Free Fuzzy Subgroups and Fuzzy Subgroup Presentations

Abstract

In this chapter, we define a notion of a free fuzzy subgroup and study its basic properties. We examine two approaches. The first approach is based on the work appearing in [18]. It uses the notion of levels and leads to the development of the notion of a presentation of a fuzzy subgroup. The definition of a presentation for a fuzzy subgroup provides a convenient method of defining fuzzy subgroups and opens the door for a development of a combinatorial group theory for fuzzy subgroups. The second approach follows along the lines of [28, 36]. The development here is presented in Section 5.3.