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Granular Structures Induced by Interval Sets and Rough Sets

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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

An interval set is a family of sets restricted by a upper bound and lower bound. Interval-set algebras are concrete models of granular computing. The triarchic theory of granular computing focuses on a multilevel and multi-view granular structure. This paper discusses granular structures of interval sets under inclusion relations between two interval sets from a measurement-theoretic perspective and set-theoretic perspective, respectively. From a measurement-theoretic perspective, this paper discusses preferences on two objects represented by interval sets under inclusion relations on interval sets. From a set-theoretic perspective, this paper uses different inclusion relations and operations on interval sets to construct multilevel and multi-view granular structures.

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Acknowledgements

Authors thanks Prof. Yiyu Yao from the University of Regina for his constructive suggestions on this paper.

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Authors and Affiliations

  1. Department of Life Science and Informatics, Maebashi Institute of Technology, Maebashi City, 371-0816, Japan

    Ning Zhong

  2. International WIC Institute, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Ning Zhong & Jia-jin Huang

Authors
  1. Ning Zhong
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  2. Jia-jin Huang
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Corresponding author

Correspondence to Ning Zhong .

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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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Zhong, N., Huang, Jj. (2015). Granular Structures Induced by Interval Sets and Rough Sets. 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_5

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  • DOI: https://doi.org/10.1007/978-3-319-25783-9_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25782-2

  • Online ISBN: 978-3-319-25783-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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