On the conditional distributivity of nullnorms over uninorms

•Conditional distributivity of nullnorm over uninorm with continuous operators is discussed.•The structure of uninorms with idempotent operators is discussed.

The problem of conditional distributivity for different two aggregation operators plays an important role in many different fields such as utility theory and integration theory. This paper deals with the conditional distributivity of a continuous nullnorm with respect to a uninorm with the continuous underlying t-norm and t-conorm.