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Attribute reduction in inconsistent formal decision contexts based on congruence relations

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Abstract

In this paper, notions and methods of attribute reduction are investigated for an inconsistent formal decision context. Based on congruence relations defined on the object power set, we first introduce notions of distribution attribute reduct and maximum distribution attribute reduct for an inconsistent formal decision context, and discuss their relations in detail. We then define discernibility matrices and discernibility functions associated with the proposed attribute reducts, from which we can calculate all attribute reducts. Finally, we compare the proposed consistent sets with four types of consistent sets in previously published papers. The results show that a distribution consistent set belongs to any of those four types of consistent sets. Therefore, it has all the properties of those four types of consistent sets.

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Acknowledgments

This work was supported by the Natural Science Foundation of China (Nos. 11202187, 61573321, 61202206 and 61272021) and the Open Foundation from Marine Science in the Most Important Subjects of Zhejiang.

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Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, China

    Jun-Yu Li, Xia Wang, Wei-Zhi Wu & You-Hong Xu

  2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, 316022, Zhejiang, China

    Jun-Yu Li, Xia Wang, Wei-Zhi Wu & You-Hong Xu

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  1. Jun-Yu Li
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Correspondence to Xia Wang.

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Li, JY., Wang, X., Wu, WZ. et al. Attribute reduction in inconsistent formal decision contexts based on congruence relations. Int. J. Mach. Learn. & Cyber. 8, 81–94 (2017). https://doi.org/10.1007/s13042-016-0586-z

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