Idempotent uninorms on a bounded chain

Abstract

Ouyang et al. characterized idempotent uninorms on a complete chain in terms of decreasing unary functions with a symmetry-related property. In this paper, we generalize the results of Ouyang et al. and show that each idempotent uninorm on a bounded chain can be extended to an idempotent uninorm on a complete chain isomorphic to its Dedekind-MacNeille completion such that the restriction of the latter idempotent uninorm to this bounded chain coincides with the previous uninorm, which, together with the results of Ouyang et al. [7], gives a characterization of idempotent uninorms on a bounded chain.