Restricted distributivity for aggregation operators with absorbing element

The problem of restricted distributivity, i.e., a form of relaxed distributivity on the restricted domain, plays an important role in many different fields such as utility theory and integration theory. This paper considers the following two cases of restricted distributivity: (i) a continuous nullnorm with respect to a continuous t-conorm and (ii) a continuous nullnorm with respect to a uninorm of the form Umin or Umax with continuous underlying t-norm and t-conorm.