Idempotent semi-t-operators on bounded lattices

As a generalization of nullnorms, semi-t-operators are interesting both in theory and practical applications. In this paper, we investigate some properties of idempotent semi-t-operators on bounded lattices. Furthermore, we propose two construction methods of idempotent semi-t-operators on bounded lattices containing only two different elements which are incomparable with a but comparable with b. These methods are the generalization of several known ones in the literature.