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Generalizations of Rough Sets and Rule Extraction

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Transactions on Rough Sets I

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3100))

Abstract

In this paper, two kinds of generalizations of rough sets are proposed based on two different interpretations of rough sets: one is an interpretation of rough sets as approximation of a set by means of elementary sets and the other is an interpretation of rough sets as classification of objects into three different classes, i.e., positive objects, negative objects and boundary objects. Under each interpretation, two different definitions of rough sets are given depending on the problem setting. The fundamental properties are shown. The relations between generalized rough sets are given. Moreover, rule extraction underlying each rough set is discussed. It is shown that rules are extracted based on modified decision matrices. A simple example is given to show the differences in the extracted rules by underlying rough sets.

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Authors and Affiliations

  1. Division of Mathematical Science for Social Systems, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, Osaka, 560-8531, Japan

    Masahiro Inuiguchi

Authors
  1. Masahiro Inuiguchi
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron  & Marcin S. Szczuka  & 

  3. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

  4. Multimedia Systems Department, Gdańsk University of Technology, Narutowicza 11/12, 80-952, Gdańsk, Poland

    Bożena Kostek

  5. Department of Mathematical and Computer Sciences, San Diego State University, 5500 Campanile Drive, CA 92182, San Diego, USA

    Roman W. Åšwiniarski

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© 2004 Springer-Verlag Berlin Heidelberg

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Inuiguchi, M. (2004). Generalizations of Rough Sets and Rule Extraction. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Świniarski, R.W., Szczuka, M.S. (eds) Transactions on Rough Sets I. Lecture Notes in Computer Science, vol 3100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27794-1_4

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  • DOI: https://doi.org/10.1007/978-3-540-27794-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22374-0

  • Online ISBN: 978-3-540-27794-1

  • eBook Packages: Springer Book Archive

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