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 image in a group G, a fuzzy subgroup image generated by image is defined which helps to establish that the set image of all fuzzy subgroups with sup property constitutes a lattice. Consequently, many other sublattices of the lattice image of all fuzzy subgroups of G like image, etc. are also obtained. The notion of infimum is used to construct a fuzzy subgroup image generated by a given fuzzy set image, in contrast to the usual practice of using supremum. In the process a new fuzzy subgroup image is defined which we shall call a shadow fuzzy subgroup of image. It is established that if image has inf property, then image also has this property.