Abstract: Following Cantor set and fuzzy set, extension set is another basic set put forward by Chinese scholars. It explored the degrees that research objects possessed certain characteristics and their transformations from transformable perspective. The degrees were weighed quantitatively by the use of dependent functions. Then, they were used to study changing classifications, classified changes and the transforming of contradictory problems. The differentiation and affiliation of the three sets mentioned above were analyzed, and the recent research progress in the formation of elementary dependent functions in extension sets was introduced. The farther lucubrating for dependent functions in extension sets will have important scientific significance and applied values for extension strategy generating system, extension data mining, extension control and extension detecting, etc.