In 2021, Jayaram et al. demonstrated that a~property called \emph{Quasi-Projectivity} $(QP)$ is a~necessary condition for Clifford's relation to produce a partial order. Furthermore, their research revealed that although all triangular norms and triangular conorms satisfy $(QP)$ and thus can generate posets, their generalized operator, uninorms, does not always possess this property, resulting in not all uninorms being able to generate a poset. In this work, we first investigate the satisfaction of $(QP)$ for uninorms with continuous underlying operators, concluding that such uninorms are capable of yielding partial orders if and only if they are locally internal in $A(e)$, and the resulting partially ordered set is a chain. Based on this, we further explore the performance of inducing partial orders within the framework of 2-uninorms, and the results show that it is entirely determined by the underlying uninorms.
triangular norms, uninorms, triangular conorms, Quasi-Projectivity
03B52, 03E72, 94D05