On the min-transitive approximation of symmetric fuzzy relations

Two new algorithms are proposed for generating a min-transitive approximation of a given reflexive and symmetric fuzzy relation which, in general, deviates less from the given fuzzy relation than its min-transitive closure, and which is guaranteed to be still reflexive and symmetric. Since the new algorithms are weight-driven, they can be used to generate layer by layer the partition tree associated to the corresponding min-transitive approximation. We report on numerical tests that have been carried out on synthetic data to compare the approximations generated by the new algorithms to the min-transitive closure and the min-transitive approximation delivered by the UPGMA clustering algorithm.