Structures on Fuzzy Groups and L- Fuzzy Number

The theory of fuzzy sets has developed in many directions and is finding applications in a wide variety of fields. Resentful in 1971 used this concept to develop the theory of fuzzy groups in this paper we have given independent proof of several theorems on fuzzy groups. We discuss about Fuzzy groups and investigate some of their structures on the concept of Fuzzy Group family and L- fuzzy number.