Constructing Uninorms Based on Closure and Interior Operators in Bounded Lattices

Uninorms generalizing triangular norms and triangular conorms on bounded lattices have attracted considerable attention recently. In this article, two new approaches are suggested to generate uninorms with an identity element on a bounded lattice. These approaches exploit the existences of a triangular norm (triangular conorm) and a closure operator (interior operator) on a bounded lattice. Meanwhile, two structures of idempotent uninorms on bounded lattices are obtained. In addition, the relationship between the proposed approaches and the existing constructions is investigated.