- Mathematical definition
- References
- See also
- External links
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.[1] 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 
is characterized by
- its true membership function
- its false membership function
- with
The grade of membership for x is not a crisp value anymore, but can be located in 
. This interval can be interpreted as an extension to the fuzzy membership function. The vague set degrades to a fuzzy set, if 
for all x.
The uncertainty of x is the difference between the upper and lower bounds of the membership interval; it can be computed as 
.
References
See also
- Fuzzy set
- Fuzzy concept
External links
- Vague Sets
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