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Dependence space of topology and its application to attribute reduction

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Abstract

Attribute reduction plays an important role in pattern recognition and machine learning. Covering-based rough sets, as a technique of granular computing, can be a useful tool for studying attribute reduction. Topology has a close relationship with rough sets and plays a significant role in attribute reduction in information systems. So it is meaningful to combine topology with rough sets to address the problems of attribute reduction. In this paper, we mainly discuss and address the problem of attribute reduction in incomplete information systems with dependence space induced by topological base. Firstly, we investigate the topological structure induced by covering-based rough sets and some characteristics of the topological structure are presented. Secondly, a new type of dependence space is constructed in terms of the base of topological structure, and some characteristics of the dependence space are investigated. Finally, we apply the obtained results of the space to the attribute reduction in incomplete information systems. Especially, a discernibility matrix is defined for the attribute reduction in incomplete information systems.

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Acknowledgments

This work is in part supported by the National Science Foundation of China under Grant Nos. 61472406, 61379049, and 61379089, the Natural Science Foundation of Fujian Province under Grant No. 2015J01269 and No. 2016J01304.

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Authors and Affiliations

  1. Department of Computing, Dongfang College, Fujian Agriculture and Forestry University, Fuzhou, 350017, China

    Lirun Su

  2. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610054, China

    William Zhu

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  1. Lirun Su
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  2. William Zhu
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Correspondence to Lirun Su.

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Su, L., Zhu, W. Dependence space of topology and its application to attribute reduction. Int. J. Mach. Learn. & Cyber. 9, 691–698 (2018). https://doi.org/10.1007/s13042-016-0598-8

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  • DOI: https://doi.org/10.1007/s13042-016-0598-8

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