T -Tribes and T -Measures

We show that any fundamental triangular norm-based Ts-tribe T, sg 0, `., is a weakly generated tribe. Consequently, T is a T-tribe for any measurable t-norm T if and only if it is a Ts-tribe for some sg 0, `.. Further we prove that each Ts-measure m, sg 0, ` x, defined on a Ts-tribe T, is a generated measure; i.e., the irreducible part in the Butnariu]Klement decomposition of Ts-measures is always trivial