  IIn this note we continue the work of Chon, as well as Mezzomo, Bedregal, and
Santiago, by studying algebraic operations on fuzzy posets and bounded fuzzy
lattices. We first prove that fuzzy posets are closed under finite direct
products whenever the triangular norm realizing the product construction has no
zero divisors. This result is then extended to the case of bounded fuzzy
lattices. Some immediate consequences are then obtained within the setting of
direct products realized by triangular norms with no nilpotent elements as well
as strictly monotone and cancellative triangular norms. We then introduce a
triangular norm based construction of ordinal products and similarly show that
fuzzy posets are closed under ordinal products whenever the triangular norm
realizing the product construction has no zero divisors.
