On the structure of 2-uninorms

In this paper, we describe the structure of 2-uninorms defined on the unit interval. We divide the class of 2-uninorms into five mutually exclusive subclasses based on their boundary behaviour, as determined by the absorbing element and the conjunctive/disjunctive nature of the underlying uninorms, which every 2-uninorm is known to have. For each of these subclasses, we fully characterize the structure of its members, albeit for two subclasses only under an additional continuity assumption, a common practice in the study of associative operations.