Fuzzy homomorphisms of algebras

  • Authors:

  • Jelena Ignjatović;Miroslav Ćirić;Stojan Bogdanović

  • Affiliations:

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

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2009

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Abstract

In this paper we consider fuzzy relations compatible with algebraic operations, which are called fuzzy relational morphisms. In particular, we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations, called uniform fuzzy relational morphisms, and those which are partially uniform F-functions, called fuzzy homomorphisms. Both uniform fuzzy relations and partially uniform F-functions were introduced in a recent paper by us. Uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras. We give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms, we establish certain relationships between them and fuzzy congruences, and we prove homomorphism and isomorphism theorems concerning them. We also point to some applications of uniform fuzzy relational morphisms.