The additive generators of t-norms and t-conorms on bounded lattices

Abstract

In this paper we study the additive generators of t-norms and t-conorms on bounded lattices. They are not only good tools to construct but also crucial to studying the representations of t-norms and t-conorms. First we extend the classical additive generators theorem to the partially ordered cases by adding one more condition. Then we discuss some properties of these constructed t-norms such as the Archimedean property, nilpotent elements, strict monotonicity, et cetera. Besides, we give a more convenient modification of our theorem on finite bounded lattices and several examples for a further step on the characteristics of the additive generators.