Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice.

For a t-norm T on a bounded lattice (L, <=), a partial order <=(T) was recently defined and studied. In [11], it was pointed out that the binary relation <=(T) is a partial order on L, but (L, <=(T)) may not be a lattice in general. In this paper, several sufficient conditions under which (L, <=(T)) is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on L such that (L, <=(T)) is a lattice are presented.