The conditional distributivity of semi-t-operators over uni-nullnorms

The conditional distributivity, that is, distributive equation with additional restriction imposed on the domain of aggregation functions, is an issue of interest for many different theoretical and practical areas. In this paper, we continue the investigation of this same topic by focusing on semi-t-operators over uni-nullnorms, where semi-t-operators are generalizations of t-operators without commutativity, and because of this, we need to take into account the left and right conditional distributivity. The obtained results characterize the left (right) conditional distributivity of semi-t-operators over uni-nullnorms and illustrate that the left (right) distributivity and the left (right) conditional distributivity of semi-t-operators over uni-nullnorms are not equivalent.