On a new class of uninorms on bounded lattices

We study and propose some new construction methods to obtain uninorms on bounded lattices. Considering an arbitrary bounded lattice L, we show the existence of idempotent uninorms on L for any element e ∈ L\{0, 1} playing the role of a neutral element. By our construction method, we obtain the smallest idempotent uninorm and the greatest idempotent uninorm with the neutral element e ∈ L\{0, 1}. We see that the obtained uninorms are conjunctive and disjunctive uninorms, respectively. On the other hand, if L is not a chain, we also provide an example of an idempotent uninorm which is neither conjunctive nor disjunctive.