New construction methods for uninorms via functions with q and uninorms on bounded lattices

In this paper, we study the construction methods for uninorms on bounded lattices via functions with the given uninorms and $q\in {\mathbb{L}}_{\mathbb{B}}$ (or $p\in {\mathbb{L}}_{\mathbb{B}}$). 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.