Abstract
Recently, Zhang et al. studied the distributivity between uni-nullnorms and overlap (grouping) functions [68]. They obtained the sufficient and necessary conditions for the distributivity equations between them. However, the distributivity between null-uninorms and overlap (grouping) functions is missing. To fill this gap, in this paper, we explore some new results on the distributivity equations between overlap (grouping) functions and null-uninorms, which are the generalization of uninorms and nullnorms. Meanwhile, we give the full characterization of any idempotent null-uninorm.
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