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Uncertainty Measurement for Set-Valued Data and Its Application in Feature Selection

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Abstract

Uncertainty measurement (UM) provides a new perspective on feature selection in an information system (IS). The intent of this paper is to measure the uncertainty of a set-valued information system (SVIS) from the perspective of “The similarity between information values is fed back to the feature set” and consider its application in feature selection. Based on the similarity between information values, fuzzy symmetry relations on the object set of an SVIS are first established. Secondly, \(\theta\)-information granules based on the fuzzy symmetry relations are obtained. Thirdly, four UMs for an SVIS, including \(\theta\)-information granulation (\(G^\theta\)), \(\theta\)-information entropy (\(H^\theta\)), \(\theta\)-rough entropy (\(E_\mathrm{{r}}^\theta\)) and \(\theta\)-information amount (\(E^\theta\)), are proposed. Moreover, numerical experiments and statistical tests to evaluate the performance of the proposed measurements are carried out. Finally, an application in feature selection for an SVIS is given and the corresponding algorithms based on \(G^\theta\) and \(H^\theta\) are presented, clustering analysis on the reduced SVIS is conducted. The experimental results show that the proposed algorithms are effective according to three evaluation indicators of clustering performance.

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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 study is supported by grants from 2021 High-Level Talent Project of Yulin Normal University (G2021ZK05).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Yulin Normal University, Yulin, 537000, Guangxi, People’s Republic of China

    Yichun Peng

  2. School of Big Data and Artificial Intelligence, Chizhou University, Chizhou, 247000, Anhui, People’s Republic of China

    Qinli Zhang

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  1. Yichun Peng
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Correspondence to Qinli Zhang.

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Peng, Y., Zhang, Q. Uncertainty Measurement for Set-Valued Data and Its Application in Feature Selection. Int. J. Fuzzy Syst. 24, 1735–1756 (2022). https://doi.org/10.1007/s40815-021-01230-7

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  • DOI: https://doi.org/10.1007/s40815-021-01230-7

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