Algorithms for computing the min-transitive closure and associated partition tree of a symmetric fuzzy relation

Based on a previously derived weight-driven algorithm for the computation of the T -transitive closure of an arbitrary binary fuzzy relation on a finite universe, with T a triangular norm, we establish three algorithms for the computation of the min-transitive closure of a symmetric matrix with elements in [0,1]. As a by-product, these algorithms enable to generate the partition tree associated with the min-transitive closure of the given matrix in descending order of the cutting parameter.