Relations in Fuzzy Class Theory: Initial steps

Libor Běhounek, Ulrich Bodenhofer, Petr Cintula

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1729-1772
Number of pages44
JournalFuzzy Sets and Systems
Issue number14
Publication statusPublished - 16 Jul 2008
Externally publishedYes


  • Fuzzy Class Theory
  • Fuzzy equivalence relation
  • Fuzzy preorder
  • Fuzzy relation
  • Graded properties
  • Similarity


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