Uninorms with non-trivial unit element on the bounded lattices

Abstract

In this paper, we focus uninorms with non-trivial unit on bounded lattices. Based on the existence a t-norm $T$  acting on $[0,e]$ as well as a t-conorm $S$  acting on $[e,1]$, we present some construction methods for uninorms on a bounded lattice,where some additional conditions on the bounded lattice and the neutral element $e$  are required.The role of these additional conditions is emphasized. Finally, we present some results and some illustrative examples derived from these methods.