On the structure of special classes of uninorms

In this paper, the concept of the Reidemeister closure condition is adopted in order to characterize associativity of uninorms with a special attention paid to the class of representable uninorms. Thus, conditions replacing the associativity requirement for such uninorms are given. Further, the attention is focused on the uninorms where the underlying t-norm and t-conorm are idempotent or induce an involutive negator. Based on the aforementioned results, the structure of these classes of uninorms is fully described.