Construction methods for interval-valued t-norms on bounded lattices

In this paper, some construction methods for interval-valued t-norms (t-conorms) based on a down-set or an upset are presented. It is worth noting that the new construction methods do not have to be t-representable, which is a significant difference between the construction methods proposed in this paper and the commonly used construction methods of interval-valued t-norms (t-conorms) on other truth values sets. Some illustrative examples and remarks are also included to clarify the methods.