A fuzzy system is a kind of system based on knowledge or rule. The development of fuzzy techniques in knowledge processing results in the emergence of extensions of fuzzy sets theory. In this paper, the generation and evolution of fuzzy sets theory, their applications in and effects on the area of AI and knowledge processing are first described. Then, the definitions and descriptions of extensions of fuzzy sets, such as intuitional fuzzy sets, L-fuzzy sets and L-IFS, interval - valued fuzzy sets and IVIFS, vague sets, etc., are exposed. Finally, a discussion is made with emphasis on the relations among the extensions of fuzzy sets theory and all - sets theory, which could probably result in a significant impact on the evolution of the theory, and a hypothesis is proposed on building the links among extensions of fuzzy sets by means of a kind of mapping or operators. The conclusion is that the IFS is one of the most important extensions of fuzzy sets theory.