Construction of uninorms on bounded lattices: a closer look into the structure of the set of elements incomparable with the neutral element

In recent years, the construction and characterization of certain uninorms on bounded lattices have been exhaustively studied. In this paper, we study the structure of the set of elements incomparable with the neutral element, and provide a taxonomy of different types of bounded lattices. Moreover, we present different methods for constructing uninorms on some of these types of bounded lattices. The presented construction methods extend existing construction methods in the sense that the constructed uninorm may take a more general range of values on the set of elements incomparable with the neutral element.