A Theory of Isomorphisms of Fuzzy Groups

<正> In this paper, a theory of isomorphisms of fuzzy groups is put forward. First, a new definition of isomorphisms of fuzzy groups is proposed and compared with the corresponding ones given in other related papers. Next, some basic properties of this kind of isomorphisms are roughly examined. Then, as the main results of this paper, two basic isomorphism theorems for fuzzy groups are establised. Finally, presenting applications of these theorems, we point out that for any given t-norm T∈■ss∪■H∪■F∪■Y)/{Min}, every T-fuzzy group is isomorphic to a Prod-fuzzy or Tm-fuzzy group, where ■ss, ■H, ■F and ■Y denote the Schweizer-Sklar, Hamacher, Frank and Yager families of t-norms, respectively.