A comparative study of fuzzy rough sets

  • Authors:

  • Anna Maria Radzikowska;Etienne E. Kerre

  • Affiliations:

  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, Warsaw, Poland;Department of Applied Mathematics and Computer Science, University of Gent, Krijgslaan 281 (S9), Gent, Belgium

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2002

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Abstract

The notion of a rough set was originally proposed by Pawlak (1982). Later on, Dubois and Prade (1990) introduced fuzzy rough sets as a fuzzy generalization of rough sets. In this paper, we present a more general approach to the fuzzification of rough sets. Specifically, we define a broad family of fuzzy rough sets, each one of which, called an (I, J)-fuzzy rough set, is determined by an implicator I and a triangular norm J. Basic properties of fuzzy rough sets are investigated. In particular, we define three classes of fuzzy rough sets, relatively to three main classes of implicators well known in the literature, and analyse their properties in the context of basic rough equalities. Finally, we refer to an operator-oriented characterization of rough sets as proposed by Lin and Liu (1994) and show soundness of this axiomatization for the Lukasiewicz fuzzy rough sets.