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On Lattice–Based Fuzzy Rough Sets

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35 Years of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 261))

Abstract

Rough sets were originally proposed by Pawlak as a formal tool for analyzing and processing incomplete information represented in data tables. Later on, fuzzy generalizations of rough sets were introduced and investigated to be able to deal with imprecision. In this paper we present L-fuzzy rough sets as a further generalization of rough sets. As an underlying algebraic structure we take an extended residuated lattice, that is a residuated lattice endowed with a De Morgan negation. The signature of these structures gives algebraic counterparts of main fuzzy logical connectives. Properties of L-fuzzy rough sets are presented. We show that under some conditions families of all lower (resp. upper) L-fuzzy rough sets are complete (distributive) lattices. It is also pointed out that in some specific cases lower and upper fuzzy rough approximation operators are L-fuzzy topological operators of interior and closure, respectively.

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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

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  1. Anna Maria Radzikowska
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Editors and Affiliations

  1. Ghent University, Gent, Belgium

    Chris Cornelis , Glad Deschrijver , Mike Nachtegael , Steven Schockaert  & Yun Shi , , ,  & 

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Radzikowska, A.M. (2010). On Lattice–Based Fuzzy Rough Sets. In: Cornelis, C., Deschrijver, G., Nachtegael, M., Schockaert, S., Shi, Y. (eds) 35 Years of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16629-7_6

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  • DOI: https://doi.org/10.1007/978-3-642-16629-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16628-0

  • Online ISBN: 978-3-642-16629-7

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