8.6.4. Transformations Between Fuzzy Sets and Ordinary Sets
Definition 7. Given F(W), for any l [0, 1]
Al = { wm ³ l } is called the l-level cut of .
If any w whose membership value exceeds l is considered as a member of , then fuzzy set becomes ordinary set Al .
For instance, from = (1, 0.8, 0.4, 0) we have
C1 = {0} , C0.5 = C0.8 = {a, b} .
If F(W) , it can be proven that
m = ,
where XAl is the characteristic function for Al . This theorem and the level cut concept are the linkages for conversions between fuzzy sets and ordinary sets.