Firstly, the definitions of modular operations, the relationship between intuitionistic fuzzy sets (IFSs) and their composition operations are introduced, then the definition of truncated set for IFSs is presented, and the principle for classification using intuitionistic fuzzy equivalent relations is reveled. The clustering algorithm based on intuitionistic fuzzy equivalent relations is discussed, so the basic theorems of IFSs are further generalized. Finally, a numerical example is given.