Authors: Budimirović, Branka
Budimirović, Vjekoslav
Šešelja, Branimir
Tepavčević, Andreja 
Title: Fuzzy equational classes
Journal: IEEE International Conference on Fuzzy Systems
Issue Date: 23-Oct-2012
Rank: M33
ISBN: 978-146731506-7
ISSN: 1098-7584
DOI: 10.1109/FUZZ-IEEE.2012.6251259
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.
Keywords: fuzzy algebra | fuzzy direct product | fuzzy equality | fuzzy equational class | fuzzy homomorphism | fuzzy identity | fuzzy variety
Publisher: IEEE

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