Extension collection;  Cantor collection;  Fuzzy collection;  Extensibility

Extension sets are one of the fundamental concepts of extension theory. Discussing the characteristics of the Extension set and its relationship with other sets is very important for clarifying the survival basis, research value and development prospect of extensions. By comparing the identification and classification principles of domain elements of three sets, it is pointed out that the Fuzzy set Extension set is based on the Cantor set, but each has irreplaceable uniqueness of other sets. The Extension set is characterized by its recognition angle of the potential attributes of the domain elements and the recognition of the translatability of the element attributes under specific transformations.