The reduction of binary fuzzy relations and its applications

This paper introduces the concept of T-reduction of binary fuzzy relations and establishes its properties. It presents an approach to providing the one-valued restoration of any boundary transitive and T-asymmetric binary fuzzy relation by its T-reduction. A theoretical basis for this approach is established, showing that T-reduction is the smallest fuzzy relation whose T-transitive closure coincides with the given binary fuzzy relation and where an (n × n) fuzzy relation on a finite universe with cardinality n can be represented by n − 1 values. This approach opens up an original way for constructing the membership functions of certain binary fuzzy relations. Important examples for the application of this concept are given.