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Uncertainty measurement for incomplete set-valued data with application to attribute reduction

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Abstract

A set-valued information system (SVIS) is the generalization of a single-valued information system. A SVIS with missing information values is called an incomplete set-valued information system (ISVIS). This paper focuses on studying uncertainty measurement for an ISVIS with application to attribute reduction. First, the similarity degree between information values on each attribute is presented in an ISVIS. Then, the tolerance relation induced by each subsystem is given and rough approximations based on this relation is considered. Next, some tools to measure the uncertainty of an ISVIS are put forwarded. Moreover, the validity of the proposed measures is analyzed from the statistical point of view. Finally, information granulation and information entropy are applied to attribute reduction, the incomplete rate is adopted, and the effectiveness under different incomplete rates is analyzed and verified by k-means clustering algorithm and Mean Shift clustering algorithm.

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions, which have helped immensely in improving the quality of the paper. This work is supported by National Natural Science Foundation of China (11971420), Natural Science Foundation of Guangxi (AD19245102, 2020GXNSFAA159155, 2018GXNSFDA294003), Key Laborabory of Software Engineering in Guangxi University for Nationalities (2021-18XJSY-03) and Special Scientific Research Project of Young Innovative Talents in Guangxi (2019AC20052).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yulin Normal University, Yulin, Guangxi, 537000, People’s Republic of China

    Yan Song

  2. School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, People’s Republic of China

    Damei Luo

  3. School of Artificial Iintelligence, Guangxi Minzu University, Nanning, Guangxi, 530006, People’s Republic of China

    Ningxin Xie

  4. Key Laboratory of Complex System Optimization and Big Data Processing, Department of Guangxi Education, Yulin Normal University, Yulin, Guangxi, 537000, People’s Republic of China

    Zhaowen Li

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  1. Yan Song
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  2. Damei Luo
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Correspondence to Zhaowen Li.

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Song, Y., Luo, D., Xie, N. et al. Uncertainty measurement for incomplete set-valued data with application to attribute reduction. Int. J. Mach. Learn. & Cyber. 13, 3031–3069 (2022). https://doi.org/10.1007/s13042-022-01580-0

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