Fuzzy equivalence relations and their equivalence classes

  • Authors:

  • Miroslav Ćirić;Jelena Ignjatović;Stojan Bogdanović

  • Affiliations:

  • Faculty of Sciences and Mathematics, University of Niš, Višegradska 33. P.O. Box 224, 18000 Niš, Serbia and Montenegro;Faculty of Sciences and Mathematics, University of Niš, Višegradska 33. P.O. Box 224, 18000 Niš, Serbia and Montenegro;Faculty of Economics, University of Niš, Trg Kralja Aleksandra 11, 18000 Niš, Serbia and Montenegro

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semi-partitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered complete Heyting algebra, we construct an algorithm for calculation of a minimal family of its equivalence classes which generates it. Most of the presented results are new, but some of them are generalizations of known results given in a way which simplifies and clarifies them.