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Keywords:
uninorms; triangular norms; triangular conorms; Quasi-Projectivity
uninorms; triangular norms; triangular conorms; Quasi-Projectivity
Summary:
In 2021, Jayaram et al. demonstrated that a property called 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.
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