Abstract
As generalizations of the classes Umin and Umax of uninorms on the real unit interval, we introduce the classes Umin and Umax of uninorms on a bounded lattice and lay bare the structure of their members. It is shown that uninorms in Umin (resp. Umax) are characterized by a triangular conorm (resp. triangular norm) and a triangular subnorm (resp. triangular superconorm). The characterization theorems unify all the existing construction methods for these two classes of uninorms known in the literature. We also introduce four new related classes of uninorms on a bounded lattice and present dedicated construction methods using triangular subnorms and triangular superconorms. Finally, connections among the introduced classes of uninorms are discussed.
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