, China

    Runkang Li & Jilin Yang

  2. Department of Mathematical Sciences, Sichuan Normal University, Chengdu, 610068, China

    Xianyong Zhang

  3. Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu, China

    Runkang Li, Jilin Yang & Xianyong Zhang

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  1. Runkang Li
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  2. Jilin Yang
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Correspondence to Jilin Yang.

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Li, R., Yang, J. & Zhang, X. Optimal scale selection based on three-way decisions with decision-theoretic rough sets in multi-scale set-valued decision tables. Int. J. Mach. Learn. & Cyber. 14, 3719–3736 (2023). https://doi.org/10.1007/s13042-023-01860-3

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