For a t-norm T on a bounded lattice $(L, \leq)$, a partial order $\leq_{T}$ was recently defined and studied. In \cite{Karacal11}, it was pointed out that the binary relation $\leq_{T} $ is a partial order on $L$, but $(L, \leq_{T} )$ may not be a lattice in general. In this paper, several sufficient conditions under which $(L, \leq_{T} )$ is a lattice are given, as an answer to an open problem posed by the authors of \cite{Karacal11}. Furthermore, some examples of t-norms on $L$ such that $(L, \leq_{T}) $ is a lattice are presented.
triangular norm, bounded lattice, T-partial order
03E72, 03B52