 Given a group G, a fuzzy subgroup of G is a fuzzy submonoid s of G such that 

It is possible to prove that the notion of fuzzy subgroup is strictly related with the notions of fuzzy equivalence.In fact, assume that S is a set, G a group of transformations in S and (G,s) a fuzzy subgroup of G. Then, by setting 


we obtain a fuzzy equivalence.Conversely, let e be a fuzzy equivalence in S and, for every transformation h of S, set 


Then s defines a fuzzy subgroup of transformation in S. In a similar way we can relate the fuzzy submonoids with the fuzzy orders.