Practical Applications of Data Mining

8.3 Fuzzy Set applICatIonS 341

of a fuzzy set depends on the problem that needs to be solved and the infor-

mation that is to be retrieved. Membership functions can be as simple as any

linear relation or as complicated as any mathematically complex function.

Furthermore, membership functions can be multidimensional.

Basic operations in fuzzy-set theory include union, intersection, empty,

equal, complement, and containment. For example, union (∪) and intersec-

tion (∩) are defined by the following formulas, in which m means member-

of function, A and B are fuzzy sets, Max( ) returns the largest value, and

Min( ) returns the smallest value from the set:

C = A ∪ B, where mC(x) = Max(mA(x), mB(x))

C = A ∩ B, where mC(x) = Min(mA(x), mB(x))

Extended ...