Triangular norms with continuous diagonals

Year, pages: 1999, 187 - 195

It is an old open question whether a t-norm with a continuous diagonal must be continuous [B. Schweizer, A. Sklar: Probabilistic Metric Spaces, North-Holland, New York, 1983] give a partial positive answer for t-norms with noncontinuous additive generators (constructed by the technique of [S. Jenei: Fibre-bundle triangular norms, in: Proc. EUFIT '96 (H. J. Zimmermann, ed.), ELITE Foundation, Aachen, Germany, 1996, pp. 74–77]), [E. P. Klement, R. Mesiar, E. Pap: Triangular Norms, (to appear)], Besides this, we give necessary and sufficient conditions for a function to be the diagonal of a continuous t-norm, and we characterize all continuous t-norms with a given diagonal (according to [R. Mesiar, M. Navara: Diagonals of continuous triangular norms, Fuzzy Sets and Systems, (to appear)].

Tkadlec, J. 1999. Triangular norms with continuous diagonals. In Tatra Mountains Mathematical Publications, vol. 16, no.1, pp. 187-195. 1210-3195.

Tkadlec, J. (1999). Triangular norms with continuous diagonals. Tatra Mountains Mathematical Publications, 16(1), 187-195. 1210-3195.