In the paper, new definition of type-2 fuzzy sets (T2 FSs) are introduced, and then some basic concepts such as unit fuzzy set, embedded unit fuzzy sets, closure of support (CoS), restriction of type-2 fuzzy set at a point, etc. and partition of CoS is given to represent general type-2 fuzzy sets, finally, the connections among the restriction of T2 FSs at a point, primary membership function, CoS, embedded type-2 fuzzy set are discussed.