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Rough Set Approximations in Multi-scale Interval Information Systems

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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9437))

Abstract

With the view point of granular computing, the notion of a granule may be interpreted as one of the numerous small particles forming a larger unit. There are different granules at different levels of scale in data sets having hierarchical structures. Human beings often observe objects or deal with data hierarchically structured at different levels of granulations. And in real-world applications, there may exist multiple types of data in interval information systems. Therefore, the concept of multi-scale interval information systems is first introduced in this paper. The lower and upper approximations in multi-scale interval information systems are then defined, and the accuracy and the roughness are also explored. Monotonic properties of these rough set approximations with different levels of granulations are analyzed with illustrative examples.

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Acknowledgments

This work is supported by grants from the National Natural Science Foundation of China (Nos. 61272021, 61202206 and 61173181), and the Zhejiang Provincial Natural Science Foundation of China (Nos. LZ12F03002, LY14F030001), and the Open Foundation from Marine Sciences in the Most Important Subjects of Zhejiang (No. 20130109).

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Authors and Affiliations

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

    Shen-Ming Gu, Ya-Hong Wan, Wei-Zhi Wu & Tong-Jun Li

  2. Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Shen-Ming Gu, Ya-Hong Wan, Wei-Zhi Wu & Tong-Jun Li

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  1. Shen-Ming Gu
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  2. Ya-Hong Wan
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  3. Wei-Zhi Wu
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  4. Tong-Jun Li
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Correspondence to Shen-Ming Gu .

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Editors and Affiliations

  1. University of Regina, Regina, SK, Canada

    Yiyu Yao

  2. Tianjin University, Tianjin, China

    Qinghua Hu

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Hong Yu

  4. University of Kansas, Lawrence, KS, USA

    Jerzy W. Grzymala-Busse

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Gu, SM., Wan, YH., Wu, WZ., Li, TJ. (2015). Rough Set Approximations in Multi-scale Interval Information Systems. In: Yao, Y., Hu, Q., Yu, H., Grzymala-Busse, J.W. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Lecture Notes in Computer Science(), vol 9437. Springer, Cham. https://doi.org/10.1007/978-3-319-25783-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-25783-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25782-2

  • Online ISBN: 978-3-319-25783-9

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