T-S-TRIBES AND T-S-MEASURES

We show that any fundamental triangular norm-based T-s-tribe T, s is a n element of (0, infinity), is a weakly generated tribe. Consequently, T is a T-tribe for any measurable t-norm T if and only if it is a T-s -tribe for some s is an element of (0, infinity). Further we prove tha t each T-s-measure m, s is an element of (0, infinity], defined on a T -s-tribe T, is a generated measure; i.e., the irreducible part in the Butnariu-Klement decomposition of T-s-measures is always trivial. (C) 1996 Academic Press, Inc.