On Fuzzy Relations and Partitions

摘要

Fuzzy binary relations, R, defined on a finite set, E, and associated with a distance relation, d = 1-R, are studied. Metrical properties dealing with spheres and cliques in E are given and used to construct partitions of E. The membership functions are assumed to take values in a finite set. Combinatorial results for the number of fuzzy relations and partitions are derived, generalizing classical enumeration coefficients.