Relations in Fuzzy Class Theory

  • Authors:

  • Libor Běhounek;Ulrich Bodenhofer;Petr Cintula

  • Affiliations:

  • Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic;Institute of Bioinformatics, Johannes Kepler University Linz, Altenberger Str. 69, A-4040 Linz, Austria;Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2008

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Abstract

This paper studies fuzzy relations in the graded framework of Fuzzy Class Theory (FCT). This includes (i) rephrasing existing work on graded properties of binary fuzzy relations in the framework of Fuzzy Class Theory and (ii) generalizing existing crisp results on fuzzy relations to the graded framework. Our particular aim is to demonstrate that Fuzzy Class Theory is a powerful and easy-to-use instrument for handling fuzzified properties of fuzzy relations. This paper does not rephrase the whole theory of (fuzzy) relations; instead, it provides an illustrative introduction showing some representative results, with a strong emphasis on fuzzy preorders and fuzzy equivalence relations.