|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||Abstract:||
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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