Clifford's Order obtained from Uninorms on Bounded Lattices

Inspired by the work of Clifford on obtaining order from semigroups, many works have proposed different ways of obtaining orders from associative fuzzy logic operations. However, unlike Clifford's relation, these were dependent on the subdomain of its arguments. Recently, it was shown that a property termed Quasi-Projectivity (QP) is necessary to obtain an order from Clifford's relation. Further, for the underlying domain [0,1] it was shown that while all t-norms, t-conorms and nullnorms satisfy (QP), giving rise to posets, not all classes of uninorms satisfy (QP). Several constructions of uninorms U exist on bounded lattices, which unlike [0,1] may neither be total nor complete. In this work, we investigate the satisfaction of (QP) for these constructions. This study merits attention since it offers an alternate perspective - that a uninorm U on a lattice L can be seen as a t-norm on the obtained U-poset.