Authors: Budimirović, Branka
Budimirović, Vjekoslav
Šešelja, Branimir
Tepavčević, Andreja 
Title: Fuzzy equational classes are fuzzy varieties
Journal: Iranian Journal of Fuzzy Systems
Volume: 10
Issue: 4
First page: 1
Last page: 18
Issue Date: 1-Jan-2013
Rank: M21
ISSN: 1735-0654
DOI: 10.22111/ijfs.2013.1044
In the framework of fuzzy algebras with fuzzy equalities and a complete lattice as a structure of membership values, we investigate fuzzy equational classes. They consist of special fuzzy algebras fulfilling the same fuzzy identities, defined with respect to fuzzy equalities. We introduce basic notions and the corresponding operators of universal algebra: construction of fuzzy subalgebras, homomorphisms and direct products. We prove that every fuzzy equational class is closed under these three operators, which means that such a class is a fuzzy variety.
Keywords: Fuzzy algebra | Fuzzy direct product | Fuzzy equality | Fuzzy equational class | Fuzzy homomorphism | Fuzzy identity | Fuzzy variety
Publisher: University of Sistan and Baluchestan
Project: Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Development of methods of computation and information processing: theory and applications 
Provincial Secretariat for Science andTechnological Development, Autonomous Province of Vojvodina, Grant “Ordered structures andapplications”

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