First of all an error in Reference is pointed out. It is also pointed out that in the results of the intuitionistic fuzzy set being decomposed itself appears in the decomposition as a constructive team and a great deal of teams in the decomposition are repeated. A standpoint is put forward that a decomposition theorem of a (intuitionistic) fuzzy set expresses the (intuitionistic) fuzzy set as a union or an intersection of a family of other (intuitionistic) fuzzy sets which are related to the (intuitionistic) fuzzy set and have some common characteristic. And then on the basis of introducing concepts of -cut products (strong -cut products) and -cut sums (strong -cut sums) of fuzzy sets and intuitionistic fuzzy sets, a fundamental theorem of intuitionistic fuzzy sets is given which shows that all the -cut products and -cut sums (go without saying, strong -cut products and strong -cut sums) of any intuitionistic fuzzy set are still intuitionistic fuzzy sets. It also proves that any fuzzy set or intuitionistic fuzzy set is equal to the union of all the -cut products (all the strong -cut products) as well as equal to the intersection of all the -cut sums (all the strong -cut sums) of it, these results are respectively called the decomposition theorems of fuzzy sets and intuitionistic fuzzy sets.