The conditional distributivity of aggregation operators has always been the focus of research because it is crucial for various areas including integration theory, utility theory and so on. Therefore, this article is mainly devoted to dealing with the conditional distributivity of a uni-nullnorm over a uninorm with the continuous underlying operators and also gives the full characterization of each pair (F,U) satisfying this property. Moreover, it extends the previous research results since they are now on a much wider class of uninorms.
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