A fuzzy relation is the cartesian product of mathematical fuzzy sets. Two

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s 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. From a historical perspective, the first fuzzy relation was mentioned in the year 1971 by

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. 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.

References

{{Science and technology studies Fuzzy logic