fuzzy set theory

Fuzzy set theory is one of the forms of fuzzy reasoning. Rather than saying a set has a precise collection of members, values are assigned a level of memership between 0 and 1. So that member(x,S)=1 means that x is definitely a member of the set S; member(y,S)=0 means that y definitely is not, and ; member(z,S)=0.5 means we aren't really sure about z.