Fuzzy relation

A fuzzy relation is the cartesian product of mathematical fuzzy sets.^[1] Two fuzzy sets are taken as input, the fuzzy relation is then equal to the cross product of the sets which is created by vector multiplication. Usually, a rule base is stored in a matrix notation which allows the fuzzy controller to update its internal values.^[2][3]

Cartesian Product

From a historical perspective, the first fuzzy relation was mentioned in the year 1971 by Lotfi A. Zadeh.^[4]

A practical approach to describe a fuzzy relation is based on a 2d table. At first, a table is created which consists of fuzzy values from 0..1. The next step is to apply the if-then-rules to the values. The resulting numbers are stored in the table as an array.

Fuzzy relations can be utilized in fuzzy databases.^[5]