On the existence and construction of T-transitive closures
In this paper, it is shown that any fuzzy relation R on an arbitrary universe X has a T-transitive closure. The triangular norm T involved is not subject to any conditions. This existential result can be turned into an explicit expression in the case of a left-continuous triangular norm T. Furthermore, this continuity restriction vanishes in the case of a finite universe X. In that case, the explicit expression can also be operationalized.
fuzzy relation triangular norm transitive closure transitivity