On the conditional distributivity of continuous semi-t-operators over uninorms

The issue of conditional distributivity, or how it is also called, restricted distributivity, which is a form of relaxed distributivity on the restricted domain, is crucial for many different areas such as utility theory and integration theory. The focus of this paper is on this specific form of distributivity for a continuous semi-t-operator with respect to a continuous t-conorm and for a continuous semi-t-operator with respect to a uninorm of the form Umin or Umax with continuous underlying t-norm and t-conorm.