Distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t-conorm

This paper deals with the distributivity and conditional distributivity of uninorms with continuous underlying operators over continuous triangular conorms. In particular, the involved triangular conorm is either maximum operator or an ordinal sum with only one summand in which the corresponding triangular conorm is strict. From the obtained results, it is deduced that distributivity and conditional distributivity are equivalent. Moreover, we obtain the full characterization of some cases of this class of uninorms of which either the underlying triangular norm or triangular conorm is strict.