The mathematic tools describing large scale systems: fuzzy set, extension set, vague set, set pair analysis and their relation

For the development of artificial intelligence, several new related theories have been formulated to describe fuzzy things, such as fuzzy set, rough set, extension set, vague set and set pair analysis. This paper provides a description of the concept of all set, and analyses the relationships of fuzzy set, rough set, extension set, vague set and set pair analysis.