Fuzzy rough sets based on residuated lattices

  • Authors:
  • Anna Maria Radzikowska;Etienne E. Kerre

  • Affiliations:
  • Faculty of Mathematics and Information Science, Warsaw university of Technology, Warsaw, Poland;Dept. of Mathematics and Computer Science, Ghent University, Gent, Belgium

  • Venue:
  • Transactions on Rough Sets II
  • Year:
  • 2005

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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.