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Springer Handbook of Computational Intelligence pp 413–424Cite as

Generalized Rough Sets

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Abstract

This chapter reviews three formulations of rough set theory, i. e., element-based definition, granule-based definition, and subsystem-based definition. These formulations are adopted to generalize rough sets from three directions. The first direction is to use an arbitrary binary relation to generalize the equivalence relation in the element-based definition. The second is to use a covering to generalize the partition in the granule-based definition, and the third to use a subsystem to generalize the Boolean algebra in the subsystem-based definition. In addition, we provide some insights into the theoretical aspects of these generalizations, mainly with respect to relations with non-classical logic and topology theory.

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Abbreviations

DAL:

logic for data analysis

NIL:

nondeterministic information logic

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Author information

Authors and Affiliations

  1. Dep. Computer Science, University of Regina, 3737 Wascana Parkway, S4S 0A2, Regina, Saskatchewan, Canada

    JingTao Yao & Yan Zhang

  2. Dep. Informatics, Systems and Communications, University of Milano-Bicocca, viale Sarca 336/14, 20126, Milano, Italy

    Davide Ciucci

Authors
  1. JingTao Yao
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  2. Davide Ciucci
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  3. Yan Zhang
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Correspondence to JingTao Yao .

Editor information

Editors and Affiliations

  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

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Yao, J., Ciucci, D., Zhang, Y. (2015). Generalized Rough Sets. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_25

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  • DOI: https://doi.org/10.1007/978-3-662-43505-2_25

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