Authors: Budimirović, Branka
Budimirović, Vjekoslav
Šešelja, Branimir
Tepavčević, Andreja 
Title: Fuzzy identities with application to fuzzy semigroups
Journal: Information Sciences
Volume: 266
First page: 148
Last page: 159
Issue Date: 10-May-2014
Rank: M21a
ISSN: 0020-0255
DOI: 10.1016/j.ins.2013.11.007
The notion of a fuzzy identity is introduced on a fuzzy subalgebra in the framework of fuzzy equalities instead of the crisp one. A fuzzy identity may be satisfied by a fuzzy subalgebra, while the underlying crisp algebra need not satisfy the analogous crisp identity. Among other properties, it is shown that for every fuzzy subalgebra μ of A there is a least fuzzy equality such that a fuzzy identity holds on μ. As an application, fuzzy semigroups are introduced with respect to a fuzzy equality. In particular, fuzzy semilattices, cancellative and regular fuzzy semigroups are investigated.
Keywords: Complete lattice | Fuzzy algebra | Fuzzy congruence | Fuzzy equality | Fuzzy identity | Fuzzy semigroup
Publisher: Elsevier
Project: Development of methods of computation and information processing: theory and applications 
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 
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, grant ”Ordered structures and applications”

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