The modularity law in some classes of aggregation operators

In this study, we consider the functional equation of modularity in a special class of aggregation operators with an absorbing element. First, we focus on the modularity between commutative binary operators and their duals, and then we examine the modularity for operators from the class of 2-uninorms, which generalize nullnorms by extending their certain conditions. In particular, for these operators, depending on the positions of their neutral elements and possessing the same absorbing element, we obtain positive and negative results, which are analogous to the results in the general case for operators with different absorbing elements.