E-fuzzy groups

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 . 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.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 . 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. B.&V. Budimirović, B. Šešelja, A. Tepavčević E-Fuzzy Groups