Some constructions of the join of fuzzy subgroups and certain lattices of fuzzy subgroups with sup property
In this paper, some new lattices of fuzzy substructures are constructed. For a given fuzzy set ? ? in a group G , a fuzzy subgroup S(?) S ( ? ) generated by ? ? is defined which helps to establish that the set Ls L s of all fuzzy subgroups with sup property constitutes a lattice. Consequently, many other sublattices of the lattice L L of all fuzzy subgroups of G  like L s t , L s n , L s n t , etc. are also obtained. The notion of infimum is used to construct a fuzzy subgroup i(?) i ( ? ) generated by a given fuzzy set ? ? , in contrast to the usual practice of using supremum. In the process a new fuzzy subgroup i(?)? i ( ? ) ? is defined which we shall call a shadow fuzzy subgroup of ? ? . It is established that if ? ? has inf property, then i(?)? i ( ? ) ? also has this property.
fuzzy subgroup lattice sup property shadow fuzzy subgroup inf property generated fuzzy subgroup