E-fuzzy groups

Branka Budimirović, Vjekoslav Budimirović, Branimir Šešelja, Andreja Tepavčević
2016 Fuzzy sets and systems (Print)  
B.&V. Budimirović, B.Šešelja, A. Tepavčević E-Fuzzy Groups Abstract 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
more » ... uations, 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.
doi:10.1016/j.fss.2015.03.011 fatcat:3luabpguezdhpc3ydhtnm5ap7a