Triangular norms. Position paper III: Continuous t-norms

This third and last part of a series of position papers on triangular norms (for Parts I and II see E. P. Klement, R. Mesiar, E. Pap, Triangular norms. Position paper I: Basic analytical and algebraic properties. Fuzzy Sets and Systems (in press, also FLLL-TR-0208) and E. P. Klement, R. Mesiar, E. Pap, Triangular norms. Position paper I: Basic analytical and algebraic properties. Submitted for publication (FLLL-TR-0208)) presents the representation of continuous Archimedean t-norms by means of additive generators, and the representation of continuous t-norms by means of ordinal sums with Archimedean summands, both with full proofs. Finally some consequences of these representation theorems in the context of comparison and convergence of continuous t-norms, and of the determination of continuous t-norms by their diagonal sections are mentioned.