ABSTRACT
Extension set is a concept of sets proposed and gradually developed against the background of variable classification and a contradictory problem's quantitative judgement. It is a formalized quantitative tool that can be used to describe the contradictory problem and its converting process. It is also a set theoretic basis for judging contradictory degree and converting degree before and after a transformation is employed. Extension sets can be used to study variables' classification, cluster, recognition, control, and so on.
