  In this paper, we study the construction methods for uninorms on bounded
lattices via functions with the given uninorms and $q\in \mathbb{L_{B}}$ (or
$p\in \mathbb{L_{B}}$). Specifically, we investigate the conditions under which
these functions can be uninorms on bounded lattices when $q\in
(0,\mathfrak{e})\cup I_{\mathfrak{e}}^{\varrho}$ and $q\in
I_{\varrho}^{\mathfrak{e}}$ (or $p\in (\mathfrak{e},1)\cup
I_{\mathfrak{e}}^{\sigma}$ and $p\in I_{\sigma}^{\mathfrak{e}}$), respectively.
Moreover, some illustrative examples and figures are provided.
