In this paper, a new weak transitive property for interval-valued fuzzy relations  is introduced. The weak -transitive property is equivalent to -transitivity when the is a fuzzy relation and  for a triangular norm T. However, it is a weaker property than the -transitive one, that satisfies all the transitive inequalities, relaxing the need that all intervals must be comparable, by just the need of not having comparable non -transitive cycles. This paper also defines a weak concept of closure, and it is proved that there exists just one -transitive and weak -transitive closure, there does not exist a -transitive weak closure, but there are many weak -transitive weak closures of the

interval-valued fuzzy relations, interval-valued fuzzy sets, T‑transitivity, T-transitive closure, P weak closures, weak T-transitivity.