A Brief Introduction to Some Pure Mathematical Topics

As known to us, the theory of classical sets is the foundation on which modern mathematics rests. When sets are fuzzified, some traditional pure mathematical branches are accordingly generalized. In this chapter, we introduce three well-developed fuzzified mathematical areas briefly to have a glance at how a pure mathematical theory can be fuzzified. The three areas are (i) fuzzy measures and fuzzy integrals (ii) fuzzy algebraic structures including fuzzy groups, fuzzy rings and fuzzy fields (iii) fuzzy topology. This chapter will be mainly for authors with the elementary knowledge of the corresponding classical mathematical branches and it will supply them with basic materials for further reading or research.