New methods to construct uninorms on bounded lattices

Abstract

In this paper, we study idempotent uninorms on bounded lattices. We demonstrate that there need not always exist an idempotent uninorm on a bounded lattice L having the neutral element e∈L\\{0,1} which differs from the least and the greatest idempotent uninorms. In addition, we propose two new methods to obtain uninorms on bounded lattices with a neutral element, where some sufficient and necessary conditions on the underlying t-norms and t-conorms are required. In particular, two new types of idempotent uninorms on bounded lattices are obtained. We also give an illustrative example for clarity.