New Results on the Distributive Laws of Uninorms Over Overlap Functions

Recently, Qiao studied the distributive laws of uninorms over overlap functions when the uninorms were one of the usual classes
U
_min
and
U
_max
, the family of representable uninorms or uninorms continuous in $(0,1)^{2}$ and obtained some partially characterizations. This article will continue to consider the characterizations of this kind of distributivity equations when the uninorms lie in the family of uninorms continuous in $(0,1)^{2}$. First of all, we investigate the distributive laws of continuous t-norms over overlap functions and give their full characterizations. Then, we give the necessary and sufficient conditions for the solutions of the distributivity equations when uninorms are continuous in $(0,1)^{2}$.