In mathematics, vague sets are an extension of fuzzy sets.
In a fuzzy set, each object is assigned a single value in the interval [0,1] reflecting its grade of membership. This single value does not allow a separation of evidence for membership and evidence against membership.
Gau et al. proposed the notion of vague sets, where each object is characterized by two different membership functions: a true membership function and a false membership function. This kind of reasoning is also called interval membership, as opposed to point membership in the context of fuzzy sets.
Mathematical definition
A vague set
The grade of membership for x is not a crisp value anymore, but can be located in