  In this paper, we further investigate new construction methods for uninorms
on bounded lattices via given uninorms. More specifically, we first construct
new uninorms on arbitrary bounded lattices by extending a given uninorm on a
subinterval of the lattices under necessary and sufficient conditions on the
given uninorm. Moreover, based on the new uninorms, we can give another
sufficient and necessary condition under which $S_{1}^{*}$ is a $t$-conorm
($T_{1}^{*}$ is a $t$-norm) in \cite{SS06}. Furthermore, using closure
operators (interior operators), we also provide new construction methods for
uninorms by extending the given uninorm on a subinterval of a bounded lattice
under some additional constraints and simultaneously investigate the additional
constraints carefully and systematically. Meanwhile, some illustrative examples
for the above construction methods of uninorms on bounded lattices are
provided.
