When is the operation ${\tau }_{T,L}$ a triangle function on ${\text{Del}}^{+}$?

This paper resolves an open problem posed by Schweizer and Sklar in 1983. We establish that the binary operation $\text{tauTL}$ is a triangle function on $\text{Delp}$ if and only if the following three conditions hold: (a) $L$ is a continuous t-conorm on $[0,\mathrm{\infty }]$ satisfying $(LCS)$; (b) $T$ is a t-norm on $[0,1]$; and © $T$ is weakly left continuous, with left continuity required when $L$ is non-Archimedean.