Representations of T-similarity relations

Convergence of sequences of triangular norms and their quasi-inverses, stability of the representation theorem for T-similarity relations, and the density property of the family of Z-similarity relations are investigated. It is shown, in particular, that under some hypothesis the representation theorem is stable under taking limits of continuous t-norms, and that any strictly reflexive and symmetric fuzzy relation can be approximated up to any precision level by a T-similarity relation with T being a strict t-norm.