Authors: Budimirović, Branka
Budimirović, Vjekoslav
Šešelja, Branimir
Tepavčević, Andreja 
Title: E-fuzzy groups
Journal: Fuzzy Sets and Systems
Volume: 289
First page: 94
Last page: 112
Issue Date: 15-Apr-2016
Rank: M21a
ISSN: 0165-0114
DOI: 10.1016/j.fss.2015.03.011
Abstract: 
An E-fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one - denoted by E. The classical group-like properties are formulated as appropriate fuzzy identities - special lattice-theoretic formulas. We prove basic features of E-fuzzy groups: properties of the unit and inverses, cancellability, solvability of equations, subgroup properties and others. We also prove that for every cut of an E-fuzzy group, which is a classical subalgebra of the underlying algebra, the quotient structure over the corresponding cut of the fuzzy equality is a classical group.
Keywords: Complete lattice | Fuzzy algebra | Fuzzy congruence | Fuzzy equality | Fuzzy group | Fuzzy identity
Publisher: Elsevier
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 and Technological Development, Autonomous Province of Vojvodina, Grant “Ordered structures and applications”

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