Fuzzy equational classes

Abstract

The paper deals with fuzzy equational classes. These are defined as classes of particular fuzzy algebras refereing to a fuzzy equality (which replaces the crisp one), closed with respect to fuzzy identities. In this fuzzy framework we introduce basic notions of universal algebra, (fuzzy) subalgebras, homomorphisms and direct products. Our main result is that every fuzzy equational class is closed under these three constructions, hence forming a fuzzy variety. AMS Mathematics Subject Classification (2000): 03E72. Key words and phrases: fuzzy algebra, fuzzy identity, fuzzy equality, fuzzy homomorphism, fuzzy direct product, fuzzy equational class, fuzzy variety.