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Transactions on Rough Sets II pp 278–296Cite as

Fuzzy Rough Sets Based on Residuated Lattices

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Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3135))

Abstract

Rough sets were developed by Pawlak as a formal tool for representing and processing information in data tables. Fuzzy generalizations of rough sets were introduced by Dubois and Prade. In this paper, we consider L–fuzzy rough sets as a further generalization of the notion of rough sets. Specifically, we take a residuated lattice L as a basic structure. L–fuzzy rough sets are defined using the product operator and its residuum provided by the residuated lattice L. Depending on classes of binary fuzzy relations, we define several classes of L–fuzzy rough sets and investigate properties of these classes.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Information Science, Warsaw university of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland

    Anna Maria Radzikowska

  2. Dept. of Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000, Gent, Belgium

    Etienne E. Kerre

Authors
  1. Anna Maria Radzikowska
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  2. Etienne E. Kerre
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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

  3. Institut de Recherche en Informatique de Toulouse, France

    Didier Dubois

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

    Jerzy W. Grzymała-Busse

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

    Masahiro Inuiguchi

  6. Polish-Japanese Institute of Information Technology Warsaw, Poland Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

    Lech Polkowski

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© 2004 Springer-Verlag Berlin Heidelberg

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Radzikowska, A.M., Kerre, E.E. (2004). Fuzzy Rough Sets Based on Residuated Lattices. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds) Transactions on Rough Sets II. Lecture Notes in Computer Science, vol 3135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27778-1_14

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  • DOI: https://doi.org/10.1007/978-3-540-27778-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23990-1

  • Online ISBN: 978-3-540-27778-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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