New Results on the Distributive Laws of Uninorms Over Overlap Functions
Hui Liu, Bin Zhao · IEEE Transactions on Fuzzy Systems · 2020
Recently, Qiao studied the distributive laws of uninorms over overlap functions when the uninorms were one of the usual classesUminandUmax, 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 $(0,1)^{2}$.